JOURNAL OF PETROLOGY
VOLUME 52
NUMBERS 7 & 8
PAGES 1333^1362
2011
doi:10.1093/petrology/egq048
Density and Viscosity of Hydrous Magmas and
Related Fluids and their Role in Subduction
Zone Processes
ALISTAIR C. HACK1* AND ALAN B. THOMPSON1,2
1
INSTITUTE OF GEOCHEMISTRY & PETROLOGY, ETH ZURICH, CH8092, SWITZERLAND
2
FACULTY OF NATURAL SCIENCES, UNIVERSITY OF ZURICH, CH-8006, ZURICH, SWITZERLAND
RECEIVED SEPTEMBER 9, 2009; ACCEPTED AUGUST 3, 2010
ADVANCE ACCESS PUBLICATION SEPTEMBER 21, 2010
We have developed density^viscosity^composition (r^m^X)
models for natural aqueous fluids and hydrous melts, based on experimental data for silicate þ H2O, especially for the pressure (P)
and temperature (T) conditions above subduction zones. We examine hydrothermal and melt pathway systematics above subducting
slabs into the Earth’s mantle, back up along the top-of-slab, and
downward with the subduction. Aqueous slab fluids and hydrous
mantle melts show distinct flow properties (as observed in activation
energy in viscosity data) despite continuity in solute-polymerization
characteristics. Buoyancy changes are small for fluids except in the
localized vicinity of critical behaviour and at solidi where H2O partitions also into melt. Our model predicts dilute high-PT potassic
haplogranite fluids to be less viscous than sodic varieties whereas for
concentrated fluids a deep viscosity minimum occurs in mixed K/Na
(c. 1:1 molar) compositions. Higher dissolved silicate concentrations
increase fluid density and viscosity leading to slower less-buoyant
flow with increasing PT. Thus ascent rates of slab fluid increase by
about an order of magnitude (from c. 103·5 to 104·3 m s1 for
porous flow; c. 1 to 7 m s1 for flow through 1mm wide fractures)
with decompression from 5 to 3 GPa, as a result of decreasing solute
loads, r and m. Mantle fluid viscosities are predicted (104 to
103·7 Pa s) to be approximately half those of crustal fluids (103·9
to 103·1 Pa s) and of lower density (e.g. 1·4 compared to
1·6 g cm3), reflecting their compositional differences (here mainly
SiO2). Thus, ascending slab fluids tend to accelerate as they move
back up the slab and also moving from slab to porous mantle. Slab
melts are up to c. 6 orders of magnitude less viscous (e.g. c. 100·5
to 102·5 Pa s) and therefore faster flowing than hydrous deep crustal
granitoids (e.g. c. 106·5 to 103·5 Pa s), reflecting higher water contents of the former (e.g. 30 vs 10 wt %). Concentrated crustal
fluids migrate 5^6 orders of magnitude faster than hydrous melt,
mostly because of calculated viscosity differences. We find that
fluids flow faster in the mantle than in the crust, and that most of
the mass transfer through the mantle occurs via hydrous melt.
*Corresponding author (address after 1 September 2010: School of
Environmental & Life Sciences, The University of Newcastle, New
SouthWales 2308, Australia). E-mail: [email protected]
ß The Author 2010. Published by Oxford University Press. All
rights reserved. For Permissions, please e-mail: journals.permissions@
oup.com
KEY WORDS:
fluids; density; viscosity; fluid^rock interaction; PT
paths
I N T RO D U C T I O N
Density (r) and viscosity (m) of hydrous silicate melts and
fluids are two geologically important physical properties
that determine their migration through the Earth’s mantle
and crust. Changes in r and m affect buoyant ascent potential and ease of flow. In natural environments r and
m change in response to changing pressure (P), temperature (T) and composition (X) along a flow path.
Understanding the relations between P, T, X, r and m is of
general interest because we wish to answer questions such
as how far and how fast do fluids flow inside the planet,
and how much mass transport occurs in different tectonic
environments.
Here we focus on evaluating the viscosity and density
range of fluids containing dissolved minerals, and determining how compositional variation influences flow rates,
and thus also the length-scales of fluid migration. In
nature, differences in fluid physical properties will also be
reflected in fluid/rock interaction ratios and the life spans
of hydrothermal pathways.
In this contribution we present general models for
silicate-bearing fluid r and m based on available
JOURNAL OF PETROLOGY
VOLUME 52
experimental data and theoretical considerations by supplementing existing models for hydrous aluminosilicate
melts (e.g. Shaw, 1972; Lange & Carmichael, 1990;
Giordano et al., 2008a). The implications of the results for
migration of hydrous fluids and melt are examined in the
context of processes of slab^mantle^crust interaction at
convergent boundaries involving subducting oceanic crust.
We discuss only data for H2O, although other components
with carbon, nitrogen and sulfur are important in certain
natural fluids and melts (e.g. Wallace, 2005; Appendix 6).
G E N E R AT I O N O F F L U I D S A N D
M E LT S A B O V E S U B D U C T I N G
SLABS
Oceanic lithosphere sinking into the mantle at a convergent subduction boundary modelled at the indicated geometric, thermal and kinematic parameters is illustrated in
Fig. 1. As the subducted slab heats by heat conduction
from the overlying mantle wedge, mineral dehydration reactions liberate water, which may ascend into and become
heated by the overlying mantle wedge. Where such ascending fluids encounter the mantle wet solidus they may trigger melting, or in cooler regions may generate subsolidus
metasomatism. Such vertical ascent paths for slab fluids,
labeled 1, are shown above three model distances to the
trench, marked A (fore-arc), B (proximal to arc) and C
(far from trench) in Fig. 1. For each of these, a point ‘a’
marks the mantle^mid-ocean ridge basalt (MORB) interface (Moho) within the slab, whereas point ‘b’ marks the
top-of-slab (ToS). Point ‘c’ represents the mantle wedge
thermal maximum and point ‘d’ marks the mantle^crust
Moho (continental at 35 km, or if oceanic at 8 km) overlying the mantle wedge. PT along these flow paths are
mapped relative to major water-saturated melting reactions in Fig. 2.
The subduction model results of Furukawa (1993) were
used. This was an early study to deal with dependence of
mantle viscosity upon T, P and used wet rheology. We
have combined this thermal model with experimental results for dehydration and melting of subducted crust and
overlying melt-undepleted fertile mantle. The model of
Furukawa (1993) has a surface potential temperature (Tp)
of c. 13008C, much cooler than several recent models for
mantle convection (e.g. van Keken et al., 2002, where
Tp ¼14208C). It is noted that the hottest natural arcs
lavas are c. 13008C (e.g. Eggins, 1993; Ulmer, 2001), and
are consistent with experimental phase equilibria and the
Average Current Mantle Adiabat (ACMA) (e.g.
Thompson, 1992). The ACMA has a surface potential Tp
of around 12808C and a @T/@z of 0·48C km1. Above subduction zones, hotter Tp leads to more dynamic wedge behavior as a result of decreased mantle viscosity. The main
consequences of higher Tp are to shift the thermal
NUMBERS 7 & 8
JULY & AUGUST 2011
structure to higher temperatures, thereby reducing the
extent of subsolidus mantle wedge regions, and to generate
higher thermal gradients through the upper portion of
the subducting slab (e.g. van Keken et al., 2002).
It is often assumed that very hot back-arcs require a
hotter geotherm with Tp around 14008C. This would
result in much more and compositionally more primitive
magma compositions than generally observed (e.g.
McKenzie & Bickle, 1988; Annen et al., 2006). The thermal
structure in subduction models reflects very much the
geotherm taken for upwelling in convecting mantle and
the details of coupling between slab and mantle, as well
as the viscosity data used. The relative importance of
these three effects needs to be further investigated also in
terms of their effects on magnitude, timescales and
length-scales of thermal perturbations in hot arc orogens.
The location of the H2O-saturated (wet) peridotite solidus, hereafter WPS (Figs 1 and 2) limits the size of the regions characterized by subsolidus mantle fluid and
metasomatic processes, and separates them from those
involving hydrous melt in the mantle wedge. The location
of the WPS represents a first-order petrological boundary
above subduction zones because of its role in delimiting
rheological behaviour. Until recently it was believed that
the water-saturated (wet) solidus for mantle peridotite
was depressed from the dry mantle solidus (T413008C)
to around 10008C at c. 2 GPa, c. 70 km depth (hereafter
1000WPS; Kushiro et al., 1968a, 1968b; Green, 1973, 1976;
Kushiro, 1974; Millhollen et al., 1974; Kawamoto &
Holloway, 1997). This PT location (1000WPS) was broadly
accepted despite some early experimental evidence that
the wet solidus could lie even lower at c. T ¼ 8008C at
3 GPa (Mysen & Boettcher, 1975). Recent work by Grove
et al. (2006, 2009) adds further support to the 8008C wet
solidus for peridotite (800WPS). Reconciling the present
experimental WPS datasets is a priority but beyond the
scope of this study. We discuss the possible effects of each
separately. The 1000WPS occurs much further inside the
mantle wedge than does 800WPS, and the latter occurs
very close to ToS (Fig. 1).
For the subduction zone modelled (Fig. 1) where the ToS
depth is 4120 km (e.g. between B and C) H2O partitions
into 800WPS mantle wedge melts immediately at the ToS
in that region, indicating that for 800WPS subsolidus
mantle fluid properties would not be relevant to
slab-to-mantle melt transport times. In contrast, the
1000WPS does not intersect ToS, implying that subsolidus
mantle fluid would always be present for some distance
above the slab. For either WPS, for most of the illustrated
subduction zone more than half of the H2O ascent length
to surface is as mantle melt. From the core of the supersolidus wedge hydrous mantle melt decompresses and fractionates down T (e.g. picrite to basalt) within the mantle (e.g.
Tatsumi & Eggins, 1995). Magma chamber occurrences
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HACK & THOMPSON
FLUID AND MELT PHYSICAL PROPERTIES
Fig. 1. Depth^distance from trench subduction zone thermal structure corresponding to the kinematic^geometric^thermal parameters indicated (V ¼ 4 cm a1, Tp ¼13108C; a ¼ 308, after Furukawa, 1993). Wet solidi (H2O-saturated) for mantle wedge peridotite (at 10008C;
1000WPS, Green, 1973, 1976; Millhollen et al., 1974; Kawamoto & Holloway, 1997; 800WPS is the alternative at 8008C, Mysen & Boettcher,
1975; Grove et al., 2006), for wet basalt (WBS, Lambert & Wyllie, 1972; Kessel et al., 2005), and granite (WGS, Huang & Wyllie, 1975) in continental crust are superimposed. Physical behaviour of fluids or melts along slab dehydration H2O ascent paths originating at A, B (from subducted oceanic crust) and C (from serpentinized mantle) is discussed in the text. The three fluid/melt ascent directions (1, vertically from slab
to mantle; 2, back up top-of-slab (ToS); 3, down ToS) are discussed for three distances to the trench (A, B, C). The locations a ¼12 km into
slab, b ¼ToS, c ¼ hot core of mantle wedge, d ¼ crustal Moho, are referred to for each path discussed initiating from A, B or C. Reference distances to trench (tt ¼130, 145, 220, 280 km) are indicated. Talong extrapolated mantle adiabat is indicated at right side.
near the Moho and within the crust would facilitate further melt fractionation and fusion processes leading to
intermediate and felsic compositions (e.g. Annen et al.,
2006; Reubi & Blundy, 2009). At the relevant wet solidus,
cooling melts will usually exsolve aqueous fluid.
Subsequent fluid ascent is subsolidus through the crust.
We consider below the composition of such slab fluids
and mantle melts at these PTconditions and their deduced
density and viscosity. The results derive from a transport
property model that we developed (below).
P H Y S I C A L P RO P E RT I E S O F
H Y D RO U S S I L I C AT E F L U I D S
A N D M E LT S
Changes in PT during large-scale natural tectonic processes will encourage fluids to change composition by dissolution or precipitation of minerals. In turn, these
compositional changes affect fluid viscosity (m) and density
(r) and thus influence the rates of mass and H2O transport
in different locations.
Viscosity is a first-order property when considering rates
of fluid/melt flow in rocks whereas density determines
fluid buoyancy with respect to the ambient pressure gradient. The difference in viscosity from dry melt to aqueous
fluid is typically at least 12 orders of magnitude (e.g.
Dudziak & Franck, 1966; Shaw, 1972; Lange, 1994). Across
the same compositional range, this phenomenal viscosity
difference contrasts starkly with density difference, which
is at most 10 times. The difference in viscosity of 12 orders
of magnitude owing to water content is much larger than
that owing to silicate composition (five orders of magnitude from granite to basalt) and T (five orders of magnitude from 650 to 13008C), which reflect both higher T and
contrasting composition in the mantle compared with the
crust.
Here we wish to address how r and m influence flow
rates, and thereby examine time- and length-scale characteristics of mass transfer by dehydration fluids (and melts)
from subducted slabs and hydrous melts generated in the
overlying mantle wedge. We also consider melts that form
in the crust overlying the mantle wedge from vertical
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JULY & AUGUST 2011
Fig. 2. PT paths followed by descending oceanic lithosphere and by ascending fluids and melts corresponding to paths originating at A (100 km
to trench, tt), B (from oceanic crust) and C (from serpentinized mantle) of Fig. 1 (V ¼ 4 cm a1, Tp ¼13108C; a ¼ 308, after Furukawa, 1993).
Reference distances to trench (A ¼100, B ¼165, C ¼ 280 km tt) are indicated in Fig. 1. Solidi separate subsolidus fluid and partial melt path intervals through the mantle wedge (shaded; 1000WPS, Kawamoto & Holloway, 1997; 800WPS ¼ wet peridotite mantle solidi, Grove et al., 2006),
oceanic crust (WBS ¼ wet basalt solidus, Kessel et al., 2005), continental crust (WGS ¼ wet granite solidus, Huang & Wyllie, 1975). Three paths
for the chosen subduction model for ToS (grey dashed line for free-slipping ToS to 65 km depth), 7 km (subducted oceanic Moho) and 12 km (possible thickness of hydrated peridotite) into the slab are indicated.
influx of heat and fluids from the mantle beneath. Thus, we
develop a general r^m model for hydrous fluids and melts,
and then concentrate on PT regions specific to subducted
slab, mantle and lower crustal processes (Fig. 1).
Simple models for density and viscosity of
hydrous silicate fluids and melts
In nature, because silicates dissolve increasingly in water at
high PT, it is necessary to quantify the amount by which
density and viscosity are modified from pure H2O in
order to assess how much faster or slower fluids flow with
increasing depth in the Earth. Density data for
high-pressure solute-rich aqueous fluids are not available,
density data for hydrous melts are sparse compared with
those for dry melts, viscosity data for hydrous melts typically extend over a very limited range of H2O contents
(commonly c. 10 wt % H2O), and viscosity data for
fluids are rare. In summary, available experimental data
cover only a small proportion of the total PTX space
occupied by natural melts and fluids. Because of these limitations, simple ideal and Arrhenian models for density
and viscosity were developed perforce. Our models incorporate few parameters, but nonetheless describe the fundamental properties of the data. Emphasis has been firmly
given to identifying trends and limits on ranges in physical
behaviour as functions of T, P and X.
Density and viscosity measurements made on molten
silicate liquids were needed for model calibration but in
many cases only r and m values for supercooled silicate
melts are available. As is evident in the available density
and viscosity variation with temperature data, there are
clear differences between the r and m properties of a silicate melt that is undercooled and metastable compared
with that melt in a stable molten condition. Each phase is
better described by (1) separate linear functions that intersect near the glass transition temperature (Tg; see
Riebling, 1968, fig. 1, p. 144), or (2) as a curved function
(e.g. non-Arrhenian) that extrapolates through Tg
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FLUID AND MELT PHYSICAL PROPERTIES
(e.g. Moynihan, 1995; Ochs & Lange, 1999; Whittington
et al., 2009b). Here we have chosen to simplify these details
with linear models that allow exploration of natural
ranges of high-PTX fluids and molten hydrous silicate
liquids (rather than glassy materials). Our conclusions are
naturally subject to the limitations of a simple model and
those of the data used in its calibration. A more complex
approach to modeling physical properties should be undertaken when more experiments are available. The equations
we used to model r and m (Appendices 1 and 2) are given
in a form that can be easily modified as new experimental
data become available.
D E N S I T Y O F H Y D RO U S S I L I C AT E
F L U I D S A N D M E LT S
We have some idea of the composition of natural fluids
in different tectonic settings, deduced from metasomatic
effects recorded by mineral assemblages. However, there
is a distinct paucity of relevant experimental mineral
solubility data and associated transport properties at elevated PT. We develop our model with available experimental data principally for SiO2 þ H2O, then extend
this to NaAlSi3O8 þ H2O SiO2 KAlSi3O8 as a
model for crustal rocks, fluids and melts, and Mg2SiO4 þ
Mg2Si2O6 þ H2O NaAlSi3O8 þ CaAl2Si2O8 þ CaMgSi2O6
as a model for mantle rocks, fluids and melts. These
simplified systems were chosen because they have been
widely used as models of melting and metasomatism in
the continental crust (e.g. Burnham, 1975; Anderson &
Burnham, 1983) and in the mantle (e.g. Yoder, 1965;
Kushiro et al., 1968a; Ryabchikov et al., 1982; Schneider
& Eggler, 1986).
SiO2 (quartz) þ H2O as a reference model
for densities of slab fluids
At higher pressures, silicate mineral solubilities are
enhanced in hydrous fluids as a result of polymerization
of solutes in melt-like species to the extent that hydrous aluminosilicate melts and fluids can form completely miscible
solutions (Shen & Keppler, 1997; Bureau & Keppler, 1999;
Kessel et al., 2005; Hermann et al., 2006; Hack et al., 2007a,
2007b; Newton & Manning, 2008). In the absence of density measurements of silicate-bearing fluids but knowing
that hydrous melts and aqueous fluids share some polymerization characteristics, we have modelled SiO2 þ H2O solutions as linear binary mixtures of silica melt and liquid
water. As far as we are aware, no experimental data are
yet available to test this model assumption.
Density model formulation for hydrous
silicate fluids
Our fluid density model extends the approach to melt
density taken by Bottinga & Weill (1970) to H2O-rich
fluid compositions. Model details are provided in
Appendix 1. Fluid density is modelled assuming an ideal solution between H2O and liquid silicate components. We
view this as the simplest approximation of polymerized silicate dissolved in water, in the absence of experimental
data. In contrast, specific hydrous melt density models are
available that may provide a closer approximation of melt
properties than equation (A1.1) (Appendix 1) but fail when
extrapolated into the range of aqueous fluid with dissolved
silicate (e.g. Lange & Carmichael,1990; Ghiorso, 2004).
The density variation from 400 to 10008C and 0·1 to
10 GPa for the SiO2 and H2O end-members is from 2·3 to
2·6 (silica liquid) and 0·16 to 1·7 (liquid water) g cm3
(Holland & Powell, 1991, 2001; Mao et al., 2001; Hudon
et al., 2002). The common hydrous silicate magmas have
densities in the range 2·9^2·1g cm3 (Lange &
Carmichael, 1990; Ochs & Lange, 1999). There is more
variability in H2O densities compared with silicate melt
over this PT range, and also a significant difference in the
relative buoyancies of melt (higher r) and fluid (lower r).
Hydrous silicate fluids behaving according to Darcy’s Law
would respond to higher vertical and lateral P gradients
with faster flow than hydrous melts, as a result of the relative r difference, and also thermal buoyancy gradients
owing to differences in thermal expansivity.
Figure 3 shows the composition and density of
SiO2 þ H2O fluids at quartz (Qtz) saturation. Fluid compositions were modelled to 9008C, 2·5 GPa (Manning,
1994), and extrapolated to higher T based on available experimental constraints (Kennedy et al., 1962; Nakamura,
1974; Newton & Manning, 2008). Densities were modelled
with equation (A1.1) (Appendix 1). As a result of using the
Manning (1994) solubility model as a calibration basis for
our fluid density model at applicable PT, the solubility
data of Anderson & Burnham (1965) display a slight systematic offset to lower dissolved silica (compare Manning,
1994, fig. 4, p. 4834). When experimental density measurements become available, further refinements to partial
molar properties can be made easily [or excess property
functions added to the model; equation (A1.1)]. The principal features of this diagram, however, are not expected to
change significantly.
The main features of SiO2 þ H2O PTXr (Fig. 3a) are (1)
a large single fluid field (supercritical region) of continuously variable composition and density, (2) simple linear
isotherms in logarithm XSiO2 ^r coordinates at low P, (3)
melt r decreases along the solidus with increasing P,
whereas fluid r increases, so that both converge in X and
r at the upper critical end point, and (4) with increasing
P (and also with T near the solidus), isobars change from
negative to positive @log10XSiO2/@log10r. The last feature
predicts that isobaric cooling accompanied by solute precipitation increases fluid buoyancy at mantle depths
(P41GPa) whereas fluid buoyancy would decrease at continental crustal depths (P51GPa) down to c. 7008C.
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Fig. 3. (a) Composition^density relations for SiO2 þ H2O molar solutions modelled at Qtz saturation (the experimental solubility data sources
are indicated). The fits in log^log space are nearly linear inT but widely divergent in P (and thus depth). Noteworthy features are the significant
shift to higher densities and more concentrated solutions in the broad vicinity of the wet solidus and upper critical end point (UCEP). (b) Qtz
solubility isopleths in PTcoordinates, in wt % SiO2 (MW ¼ 60·09). Qtz, quartz; Coe, coesite; Stv, stishovite. ToS (top-of-slab) subsolidus fluid
flow vectors (1, 2, 3) are superimposed at location A (from Fig. 1) near 2 GPa. ToS locations above B and C (Fig. 1) are shown in both panels,
with flow vectors 1, 2, 3, also shown in the lower panel. General composition effects and related buoyancy along different flow paths are
indicated.
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FLUID AND MELT PHYSICAL PROPERTIES
Fig. 4. Density (g cm3) of multicomponent fluid modelled at 6008C and 1GPa. (a) Granite fluids, H2O þ Si4O8 þ NaAlSi3O8 (continuous
line) or KAlSi3O8 (dashed line). (b) H2O þ Si4O8 fluid density increases with addition of dissolved silicates in the order For (forsterite) Dio
(diopside)4Ano (anorthite)4Alb (albite) Ksp (K-feldspar), shown for a reference density of 2·2 g cm3 (Appendix 1).
H2O þ Si4O8 þ NaAlSi3O8 is shown for all compositions (continuous line) with calculated densities.
Figure 3a shows that the largest variations in fluid density are observed in lower P regions, where changes in PT
have a greater effect than small continuous changes in
composition. Figure 3a and b also shows that along certain
heating paths involving dissolution, fluids may become
more concentrated but actually less dense and more buoyant (e.g. along path 1A). Other possible behaviours are discussed below.
Extrapolation of the fluid/melt density
model to natural crust and mantle
compositions
For natural aqueous solution densities we expect a PT behavior like that shown for SiO2 þ H2O at quartz saturation. More chemically complex aqueous solutions are
expected to have densities similar to SiO2 þ H2O at a
given XH2 O because of the relatively small differences between densities of various liquid silicate components.
Generally we expect the dissolution of silicate minerals in
addition to quartz to further increase fluid densities (and
viscosities, below). Here, we quantitatively predict the
density variation of more complex silicate fluids using
simple dissolution models [Appendix 1, equation (A1.1)].
To extrapolate from Si4O8 þ H2O to multicomponent
natural fluids we use the observation that hydrous granitic
melts are well described as feldspars þ 4quartz þ H2O
mixtures that are close to ideal when silicate components
are taken on an eight-oxygen basis (e.g. Burnham, 1975;
Holland & Powell, 2001). Thus, liquid feldspar (e.g.
NaAlSi3O8) behaves like liquid silica (Si4O8) with water
(H2O). Basaltic melts have been approximated as
4/3diopside þ feldspar þ H2O on an eight-oxygen basis
(below; hydrous by, for example, Yoder, 1965; Morse, 1980,
p. 85; dry by, for example, Bowen, 1915) and will have
slightly greater densities compared with granitic
quartz þ feldspar þ H2O (as is apparent from the greater
densities of the basalt components). The density model
could be extended to even lower silica mantle compositions
by incorporating feldspathoid instead of feldspar and olivine instead of diopside.
The results of modeling densities of multi-component
haplogranite fluid at 6008C and 1GPa are shown in Fig. 4.
Granite fluids (Fig. 4a, in wt %) were modelled as
H2O þ Si4O8 with NaAlSi3O8 (Alb ¼ albite) and
KAlSi3O8 (Ksp ¼ K-feldspar). The results show density
increases with addition of dissolved silicates in the order
Ca1·33Mg1·33
For(sterite,
Mg4Si2O8) Dio(pside,
Si2·67O8)4Ano(rthite, CaAl2Si2O8)4Alb Ksp. This behaviour is shown relative to H2O þ Si4O8 in Fig. 4b (in
mol %) for H2O þ Si4O8 þ NaAlSi3O8 (continuous isolines) and for other components at a reference density of
2·2 g cm3. Figure 4 shows that mafic and lower silica
mantle components, For and Dio, are expected to increase
H2O þ Si4O8 fluid densities more than equivalent molar
amounts of dissolved feldspar.
Although we model melt^fluid as a continuum of physical property versus composition, the physical distinction between fluids and melts is recovered in a manner consistent
with the phase relations. Figure 3 shows the continuous
PTXr behaviour in the miscible region and disparate
properties of fluids and melts at the H2O-saturated (wet)
Si4O8 solidus. We conclude that at the wet solidus the density (and viscosity) of hydrous solidus melt and aqueous
fluid also show a step (gap) related to differences in
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Table 1: Density (r, g cm1) of modeled subduction zone fluids and melts
Fluids
T
P
(8C)
(GPa)
Hydrous melts
H2O Reference
NaAlSi3O8 þ
SiO2 þ H2O Si4O8 þ H2O
Qtz sat.
(MgO) þ SiO2 þ H2O H2O wt %
Reference
For þ Ens sat.
NaAlSi3O8 þ H2O Si4O8 þ H2O
Alb:Qtz (50:50)*
in melt
mantle fluid albite melt
crustal fluid granite fluid
NaAlSi3O8 þ
Ano þ Dio
(50:50) þ H2O
Alb þ Qtz (50:50) mantle melt
granite melt
B
Slab Moho
450 3·2
1·31 1·31
1·32
1·31
subsolidus
subsolidus
subsolidus
ToS
620 3·0
1·25 1·28
1·31
1·26
subsolidus
subsolidus
subsolidus
subsolidus
Centre wedge 1300 2·5
1·04
Crustal Moho
700 1·0
0·94 0·97
Slab Moho
670 5·2
ToS
820 5·0
subsolidus
1·12
5
2·1
2·07
2·24
0·99
0·95
10
2·06
2·02
subsolidus
1·41 1·46
1·51
1·41
subsolidus
subsolidus
subsolidus
subsolidus
1·37 1·49
1·62
1·38
30
1·59
1·53
1·54
5
2·09
2·06
2·18
1·01
0·98
subsolidus
subsolidus
subsolidus
C
Centre wedge 1350 3·7
1·17
Crustal Moho
0·98 1·00
600 1·0
1·25
subsolidus
Density calculated: for fluids with equation (A1.1) using data from Holland & Powell (1998, 2001); for melts with equation
(A1.2) and data from Lange & Carmichael (1990); Ochs & Lange (1999).
*X(NaAlSi3O8) ¼ X(Si4O8), where X(Si4O8) ¼ Qtz sat. from Manning (1994). X(Si4O8) at For þ Ens sat. from Newton &
Manning (2002).
composition. With increasing pressure along the watersaturated solidus the discontinuity between fluid and
melt density decreases as the mutual solubilities of water
in melt and silicate in fluid increase. Immiscibility
between melt and fluid vanishes at the upper critical end
point (UCEP) as fluids form a single continuous solution with melt for which density (and viscosity) varies
smoothly with changes in composition and PT
(Appendix 5).
Values of density for selected compositions for modelled
crustal and mantle fluids were evaluated at PT pertinent
to the flow paths depicted in Figs 1 and 2. These were
obtained using equation (A1.1) (Appendix 1) and are
presented in Table 1. It is apparent that there is considerable spatial variability in fluid density and buoyancy gradients along different paths associated with subducting
slabs (detailed discussion below).
V I S C O S I T Y OF AQU EO U S F LU I D S
A N D H Y D RO U S M E LT S
There are many studies of silicate melt viscosity at various
water contents as a function of magma composition (e.g.
Bottinga & Weill, 1972; Shaw, 1972; Giordano et al., 2008a,
2008b; Hui et al., 2009; Whittington et al., 2009a). These
typically show decreases of m by up to eight (or greater)
orders of magnitude as water increases to c. 10 wt % (compare Alb þ H2O viscosity along the 8008C isotherm in
Fig. 4, from Aude¤tat & Keppler, 2004, p. 514). Water’s influence on melt viscosity is enormous. We have used the viscosity data for NaAlSi3O8 þ H2O as our reference model
(Dudziak & Franck, 1966; Urbain et al., 1982; Dingwell,
1987; Persikov et al., 1990; Holtz et al., 1999; Romano et al.,
2001; Aude¤tat & Keppler, 2004; Whittington et al., 2004).
NaAlSi3O8 (albite) þ H2O as a reference
model for viscosity of hydrous melts and
aqueous fluids
Viscosity measurements of NaAlSi3O8 þ H2O solutions
span the complete range of composition, whereas the database containing other silicate þ H2O systems is largely restricted to hydrous melt compositions with up to 10 wt %
H2O and lacks measurements for liquids with higher
water contents. For this reason NaAlSi3O8 þ H2O was
used as a m reference system, and extended to other model
crustal and mantle fluids and melts by the methods outlined below. In contrast to our density model (which we
have considered as a continuous function of composition
from hydrous fluid to anhydrous melt), m measurements
suggest that it is appropriate to separate melt and fluid viscosity models into two distinct compositional regions.
Experimental viscosity data for NaAlSi3O8 þ H2O are
plotted in Fig. 5. Hydrous melts and aqueous fluid viscosities are modelled separately according to the Arrhenius
relation (where Ea is activation energy and relates to ln
XH2 O linearly; Appendix 2). Measured versus model
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Fig. 5. Viscosity^composition^temperature relations of NaAlSi3O8 þ H2O fluids and melts (main figure shows lne m vs molar X; inset lne m vs
wt % X). Best fit to experimental data is obtained by modeling aqueous fluids independently from melts. Each phase is best described separately
using the Arrhenius relation in which activation energy is modified for composition (Appendix 2). Upper and lower experimental temperature
for each composition series are indicated. The sign of curvature is sensitive to the choice of units (molar X vs wt % X, inset), as is the molar configurational entropy model (thus the stoichiometry of the species mixing). Melt data (Alb þ H2O) give different fits compared with low-T
glass* data (*supercooled metastable melt). Data sources: Dudziak & Franck (1966); Urbain et al. (1982); Dingwell (1987); Persikov et al. (1990);
Holtz et al. (1999); Romano et al. (2001); Aude¤tat & Keppler (2004); Whittington et al. (2004).
viscosity is compared in Fig. 6a (model data sources are
given in the figure). Viscosity coefficients are reported in
Appendix 2.1 for NaAlSi3O8 þ H2O.
Separate correlations between Ea and ln X for
NaAlSi3O8 þ H2O melt and fluid indicate that distinct viscosity behaviour operates in each phase (Fig. 6b). In turn,
this points to specific structural units for the melt and
fluid phases and m reflects their concentration. The consequences of modeling m as a single continuous function of
composition, appropriate to completely miscible solutions,
are examined separately below.
Structural implications of viscosities of
NaAlSi3O8 þ H2O fluids and melts
Viscosity reflects the bonding and coordination of structural units in the solution and the relative ability of these
bonds to break and restructure during flow. Fluid and
melt activation energies for flow are correlated with water
amount (Fig. 6b). For fluids a simple linear trend describes
viscosity up to c. 60 wt % dissolved feldspar, and a separate
trend describes hydrous feldspar melt.
It is clear from Fig. 6b that the data near 80 wt % Alb
belong to neither the melt (extrapolated) nor the fluid
model trends, and are thus significantly ‘misfit’.
Interestingly, the ‘misfit’ fluid data have the best constrained Ea value of any fluids measured and refer to an
intermediate composition between more dilute fluids and
more silicate-rich melts (Fig. 6b). An explanation for the
behaviour of these data is that they may occur in a
transitional compositional region characterized by a mixture of ‘fluid-forming’ and ‘melt-forming’ structures.
Coincidentally, these data are near in composition to
NaAlSi3O8·4H2O or c. 2 H per tetrahedrally coordinated
cation (and two non-bridging oxygen per tetrahedron,
like pyroxene). Spectroscopic data for such compositions
are not yet available, but as suggested by viscosity
data would provide insight into the key speciation
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Fig. 6. (a) NaAlSi3O8 þ H2O viscosity: measured values compared with models for fluid and melt [equations (A2.1) and (A2.2)]. Data at
c. 21wt % H2O (Aude¤tat & Keppler, 2004) are anomalous; near this composition at c. NaAlSi3O8·4H2O, may be where fluid and melt structures
switch predominance as a result of stoichiometric restrictions imposed by the underlying solution species in each phase. (b) Activation energy
(Ea) vs composition for fluids, illustrating linear relation from 0 to c. 60 wt % Alb, and shift to melt-like behaviour at higher Alb concentrations.
changes associated with the breaking of hydrous frameworks into smaller chain, dimeric and monomer structures related to complete miscibility between melts and
fluids.
There is general support for a mechanism of H2O reacting with melt bridging-oxygen (O2^) to form hydroxylated
apices of tetrahedral groups and result in lower polymerization (compare Burnham, 1975, p. 1081, fig. 6; Kohn,
2000; Richet, 2005). Complete miscibility from melt to
fluid at high pressure requires a continuous transition in
structure from melt to fluid. Such extended-range hydroxylated O-bridged structures mix with molecular water in
the hydrous melt structure up to at least 10 wt % (e.g.
Stolper, 1982; Malfait & Xue, 2010). However, we suggest
that these structures must at higher H2O
(e.g.4c. 40 wt %) dissociate into simpler O-bridged
polymers (which also mix with molecular H2O) as
characteristic of fluids.
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Stepwise addition of H2O to variably hydroxylated
albite units presumably ultimately breaks the extended
polymeric framework characteristic of melt into smaller
two- and one-member species (e.g. [Al,Si]2O[OH]6, and
[Al,Si][OH]4). In fluids, such species are increasingly
recognized as being related to higher silicate solubility conditions (e.g. Newton & Manning 2002, 2009; Zotov &
Keppler, 2002; Manning et al., 2010). We suggest that the m
data at H2O up to c. 60 wt % reflect the bonding and coordination characteristics of smaller polymeric units
mixing with H2O in dilute fluids, whereas for 20 wt %
H2O
molecular
water
mixing
with
larger
(bridging-oxygen bonded) units is characteristic of hydrous melt.
To more precisely define the structural characteristics of
fluid and melt in PTX, it would be useful to combine physical properties with other datasets (e.g. Kessel et al., 2005;
Newton & Manning, 2008, 2009), which in turn may be
incorporated in more detailed geochemical and rate
models for deep fluxes of mass and water.
Viscosity model extended for
NaAlSi3O8 þ KAlSi3O8 þ Si4O8 þ H2O crustal
fluids and melts
By analogy with NaAlSi3O8 þ H2O, we developed a
simple continuous viscosity model for complex haplogranitic fluids and melts [Appendix 2.3: equation (A2.3), coefficient values, and fit data sources]. The viscosity model
extends to quartz from feldspar systems on an eight-oxygen
basis, except for H2O (following Burnham, 1975, p. 1082).
An advantage of extending the m model to quartz is that
silica solubility in H2O is constrained over a wide range
of PTX, unlike for feldspars. Thus, Si4O8 þ H2O is a convenient reference system for considering the effects related
to fluids changing PT (Fig. 3) and also for changing X
from crust to mantle (below). Figure 7 shows the different
relative effects on viscosity of dissolving Ksp (KAlSi3O8)
and Alb (NaAlSi3O8) components into Si4O8 þ H2O
fluids. Addition of feldspars into Si4O8 þ H2O increases
fluid viscosity, more so by Alb than Ksp (compare right
sides of Fig. 7a and b at high H2O). However, mixed feldspar compositions develop a deep viscosity minimum at
higher solute concentrations (Fig. 7c). Generally the
model shows extremely non-linear viscosity^composition
behaviour.
Our model extrapolates melt viscosity data to predict
compositional dependence in concentrated multicomponent fluids. Although this simple model reproduces
the general behavior observed, predicted m values tend to
be lower than measured for intermediate Alb þ H2O
fluids (Fig. A2.1). We conclude that this model probably
underestimates fluid viscosities, and thus derived flow velocities (below) can be considered maximum values.
Viscosity of sodic versus potassic versus
mixed alkali quartzofeldspathic fluids and
melts: model results
Potassic versus sodic varieties of subsolidus metasomatism
are commonly associated with different types of hydrous
granites (e.g. Carten, 1986; Cathelineau, 1986; Plu«mper &
Putnis, 2009), are also extensive in some metamorphic terrains (Oliver et al., 2004; Clark et al., 2005) and some
lower crustal granulites (e.g. Franz & Harlov, 1998). Given
these occurrences we now consider the relations between
fluid composition and viscosity in connection to flow
rates, and in turn the extent to which timescales or
length-scales vary between different examples of
metasomatism.
Model extrapolation of experimental m data to wet solidi
conditions indicates that Ksp melts are up to two orders
of magnitude less viscous compared with equivalent Alb
melts (see Fig. 7), whereas for drier melts with
H2O52 wt %, Ksp are more viscous than Alb (Figs 7
and 8; Urbain et al., 1982). The extrapolation of our viscosity model (Appendix 2.3), albeit uncertain, into binary
fluid regions indicates that potassic fluids are of lower viscosity compared with sodic compositions (Fig. 8 inset).
Modelled isotherms in logarithmic m, Xmolar coordinates
are convex-up for Alb and concave-up for Ksp (Fig. 8).
This implies that fluid m increases are much larger per
mole NaAlSi3O8 added to H2O compared with
KAlSi3O8 þ H2O.
Curvature of isotherms in logarithmic m, X coordinates
is very sensitive to the choice of molecular mixing units in
the solution entropy model (compare constant oxygen
basis aluminosilicates in this study; variable basis oxides
of Whittington et al., 2009a, fig. 15, p. 15; weight percentage
of Aude¤tat & Keppler, 2004, fig. 3, p. 515). For illustration,
we may compare Ksp þ H2O and Alb þ H2O solution
models for 8008C recalculated to wt % (inset in Fig. 8).
An analogous relation between entropy of fusion, mole formulation, and liquidus surface curvature is well known in
TX diagrams (van Laar, 1936, pp. 297^298; Prigogine &
Defay, 1954, figs 22.1 and 22.2, pp. 360^361).
Nonlinear composition^viscosity behaviour is predicted
by our model. A significant implication is that whereas
sodic compositions are mostly more viscous than potassic in
dilute fluids, concentrated mixed alkali quartzofeldspathic
fluids and melts display a deep viscosity minimum relative
to end-member sodic and potassic compositions (Fig. 7d).
Thus, with increasing solute concentration dilute potassic
fluids give way to concentrated mixed alkali compositions
as being most mobile (least viscous). This is an interesting
result, as non-additive behavior of some physical properties
(e.g. viscosity, electrical resistivity) in many other silicate
melts containing more than one alkali component is well
documented (e.g. Isard, 1969; Day, 1976). It is suggested
that the mixed alkali effect on viscosity is caused mainly
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Fig. 7. Viscosity (log10, m Pa s)^composition (molar) relations for haplogranite Qtz þ Alb þ Ksp þ H2O ternary subsystem solutions
calculated at 6008C. (a) H2O þ Si4O8(Qtz) þ KAlSi3O8(Ksp). (b) H2O þ Si4O8 þ NaAlSi3O8(Alb), (c) H2O þ KAlSi3O8 þ NaAlSi3O8.
(d) Si4O8 þ KAlSi3O8 þ NaAlSi3O8, anhydrous. Nonlinear composition^viscosity behaviour characterizes the system. Subsolidus metastable
compositions are included for illustration. Examination of feldspar^water binaries (a, b) highlights the increases in viscosity of SiO2 þ H2O
fluids by adding components Ksp (lesser) and Alb (greater). Feldspar^water ternary (c) shows that dilute sodic solutions are somewhat more
viscous than potassic; however, at higher silicate concentrations mixed alkali compositions are least viscous.
by independent alkali^silica interactions rather than
alkali^alkali interactions (Fluegel, 2007).
Modelled alkali composition^viscosity relations are
nonlinear, suggesting th\at K/Na exchange equilibria
can significantly affect the viscosity of reactive fluids
and thus flow rates. Large changes in viscosity then
can occur in response to changing K/Na and involve little to
no change in total solute concentration. Alkali exchange reactions may drive fluid toward or away from low-m mixed
alkali (or potassic) compositions depending on the relation
between fluid and rock compositions.
Our model predicts differences of several orders of magnitude in the viscosity of granite fluids/melts of different
dissolved K/Na silicate composition. Higher m solutions
(Figs 7 and 8) are expected to be associated with longer
timescale or shorter length-scale effects and processes,
when normalized to other parameters such as permeability
and porosity. Variation in metasomatic length-scales can
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Fig. 8. Viscosity (lne left and log10 right, Pa s)^composition (molar, bottom; wt % Alb, top)^temperature relations for NaAlSi3O8(Alb) þ H2O
(continuous curves) and KAlSi3O8(Ksp) þ H2O (dashed) modelled as continuous solutions [equation (A2.3)]. Natural fluid and melt composition and viscosity ranges are shaded. Extrapolation of melt data (Trange given by numbers in 8C) to pure H2O limits the range of viscosity expected in natural fluids. Inset shows that modelled viscosities for Alb þ H2O and Ksp þ H2O have same sign of curvature when recalculated
to weight per cent. Data for Alb þ H2O are the same as for Fig. 5, Ksp þ H2O (dashed) data from Urbain et al. (1982) and Romano et al. (2001).
be a manifestation of significant differences in viscosity of
fluids/melts.
Extrapolation of the hydrous fluid
viscosity model to natural crust and
mantle fluid compositions
The PTXviscosity(m) behaviour of crustal fluids can be
modelled simply at quartz saturation (as done for crustal
fluid density, r, Fig. 3). To extend our PTXm model to
mantle fluids we normalize fluid compositions to silica
solubility at For þ Ens saturation (Newton & Manning,
2002; Gerya et al., 2005). To serve as an approximation of
higher (double) solute-load multi-component natural
fluids, we have also modelled Si4O8 þ H2O with
NaAlSi3O8 added in equal molar amount to dissolved
Si4O8.
Values of viscosity for selected compositions for
modelled crustal and mantle fluids (and H2O) were evaluated at PT pertinent to the flow paths above locations
B and C shown in Figs 1 and 2. Viscosity values of
simple hydrous melts were also evaluated at relevant PT
along the flow path. These were obtained using the
equations and coefficients evaluated in Appendix 2
and are presented in Table 2 for locations along the PT
paths.
COM POSI T IONA L A N D DE NSI T Y
C H A N G E S I N M E LT S A N D F L U I D S
M I G R AT I N G A B O V E
SU B DUC T I NG SL A B S
Contrasting Xmr variations along each simplified PT path
(above locations A, B, C in Fig. 1) have been considered to
examine the behaviour of fluids and melts related to slab
dehydration and mantle/slab melting by hydrous fluids.
The implications of such changes for mass transport
amounts and velocities in different locations are discussed
below (Fig. 9).
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Fig. 9. Covariation in fluid density and viscosity for changes in PTX in crust and mantle. Superimposed is the ToS path (solid curve, open
arrow indicates upward flow direction) corresponding to Figs 1 and 2, and wet solidi (WGS, WBS, 1000WPS and 800WPS shown as labeled
dashed curves). The solidi demarcate subsolidus fluid and melt regions. Solidi upper critical end points are marked (UCEP). (a) H2O þ Si4O8
at Qtz saturation. (b) H2O þ Si4O8 at For þ Ens saturation. (c) H2O þ Si4O8 þ NaAlSi3O8(50:50), where X(Si4O8)P,T ¼ Qtz saturation value.
(d) H2O þ Si4O8 þ NaAlSi3O8(50:50), where X(Si4O8)P,T ¼ For þ Ens saturation value. It should be noted that the viscosity scale is much
larger in panels (a, c) (crust) than in (b, d) (mantle). A PT path ascending from ToS and through mantle is illustrated in (b); continuous
curve for subsolidus fluids; dashed curve for higher T (melt). Solubility of Qtz (in a, c) from Manning (1994) and For þ Ens (in b, d) from
Newton & Manning (2002). Density and viscosity modelled with equations (A1.1) and (A2.3), respectively. ToS conditions above reference positions A, B and C shown in Figure 1 are indicated on panels (b), (c) and (d).
Relevance of composition^density changes
of natural fluids at mantle depths
Density difference between magma/fluid and crystalline
residue is the driving force for magma/fluid migration.
The model buoyancy difference between aqueous fluid
and magma changes linearly with the concentration of
molar water (Appendix 1). Differences in density have the
same effect on buoyancy for flow in porous media as for
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HACK & THOMPSON
FLUID AND MELT PHYSICAL PROPERTIES
fracture flow (Appendix 3). Subsolidus aqueous solutions
with dissolved silicates will be denser than H2O, slightly
diminishing the driving pressure gradient for flow.
Fluid density varies with composition, but the character
of the dissolved silicates is much less important than their
total amount (Fig. 4, basal line), in our model. This reflects
similar compressibilities and small differences in partial
molar volumes of dissolved silicate components compared
with H2O. Although we do not have much experimental
information about fluid composition at elevated PT (see
Kessel et al., 2005), the present considerations emphasize
that such details contribute to our understanding of metasomatic transport rates and can be evaluated using our
density model. There is now no need to model such fluids
as pure H2O because impure natural fluids are demonstrably progressively more dense and therefore less
buoyant.
Solubility gradients imply mineral precipitation or dissolution, which affects both the physical properties and
pathway permeability. Thus solubility combined with
metasomatic reactivity gradients could exert very significant controls on flow vectors because fluid fluxes are expected to maximize in the most permeable locations. In
high-solubility environments such as subduction zones,
competition between pre-existing rock permeability and
solubility gradient generated permeability could be important in focusing flow. Solubility gradient induced permeability (and thus fluxes) would reflect the ambient
thermal structure, whereas pre-existing structures may be
independent of PT gradients. Fluid PT paths are likely to
have a complex transient relation to the thermal history
recorded by the rock. Reaction-generated volumetric
changes may induce dilational strain and thus also influence grain-scale permeability (e.g. Connolly et al., 1997).
Density may decrease/increase along dissolution paths depending on the relative rates of solute increase/decrease
versus decompression (Fig. 3). Fluids that increase in density decrease their buoyancy and slow their ascent through
permeable zones.
Compositional change paths (dissolution
and precipitation) of slab fluids
Solubility changes in fluids are driven by compositional
gradients along flow paths. Solubility gradients occur continually with changes in PTor abruptly with chemical environment and in turn will be seen in both r and m
gradients. Consequently, solubility gradients may influence
transport vectors by quickening fluid migration rates
along specific paths; for example, through either dissolution causing permeability enhancement or increased r/m
of fluid (Appendix 3). Subduction zone solubility gradients
(@X/@z, mol kg1 m1) vary by at least two orders of magnitude along and between different fluid flow PT paths
(such as 1, 2 and 3 near A, B and C in Fig. 1) and are even
higher if changing lithology is considered.
Where mineral dissolution or precipitation is active,
fluid pathway continuity/permeability evolves according
to detailed interactions between (1) the local flow field
within a fracture (or grain boundaries) and the local P/T
gradients (e.g. Brown, 1987; Flukiger & Bernard, 2009), (2)
rate of fluid supply, and (3) solid matrix deformation.
ToS fluids rising into the mantle wedge react in response
to changed chemical potential (activity, aSiO2 at quartz)
and precipitate much of the slab-derived solute load
where they equilibrate with mantle (aSiO2 at For þ Ens).
Hence, slab fluid solute concentration, density and
viscosity all reach maxima at the ToS (path 1 in Figs 1, 2
and 9). For ToS fluid rising further into the mantle wedge
with increasing T either (1) the fluid may continually
remain equilibrated with the mantle wedge during
upward flow, or (2) fluid flow pathways through the
mantle wedge become armoured by metasomatic selvages, which limit reaction of slab fluid with the surrounding mantle (and retain vestiges of slab chemistry).
In the first situation, involving equilibrium, fluid rising up
the T gradient would dissolve mantle and reach maximum concentration at the 1000WPS. The second
behaviour suggests hydrofracturing of subsolidus mantle,
which, depending on distance to the solidus, may be locally extensive (1000WPS) or completely insignificant
(800WPS).
Quartz-saturated crustal fluids are approximately one
order of magnitude more concentrated in SiO2 than
For þ Ens mantle fluids (Newton & Manning, 2002;
Gerya et al., 2005). Some aspects of compositional evolution
of quartz-saturated fluids flowing into model ultramafic
rocks have been discussed by others (e.g. Manning, 1997).
Greatest precipitation rates (mol kg1 m1) are expected
where ToS fluids migrate from slab to mantle (path 1,
Figs 1, 2 and 9) because, despite heating, chemical potential
gradients across the ToS occur over a much shorter
length-scale than do equivalent solubility changes induced
by PT gradients. The greatest mineral dissolution rates
(mol kg1 m1) are also expected to occur along ascent
path 1 (Fig. 9) where solute concentrations increase by a
factor of c. 10 as fluids move from subducted mantle to
oceanic crust at ‘a’ and wedge mantle to continental crust
at ‘d’ (Fig. 1). It should be noted that fluid migrating
across slab Moho ‘a’ involves heating with decompression,
whereas crossing crustal Moho ‘d’ involves cooling. Thus,
major metasomatic effects involving dissolving or precipitating (and with changing r, m) are expected at lithological
boundaries, but clearly reflect the chemical step across the
boundary more than any change in T or P. We examine
below how changing PT conditions influence fluid/melt
composition and in turn how these changes will affect
density and viscosity.
Fluids ascending along the ToS precipitate minerals
in response to cooling and decompression (ToS path 2 in
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Figs 1, 2 and 9). Along the ToS path (2) solute precipitation rates decrease continuously during ascent
from deeper hotter regions reflecting both decreasing solubility gradient [@X/@P(T)] and decreasing mineral solubility. Solubility change per meter of fluid ascent (mol
kg1 m1) at 150 km ToS depth is at least 20 times greater
than at 30 kmToS depth (Fig. 3b). (Fig. 3b), while solubility
(mol/kg) decreases about two orders of magnitude for
fluid moving from 150 to 30 km ToS depth.
If the downwards subduction rate is faster than the upwards Darcian flow rate within the subducted slab
(Davies & Bickle, 1991; Davies & Stevenson, 1992), fluids
experience increasing P and T and become more
solute-rich, less buoyant and more viscous (e.g. ToS path 3
in Figs 1, 2 and 9). Whether such ‘subducting’ fluids (1)
react to form hydrous minerals and become further subducted to mantle transition zone depths or (2) manage to
eventually ascend, depends critically on the evolution of
slab permeability and temperature.
Fluid density and buoyancy gradients along
PTX flow paths above subduction zones
Magnitude and sign of fluid density change as a result of
changes in PT or X are illustrated in Fig. 3 for flow paths
corresponding to Fig. 1 (Table 1). Generally mineral solubility and solubility gradients (@X/@P, @X/@T) increase
with slab depth. Rate of fluid density change per unit
time (@r/@t) in a given location (PT fixed) will be controlled by (1) reaction rate and (2) fluid flow rate. The
latter may vary depending on solid matrix permeability
and fluid availability.
Changes in slab fluid density (buoyancy) in fore-arc regions may be distinguished from those of slab fluids beneath mantle wedge melting zones further from the
trench. PTXr results for the model subduction conditions
(Fig. 3a) show that along flow path 1A at quartz saturation,
ascending fluid density decreases at a rate (@r/@z) of
0·011g cm3 (c. 1%) per km of flow (Figs 1 and 3a). In
contrast, along path 1B (Fig. 3a) quartz-saturated slab
fluid density increases at a rate of þ 0·002 g cm3
(c. þ0·2%) per km of vertical flow, and along path 1C the
rate of density change is an order of magnitude higher
[ þ 0·027 g cm3 (c. þ2%) per km ascended]. Although
fluid density increases from the slab along vertical ascent
paths relevant to melt production in the overlying mantle
wedge (e.g. paths 1B and 1C), slab fluids remain positively
buoyant relative to the solid matrix and thus always tend
to rise.
At the ToS, fluids migrating from basaltic slab to peridotitic mantle wedge (path 1, Fig. 3) decrease in density in response to changing composition (becoming less
concentrated in the overlying mantle as a result of silica
loss). For PT along the ToS (path 2, Fig. 3),
rfluid(Qtz)4rfluid(For þ Ens). The density contrast between
NUMBERS 7 & 8
JULY & AUGUST 2011
Qtz (slab) and For þ Ens (mantle) fluid also increases
with ToS depth. For the example of Fig. 3, ToS fluid density
difference between slab and mantle increases tenfold from
0·3% relative (ToS depth ¼ 60 km, above A) to c. 3%
relative (ToS depth ¼150 km, C, Fig. 1). Thus dense concentrated fluids moving up out of the slab are expected to
become less dense in the overlying mantle through silica
precipitation and thus increase buoyancy. Fluid density
changes along chemical potential gradients are of similar
magnitude to those related to thermal gradients along
kilometer-scale flow paths; the former, however, occur
over (shorter) length-scales commonly appropriate to
lithological contacts [e.g. basaltic slab to peridotitic
mantle (r decreases), and peridotitic mantle to continental
crust (r increases)].
Quartz-equilibrated fluids continuously moving up near
the ToS into subsolidus 1000WPS mantle (path 1) dissolve
mantle and become increasingly buoyant until they have
ascended sufficiently (and heated) to trigger melting at
the WPS, as above B and C, or simply start to cool, as
above A (Fig. 1). Fluids are typically 2^3 times less dense
than melt and hence the buoyancy force [r, equation
(A3.1)] varies significantly across the wet solidus for melt
compared with subsolidus fluids. In contrast, changes in
the relative buoyancy of fluids as a result of changes in subsolidus mineralogy are 510% relative. At For þ Ens saturation ascending fluid density decreases at a rate (@r/@z) of
0·014 g cm3 (c. 1%) per km of flow above A and
decreasing gradually to 0·007 g cm3 (c. 0·5%) per km
above C.
Density decreases for fluids migrating back up along
the ToS (path 2) at a rate (@r/@z) of about
0·003 g cm3 per km ascending at quartz saturation,
compared with about 0·002 g cm3 per km at For þ Ens
saturation (Fig. 1). Path 3 fluids show opposite behaviour,
ToS fluid density increasing at rates of þ 0·003
and þ 0·002 g cm3 per km at Qtz and For þ Ens saturation, respectively.
DENSITY AND VISCOSITY
C H A N G E S I N M E LT S A N D F L U I D S
A N D T H E I R M I G R AT I O N
V E LOC I T I E S A B OV E
SU B DUC T I NG SL A B S
Scaling relationships between aqueous fluid viscosity and
density in crust and mantle have been obtained separately
from each other using solubility (composition) relationships with PT for model mineral assemblages (Figs 3^7).
In Fig. 9 the combined viscosity^density results for the
Si4O8 þ H2O reference model at Qtz (Fig. 9a) and
For þ Ens (Fig. 9b) saturation are shown up to 10 GPa and
11008C. Porous and fracture flow velocities in crust and
mantle can be derived using the r/m information plotted
1348
HACK & THOMPSON
FLUID AND MELT PHYSICAL PROPERTIES
(Appendix 3). It should be noted that elevated solubilities
(and thus, higher m and r) expected near solidi and related
to critical behavior are not accounted for in the solubility
models (Manning, 1994; Newton & Manning, 2002) used
to construct Fig. 9.
In view of Fig. 9, in both crust and mantle rocks
(1) increasing temperature is associated with
increased fluid viscosity (as a result of increasing silicate
solubility), and (2) fluid density changes are almost
entirely P dependent. Whereas fluid viscosity is sensitive
to the ambient T, the buoyancy force (given by r) has
a simple relation to depth and is largely independent of
the geotherm.
Combined viscosity^density properties of
mantle fluids
The results of mr modeling for representative mantle and
crustal fluids are shown in Fig. 9c and d up to 10 GPa and
11008C. The ToS PT path, wet solidi for crustal and
mantle rocks and other reference locations (Figs 1 and 2)
have been added to each of the panels for the thermal subduction model considered here. Fluid viscosities are significantly less in the mantle (at For þ Ens saturation, Fig. 9b
and d) than in the crust (at Qtz-saturation, Fig. 9a and c).
Modelled values can be compared in Table 1 for fluid r
and in Table 2 for m. Of course, future experiments can
check our model extrapolations.
SiO2 þ H2O slab fluids at For þ Ens saturation show
about a factor of two variation in m and are up to twice
as viscous as pure H2O. In contrast, model
Si4O8 þ NaAlSi3O8(50:50) þ H2O fluids at Qtz saturation
vary in m by about a factor of seven and are predicted to
be up to eight times more viscous than mantle fluids in
equilibrium with For þ Ens (Table 2). Flow rates for natural fluids in subduction zone environments obtained
assuming pure H2O properties may thus be an order of
magnitude too fast.
Ascending along the ToS geotherm (Fig. 2, superimposed
in Fig. 9) fluid viscosity decreases with slight decrease in
density with decreasing P to c. 1·5 GPa; from here fluids
continue their ascent at near constant viscosity, but
strongly decreasing density, in both crustal and mantle
compositions, at values close to pure H2O. One consequence is that slab fluid ascent rates switch from
viscosity-controlled at mantle depths (41·5 GPa) to
buoyancy-controlled flow processes at shallower depths
(Appendix 3). More variability in fluid flow velocities is
expected at mantle depths than at crustal pressures, as a
result of the greater range of potentially accessible fluid
viscosity, and reflects the higher solubilities pertaining at
higher P.
Viscosity^density changes related to
subsolidus mantle metasomatism and
melting processes
Several mineral reactions are likely to significantly affect
fluid composition. The presence of clinopyroxene in the
mantle wedge can be expected to strip Na from a fresh
slab fluid via incorporation into solid solution of omphacite
(or glaucophane). SiO2 will react with olivine to
Table 2: Viscosity [log10(m, Pa s)] of modeled subduction zone fluids and melts
Fluids
T
P
(8C)
(GPa)
Hydrous melts
H2O Reference
NaAlSi3O8 þ
(MgO) þ SiO2 þ H2O H2O wt % Reference
SiO2 þ H2O
Si4O8 þ H2O
For þ Ens sat.
Qtz sat.
Alb:Qtz (50:50)* mantle fluid
in melt
NaAlSi3O8 þ
NaAlSi3O8 þ H2O Si4O8 þ H2O
albite melt
crustal fluid granite fluid
Ano þ Dio
(50:50) þ H2O
Alb þ Qtz (50:50) mantle melt
granite melt
B
Slab Moho
450 3·2
4
3·96
3·94
4·00
subsolidus subsolidus
subsolidus
subsolidus
ToS
620 3·0
4
3·86
3·79
3·99
subsolidus subsolidus
subsolidus
subsolidus
Centre wedge 1300 2·5
4
Crustal Moho
700 1·0
4
3·87
Slab Moho
670 5·2
4
3·74
3·62
3·99
subsolidus subsolidus
subsolidus
subsolidus
ToS
820 5·0
4
3·41
3·14
3·96
30
1·79
0·47
1·25
Centre wedge 1350 3·7
4
3·71
5
1·60
3·69
Crustal Moho
4
3·81
3·71
5
1·76
3·93
1·42
3·97
10
2·37
5·46
subsolidus
C
600 1·0
3·93
3·89
3·99
subsolidus subsolidus
subsolidus
1·21
subsolidus
Fluids and granite melts calculated with equation (A2.3); hydrous mantle melts calculated with equation (A2.4).
*See Table 1 notes.
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JOURNAL OF PETROLOGY
VOLUME 52
NUMBERS 7 & 8
JULY & AUGUST 2011
precipitate serpentine/enstatite, and any excess dissolved
Al will form garnet/spinel. The contribution to density
from most other dissolved species, in addition to that of dissolved silica, is small because of their relatively low concentrations. K components may be an exception to this, as
these remain soluble in fluid moving from slab to mantle,
compared with mineral-compatible sodic components in
slab fluids (Kessel et al., 2005). K and H2O transport patterns and rates through metasomatic regions of mantle
are, however, likely to be significantly changed by saturation in phlogopite (e.g. Wyllie & Sekine, 1982; Malaspina
et al., 2009) or K-amphibole (e.g. Konzett & Ulmer, 1999).
It is deduced from Figs 3 and 7 that mantle fluid viscosity,
more than density, is dependent on its K/Na composition
and total solute concentration.
Across a melt^fluid miscibility gap there is a difference
in water content between fluid and melt. The viscosity contrast here is inferred to be relatively large (about four
orders of magnitude; see Table 2) compared with the
much smaller density contrast (Table 1). Thus above subducting slabs differences in m, more than r, allow fluid
influx into a melting region to be faster than melt extraction from that region. Consequently, build-up of mantle
melt fractions in the vicinity of the WPS is expected.
Conversely, no significant accumulation of fluid above
degassing magma is expected, as low mr fluid can physically separate from hydrous mantle melt and disperse rapidly
upward in overlying subsolidus regions.
more viscous as a result of increasing solute concentration
and pressure. Thus, once trapped in a sinking slab, the potential for slab fluid ascent decreases.
Slab dehydration will generate concentrated aqueous
fluids of greater density than H2O but of much lesser density than rock. This fluid rises from subducted slab to
mantle wedge, which when below its wet solidus will
permit transport by porous flow or fracture flow depending upon the local stress field and related strain rate. The
main effect of concentrated aqueous fluids passing from
slab to wedge will be chemical (large silica activity
change) rather than physical (small density change). This
fluid rising up the T gradient induces melting by an
amount proportional to both the solubility of H2O in the
melt and the amount of mantle that can be locally melted
(a function of the volume of mantle to which the rising
aqueous fluid has access and the rate of melt extraction
versus fluid influx).
Because the melt density is much closer to rock density
than water density, the rise of the resulting magma
even up fractures will be proportionally slower than
for aqueous fluids (in direct relation to the buoyancy
contrast).
Relevance of viscosity and density changes
of natural fluids at mantle depths
The density and viscosity PT models developed here have
been related to fluid composition in PTXSiO2 space for
crust and mantle, at Qtz and For þ Ens saturation in
Fig. 9. Values of ascent velocities for selected compositions
for modelled crustal and mantle fluids were evaluated at
PT pertinent to the flow at reference distances to the
trench shown as B and C in Figs 1 and 2. Velocities are
given for porous media and fracture flow for ranges of permeability and crack width. These were obtained using the
m, r results presented in Tables 1 and 2 and flow equations
in Appendix 3, and are presented in Table 3 (fluids) and
Table 4 (melts).
Combining m with r we expect fluid flow velocities
within crustal slab layers to vary by up to an order of magnitude, compared with the mantle where flow velocity
varies by a factor of two along porous grain boundaries
and similarly in fractures (Table 3). Flowing back up ToS
the slab fluid velocities generally increase during ascent,
reflecting decreasing solute concentrations and fluids tending towards dilute H2O. Thus at lower P, slab fluids migrate more quickly but transport less mass over long
distances than do deeper fluids. Mantle fluids flow at
faster rates than crustal fluids, up to about nine times [e.g.
ToS (above C), 8208C, 5 GPa, Table 3, Fig. 9].
Unlike fluids, melts tend to slow during ascent as their
viscosity increases in response to decreasing T, decreasing
Fluids migrating upward along the ToS (Figs 1, 2 and 9)
will show gradual decreases in viscosity with cooling as a
result of increasing XH2 O and much larger decrease in
density. Fluids migrating into the mantle wedge would
show a rapid viscosity decrease moving from slab to
mantle, but then slightly increase in viscosity as the fluids
heat and dissolve mantle minerals over the few kilometers
until the wet solidus is reached (1000WPS, Fig. 9d). At the
1000WPS there will be a large (about four orders of magnitude) stepped increase in viscosity from fluid to hydrous
melt. The m(melt^fluid) at the 800WPS is expected to
be smaller than for 1000WPS, because 800WPS melts
probably contain much more H2O (reflecting the greater
melting point depression implied by lower T melting in
contrast to the relatively small P difference between the
800 and 1000WPS locations plotted in Fig. 1). Hence at
< m1000WPS
seems posthe respective wet solidus, m800WPS
melt
melt
sible. Hydrous mantle melt viscosity changes continually
upon ascent into the hotter wedge core region. Distance
intervals across which these viscosity changes occur
depend on location in the subduction zone and T of the
wet mantle solidus (e.g. 800 vs 10008C) and can be read
from Fig. 1. In comparison, fluid caught in a sinking slab
(ToS path 3, inset Fig. 9a) becomes increasingly dense and
Changes in ascent velocities related to
changes in density and viscosity of
natural fluids along the PT paths of
different tectonic processes
1350
HACK & THOMPSON
FLUID AND MELT PHYSICAL PROPERTIES
dissolved H2O, and fractionation of melt towards polymerized eutectic compositions (Table 4). Ascent velocities near
or slower than 1010 to 109 m s1 are predicted for very
low fractions of migrating melt (see Table 4). These slow
melt velocities approach the velocities for slab sinking and
mantle wedge convection. The paths of such very slowly
moving melts can deviate significantly from simple vertical
ascent as a result of downward (and lateral) advective
motion of the solid matrix (McKenzie, 1984; Davies &
Bickle, 1991).
The solubility model shows different behavior at crustal
(more P dependent) compared with mantle (more T dependent) depths (Fig. 3). Although this is shown for
quartz solubility, thermodynamic modeling suggests that
the isopleths are sub-parallel also for lower silica activity
(e.g. Newton & Manning, 2002; Gerya et al., 2005), but
the slope change occurs at lower pressure than for quartz
(Fig. 3b). The slope change is probably related to change
of predominant speciation in the fluid [Si(OH)4·2H2O at
lower PT and higher-order dimers and oligomers at
higher T towards the wet solidus; Walther & Orville, 1983;
Newton & Manning, 2008]. The experimentally determined wet solidi for principal rock types (WBS, wet
basalt solidus; WGS, wet granite solidus pelite) are superimposed onto the other data in Fig. 9a and b.
Changes in density and viscosity of
natural fluids from slab to wedge
Slab fluids in equilibrium with metabasalt and metasediment decompressing into the wedge will metasomatically
change composition when encountering the subsolidus
mantle, resulting in conversion of forsterite to enstatite/serpentinite. As the slab fluids lose silica, perhaps creating
veins, they become less dense and distinctly less viscous as
they heat in the positive T gradient. Upon reaching the
mantle wet solidus the amount of mantle melting is determined by the amount of water (and alkalic components).
For melts in open fractures the continued decrease in viscosity with temperature up to the wedge core results in an
increase in m^r controlled flow rates (Table 4). Over a
wide depth range (c. 90^240 km) For þ Ens mantle melting
at the H2O-saturated solidus does not involve hydrous
minerals and so melt generation is directly proportional
to the amount of available dehydration water for a given
melt H2O solubility model. Because wet solidi (either
800WPS or 1000WPS, Fig. 1) bound most of the hot thermal core of the corner-flow of the peridotitic mantle
wedge, this effectively means that fluid transfer through
the mantle must be via melt. Compared with fluid, melt
advection of mantle components (and heat) is far slower
(e.g. Tables 3 and 4).
Table 3: Ascent velocities [log10(~vf , m s1)] of silicate-bearing fluids
Porous flow
T
P
H2O
(8C) (GPa)
Fracture flow
Reference
NaAlSi3O8 þ
(MgO) þ SiO2 þ H2O
Reference
SiO2 þ H2O
Si4O8 þ H2O
H2O
SiO2 þ H2O Si4O8 þ H2O
Qtz sat.
Alb:Qtz (50:50)* For þ Ens sat.
Qtz sat.
crustal fluid
granite fluid
crustal fluid granite fluid
mantle fluid
NaAlSi3O8 þ
(MgO) þ SiO2 þ
H2O
Alb þ Qtz (50:50) For þ Ens sat.
mantle fluid
B
Slab Moho
450 3·2
0·32 (3·3) 0·36 (3·36) 0·38 (3·38)
0·32 (3·32)
1·09 [5·09] 1·04 [5·04]
1·02 [5·02]
1·08 [5·08]
ToS
620 3·0
0·30 (3·3) 0·45 (3·45) 0·53 (3·53)
0·31 (3·31)
1·10 [5·10] 0·95 [4·95]
0·87 [4·87]
1·09 [5·09]
Centre wedge 1300 2·5
0·24 (3·2)
0·55 (3·55)
1·16 [5·16]
Crustal Moho
700 1·0
0·22 (3·2) 0·36 (3·36) 0·42 (3·42)
0·25 (3·25)
1·18 [5·18] 1·04 [5·04]
0·98 [4·98]
1·15 [5·15]
Slab Moho
670 5·2
0·35 (3·3) 0·62 (3·62) 0·76 (3·76)
0·36 (3·36)
1·06 [5·06] 0·78 [4·78]
0·64 [4·64]
1·04 [5·04]
ToS
820 5·0
0·33 (3·3) 0·96 (3·96) 1·28 (4·28)
0·37 (3·37)
1·07 [5·07] 0·44 [4·44]
0·12 [4·12]
Centre wedge 1350 3·7
0·28 (3·3)
0·58 (3·58)
1·12 [5·12]
Crustal Moho
0·23 (3·2) 0·31 (3·31) 0·34 (3·34)
0·24 (3·24)
1·17 [5·17] 1·09 [5·09]
0·85 [4·85]
C
600 1·0
1·03 [5·03]
0·82 [4·82]
1·06 [5·06]
1·16 [5·16]
Modeled parameters. Porous flow: solid matrix density, rs ¼ 2800 kg m3; grain size, b ¼ 5 mm; fluid-filled porosity,
f ¼ 1%, or log10(v~f , m s1) values in parentheses for f ¼ 0·001% ( ¼ 105) [equation (A3.2)]. Fracture flow: solid matrix
density, rs ¼ 2800 kg m3; fracture width, d ¼ 103 m ( ¼ 1 mm), or log10(v~f , m s1) values in square brackets for d ¼ 101
m [ ¼ 10 cm wide] [equation (A3.4)]. (For 1% vol. fluid-filled fractures: fracture number m2, nfr ¼ 10 m2 if 1 mm cracks,
or nfr ¼ 1 m2 if 10 cm wide cracks.)
*See Table 1 notes.
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JOURNAL OF PETROLOGY
VOLUME 52
NUMBERS 7 & 8
JULY & AUGUST 2011
Table 4: Ascent velocities [log10(~vf , m s1)] of model hydrous melts
Porous flow
Fracture flow
T
P
H2O
Reference
NaAlSi3O8 þ Si4O8
Ano þ Dio
Reference
NaAlSi3O8 þ Si4O8
(8C)
(GPa)
wt %
NaAlSi3O8 þ H2O
(50:50) þ H2O
(50:50) þ H2O
NaAlSi3O8 þ H2O
(50:50) þ H2O
Ano þ Dio
(50:50) þ H2O
in melt
albite melt
granite melt
mantle melt
albite melt
granite melt
mantle melt
B
Centre wedge
Moho
1300
2·5
5
6·40 (9·40)
{8·55 (11·55)}
6·16 (9·16)
5·00 [1·00]
{7·15 [1·15]}
4·76 [1·24]
700
1·0
10
6·99 (9·99)
10·06 (13·06)
subsolidus
5·59 [0·41]
8·66 [2·66]
subsolidus
820
5·0
30
2·62 (5·62)
3·91 (6·91)
5·64 (8·64)
1·22 [4·78]
2·51 [3·49]
4·24 [1·76]
1350
3·7
5
6·23 (9·23)
{8·31 (11·31)}
5·91 (8·91)
4·83 [1·17]
{6·91 [0·91]}
4·51 [1·49]
C
ToS
Centre wedge
Modeled parameters. Porous flow: solid matrix density, rs ¼ 2800 kg m3; grain size, b ¼ 5 mm; melt-filled porosity,
f ¼ 1%, or log10(v~f , m s1) values in parentheses for f ¼ 0·001% ( ¼ 105) [equation (A3.2)]. Fracture flow: solid matrix
density, rs ¼ 2800 kg m3; fracture width, d ¼ 103 m ( ¼ 1 mm), or log10(v~f , m s1) values in square brackets for
d ¼ [1 m wide] [equation (A3.4)]. Centre wedge {granite velocities} are for model reference purposes.
Changes in density and viscosity of natural
fluids from mantle to overlying crust
Mantle melts rising from the hot region of the wedge core
to shallower depths will show viscosity increase with cooling as melts fractionate from hydrous basalt (c. 10 to 102 Pa
s) towards more evolved felsic ‘granitic’ compositions that
are only slightly more water-rich at the Moho (c. 103 to
105 Pa s; Table 2). At the top of the mantle (Moho ‘d’ is
located at 30 km depth in Fig. 1) the T at the base of the
overlying plate is higher than that of wet granite melting
over a broad area (c. 135 km). In this region intruded
mantle-derived melts can fractionate and exsolve fluids at
the wet basalt to granite solidi directly within the crust
(Fig. 9c) at PT conditions where amphibole/mica is not
stable. At the Moho (‘d’) at distance B from the trench
(Fig. 1), deep crustal granites mobilize feldspar þ quartz
components whereas their exsolved fluids are strongly peralkaline and leach alkalis and silica (Veksler, 2004; Aerts
et al., 2009).
Melt versus fluid transport effects are distinguishable in
terms of expected mass (H2O versus silicate), heat advection amounts (heat capacity), migration rates (m, r) and
compositional change. Peralkaline fluids on path 1 (at distance B) will be seen at the top of subduction-related ‘granites’ and may be recorded as great amounts of pegmatitic
veining or massive hydrothermal metasomatism in the
lower to middle crust (London, 2004; Hack et al., 2007a).
Further from the trench near the top of the wedge (e.g.
point d on path 1C, Fig. 1), fluid may exsolve from freezing
hydrous mantle melt at the wet mantle solidus (or lower T
solidi). Such buoyant fluids expelled in equilibrium with
For þ Ens will encounter quartz crust (above Moho ‘d’),
will be undersaturated in silica and will try to dissolve
crust. Thus, subsolidus mantle-derived dissolving fluids
will increase m and r (Fig. 9d to 9c) when penetrating the
crust and increase m slightly with cooling. Relatively lowT pegmatite mineralization and regional alkalic metasomatism in the absence of granite intrusions may be diagnostic of such cooler crustal regions where subsolidus
mantle fluids ascend into the crust.
Although we have considered primarily ‘granitic’ continental crust (i.e. felsic crust of evolved magmatic or metamorphic origin) overlying the mantle wedge with a Moho
near 35 km, the same discussion could apply to a thicker
continental crust (e.g. crustal Moho near 70 km, e.g.
Andean arc) or basaltic oceanic crust overlying mantle at
ocean^ocean convergent zone magmatic arcs (Moho near
8 km, enstatite-saturated crust).
Slab to surface mass and volatile flux and
time intervals
The deduced fluid and melt densities (Table 1) and viscosities (Table 2) are used to evaluate ranges of ascent velocities using the equations presented in Appendix 3. Selected
values of calculated ascent velocities for silicate-bearing
fluids at particular PT locations in the model (Figs 1 and
2) are summarized in Table 3, for the cases of porous flow
[equation (A3.2)] or fracture flow [equation (A3.3)]. For
each case, velocities for three fluid compositions are shown
for a single grain size (b ¼ 5 mm) and for two porosities
(1%, or f ¼102; 0·001% or f ¼105), or crack widths
(1mm and 10 cm for fluid; 1mm and 1 m for melt). Because
they contain solutes and are therefore denser and more viscous, each fluid flows more slowly than pure H2O.
Alb þ 4Qtz þ H2O (granite) fluid flows more slowly than
Si4O8 þ H2O, by less than an order of magnitude (OM).
1352
HACK & THOMPSON
FLUID AND MELT PHYSICAL PROPERTIES
Mafic fluid flows faster than crustal (felsic) fluid by c. 0·5
OM. For porous flow, the values in parentheses are about 3
OM lower and are for 3 OM lower porosity.
For fracture flow we have considered fracture widths of 1
m and 1mm. We have performed calculations also at 1 mm,
but at this level microcracks produce similar results to the
equations for porous media, with minor changes in
grain-pore geometry. From equations (A3.1) and (A3.2),
porosity (f) is related to permeability (kf) and grain size
(b) via the relation kf ¼ (b2f2)/(24p).
The velocity ranges for each composition in Table 3 are
seen to reflect much more the deduced m, r for the particular Xfluid than variation of this with PT in different parts
of the subduction environment. Although a mantle fluid
(Table 3) appears to accelerate during vertical ascent
from slab to centre wedge to overlying plate, this would
migrate rather as hydrous ‘mafic’ melt through most of the
wedge (Table 4). Hydrous basaltic melt flows 2^3 OM
faster than felsic melts along grain boundary pores and
through fractures, except in the PT region of the ToS for
location C. Here, very H2O-rich felsic melts appear to
flow faster than cool mafic melt.
We can use the deduced ascent velocities (Tables 3 and
4) to ascertain the duration of the fluxing event from slab
to surface for a representative length of 100 km. Fluid flow
velocities (Table 3) range from 0·1 to 0·6 m s1 for porous
flow (for porosity ¼1%, permeability c. 1010 m2) and
about 25 times faster for fracture flow (for crack
width ¼1mm). Over 100 km, these correspond to time
intervals of only 12 to 2 days (porous) and 0·5 day to 2 h
(thin cracks). This is virtually instantaneous. Timescales
lengthen to 6^70 years per 100 km for porous flow at the
lower permeability^porosity values commonly inferred
for metamorphic rocks (e.g. kf ¼1017 m2, c.
f ¼ 105 m3 m3). One implication is that fast ascent velocities of 1m s1 mean that fluids or melts would rapidly exhaust the starting reservoirs (e.g. Thompson, 1997, p. 303).
Thus the processes governing fluid production rates (typically 1010 to 1012 m3 m2 s1; Brady, 1988) become very important because flux ascent durations are essentially
source limited. This means that the thermal structure
around the slab^mantle interface and its range of permeability^porosity behaviour needs to be considered in
detail in forward models. To deduce the equivalent range
of flow values from natural (inverse) observations will require radiogenic isotope determinations over several different ranges of half-life for simultaneously moving elements.
Because flow in cracks is deduced to be typically an order
of magnitude (or more) faster than through porous
media, the controls on transition between these permeability types require detailed examination, particularly at ToS
for slab to mantle and at the Moho for mantle to crust.
Melt flow velocities (Table 4) range from 106 for mafic
melts to 1010 m s1 for felsic melts for porous flow (1% f)
and about 25 times faster for fracture flow (1mm wide
cracks). These correspond to time intervals over 100 km of
3200 years (mafic melt) and 32 Myr (felsic melt) for 1%
f, compared with 130 years (or 1 h) and 1·6 Myr (or 2
years) along 1mm (or 1 m) wide cracks for hydrous mafic
and felsic melts, respectively. Thus, for travel time-lengths
appropriate to migration above subduction zones and
probable ranges of melt/fluid m, r, satisfactory velocity^
permeability^composition relationships are readily found
but such solutions are generally non-unique. Porous flow
velocities increase for coarser grain textures and/or
increased fluid fraction [Appendix 3, equation (A3.2)]
whereas slower flow rates result for narrower cracks [equation (A3.4)]. Locally large velocity and flux variations
will occur where there are differences in fracture width or
grain size and fluid availability. Such variations are independent of r/m and rather reflect fluid/melt influx and
matrix strain rates.
Our presented values of ascent velocity of fluids and
melts above subduction zones yield ascent times through
the mantle wedge that differ noticeably from the study by
Cagnioncle et al. (2007; Table 1). For example, our results
give porous flow melt ascent times of5c. 104 years whereas
Cagnioncle et al. (2007) gave c. 105 years to a few million
years. The various parameters involved contribute to the
calculation of ascent velocity by the following per cent
amounts: density and viscosity values for pure water compared with those estimated for concentrated solutions and
hydrous melts here (10%), use of grain size cubed rather
than squared definition for porous media permeability
(10%), different melt per cent (20%), incorporation of
opposing solid matrix velocity field against the Darcian
fluid/melt flux (60%). The last and largest effect that
needs to be examined further is the degree of coupling between the subducting slab and the attached overlying
mantle.
Estimated ‘travel times’ for the transport of a fluid
phase from the slab to the base of the crust have come
from several studies of different isotopes. For fluids to
travel c. 100 km (paths beginning at B, C; from a to point
d) suggested durations range from about 50 kyr as a
minimum (from U-series measurements: Bourdon et al.,
1999; Turner, 2002) to a maximum of about 5 Myr
(from Be isotopes: Morris et al., 1990). Although
this is a range of two orders of magnitude, the flow
models indicate a much larger range of timescales. To
narrow this range we should be looking for natural indicators to show that for deduced fast flow rates fluids/melts
were stored/halted for significant periods of time (e.g.
near the Moho).
Suggested parameter ranges for future
experimental work
Further developments of this work will be provided
through experimental measurements of the density and
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VOLUME 52
viscosity of fluids and melts of appropriate composition in
equilibrium with the commonest rock types. We have indicated at which PTX conditions these experiments should
be made relative to the key regions above subduction
zones. Knowledge of the compositions and densities of hydrous fluids in equilibrium with haplogranitic rocks near
solidus temperatures and at pressures near 2 GPa are
much needed, as are the densities and viscosities of haplogranitic melts. Studies of hydrous peridotite compositions
at PTconditions appropriate to a depth profile (geotherm)
through the mantle wedge (e.g. 100 km ToS section, in
Fig. 1) are needed at different H2O contents to limit melt
PTX and related r, m.
Other volatile components are known in natural fluids
and melts (principally fluids/gases in COHNS with
associated Cl, see Appendix 6; Wallace, 2005), so simple
experiments need to be made at the boundaries of the
PTX ranges indicated to determine how they will affect
r and m as a prelude to more systematic studies. In
general, other fluid components will lower aH2 O and
decrease mineral solubility unless more soluble aqueous
complexes are generated. Lowered aH2 O will raise the
solidus T compared with pure H2O as the COHNS
gases appear to be more soluble in fluids than in melts.
This in turn will lead to increases in density and viscosity
in such melts relative to H2O at a particular PT
(Appendix 6).
It appears from the velocities calculated here that H2O
travels through the mantle wedge mostly dissolved in
melts migrating along grain boundaries for transport timescale estimates of 103 to 105 years. This finding considers
that H2O changes from fluid to melt at the ToS and from
melt to fluid at the crustal Moho overlying the mantle
wedge and that no other factors impede flow. Porous flow
models are affected by great uncertainties in the application of Darcy’s Law at the very small permeabilities
(51018 m2 s1) deduced for rocks under pressure (e.g.
Brace, 1980). Fracture flow, although much faster than
porous flow, requires that the fluids find the fractures and
keep them open to maintain sufficiently fast flow.
Improved transport models combined with flux timescale
information would allow us to better constrain the permeability structure, its evolution and control on fluid melt
flows above subduction zones.
Future work on various isotopic systems for arc
magmatic rocks will allow us to distinguish elements
that reflect partitioning into a fluid rather than a melt,
and therefore which rate-limiting processes predominate.
We need also to distinguish whether the relevant
isotopes have been stored in mantle minerals during
their ascent from slab to surface or record characteristics
of magma generation, migration, accumulation, storage
and release processes, or different degrees of crustal
assimilation.
NUMBERS 7 & 8
JULY & AUGUST 2011
CONC LUSIONS
Even though the viscosity and density of melt and fluid fall
in distinct ranges, there is enough variation in the parameters controlling permeability to cause calculated flow
velocities through mantle and crustal rocks to overlap in
some cases.
Dehydration reactions within the subducted slab release
H2O at particular depths for oceanic crust (up to
c. 100 km) compared with hydrated subducted mantle (up
to c. 150 km). Significantly different ranges in the change
in density and viscosity occur depending upon whether
the fluids flow back up the top-of-slab, are further subducted or ascend into the overlying mantle wedge.
Available dehydration H2O could induce wet mantle melting throughout most of the mantle wedge to an extent depending upon how the H2O becomes distributed and
which solidus is appropriate (800WPS or 1000WPS). If
mantle melting occurs at 800WPS compared with
1000WPS (Fig. 2) hydrous mantle melts would be much
more widespread than subsolidus mantle hydrous fluids.
Subsolidus crustal fluid viscosity may vary at most by a
factor of three between 0·01 and 4 GPa (i.e. from c. 1 to
3 104 Pa s); this is even less variable for mantle fluids.
In contrast, density may vary by more than one order of
magnitude (e.g. 0·1^1·4 g cm3 over c. 0·01^4 GPa). The
range in viscosity becomes larger with increasing P
(44 GPa), whereas the relative density changes (@r/@P, @r/
@T) are far smaller.
Analysis of the hydrous haplogranite viscosity model indicates that although potassic hydrous haplogranite fluids
could be one to two orders of magnitude less viscous than
sodic varieties, it is mixed alkali compositions in higher
concentration fluids (and melts) that have the lowest viscosities. Such distinct differences in r and m values related
to alkali composition may be manifest as measurable
order of magnitude differences in length-scales or timescales of K versus Na metasomatic processes in the upper
mantle or related to crustal granitoids. In regions of
enhanced mineral solubility such as (1) near solidus magmatic fluids, (2) thin surface-like films between grains
(Appendix 4), or (3) in the vicinity of melt^fluid miscibility
(Appendix 5), both density and viscosity may be higher
(therefore leading to slower migration) than predicted by
our simplified preliminary reference model.
Despite cooling, ascending subsolidus mantle fluids
(aSiO2 at For þ Ens) crossing the Moho and entering the
base of the continental crust (aSiO2 at quartz) or oceanic
crust in island arcs (aSiO2 at Ens) will cause dissolution.
These fluids will thus become denser, more viscous and
solute-rich. Our model suggests that quartz-saturated
fluids are far denser than pure H2O and, more importantly, are about two times more viscous and denser than subsolidus For þ Ens fluids. This means that hydrous fluids
can flow faster in the mantle than in the crust. Clearly,
1354
HACK & THOMPSON
FLUID AND MELT PHYSICAL PROPERTIES
the effect of other dissolved components in H2O in equilibrium with common rock types must be investigated in
terms of the effects upon r, m assessed thus far only for dissolved SiO2.
Hydrous slab felsic melts (such as adakites) at 8208C,
5 GPa may be 5^6 OM faster flowing than deep crustal
melts at 7008C, 1GPa as a result of a c. 6 OM difference in
viscosity. The large viscosity difference between such
melts primarily reflects the effect of pressure, with much
higher H2O contents being dissolved in the melt at slab
depths. From the top of the slab through the overlying
mantle wedge to the Moho, melt viscosities generally increase, largely following decreasing dissolved H2O, and
imply a progressive slowing of the rising melt.
Where a longer proportion of the travel path is made by
low-viscosity subsolidus fluids (closest to the mantle wedge
nose in the region above B in Fig. 1), metasomatic transport
rates are expected to be much faster compared with where
less buoyant and more viscous melts dominate advective
fluxes (in the region above C in Fig. 1). Fracture flow and/
or a larger mantle region (where subsolidus fluid is stable
rather than hydrous melt), facilitate faster slab-to-surface
transit times. This is also favoured by a higher T mantle
solidus (1000WPS).
Our models are presented in a form that can be easily
modified when new Xmr data for the appropriate compositions are determined from experiments at the PT conditions suggested here.
AC K N O W L E D G E M E N T S
We are very pleased that we can contribute to Peter
Wyllie’s celebration. We wish to thank Andreas Aude¤tat,
David Dolejs› , Maarten Aerts, Peter Ulmer and Jamie
Connolly for constructive discussions; Craig Manning,
Axel Liebscher and an anonymous reviewer for their insightful comments in helpful reviews; Joerg Hermann for
considerate editing; and the Schweizerische Nationalfonds
for funding our research.
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A P P E N D I X 1: F O R M U L AT I O N O F
D E N S I T Y ( o) M O D E L S F O R
H Y D RO U S S I L I C AT E M E LT S A N D
C O N C E N T R AT E D ( S O L U T E B E A R I NG ) AQU EO U S F LU I D S
Density variations for solute-bearing
aqueous fluids with PTX
These were obtained from the equation (see Bottinga &
Weill, 1970)
rf ðP,T,XÞ ¼
n
X
i¼1
Xi
MWi
ðP,TÞ
V i
ðA1:1Þ
where rf is the fluid/melt density in g cm3, Xi is the mole
fraction, MWi the molecular weight in g mol1 and
V i (P,T) is molar volume in cm3 mol1 of the ith component, and all values taken at the P, Tof interest. Here, the
partial molar volumes of silicates dissolved in H2O were
taken as equivalent to the pure molten silicate liquid.
End-member fluid and melt densities at elevated PT
were calculated using the experimentally calibrated
Compensated-Redlich^Kwong (CORK) equation of state
for H2O and Murnaghan equation of state for silicate
liquids (Holland & Powell, 1991, 1998, 2001).
Density variations for hydrous silicate
melts with PTX
These were obtained from the equation (see Lange &
Carmichael, 1990)
(
n
X
Xi MWi V i;Tref ;Pref
rmelt ðT; P; XÞ ¼
i¼1
1 )
dV
dV
þ
ðT Tref Þ þ
ðP Pref Þ
dT i
dP i
ðA1:2Þ
where rmelt is melt density, V i,Tref ,Pref , Tref and Pref are reference values for partial molar volume, T(emperature)
and P(ressure) respectively, and ðdV=dTÞ
i and ðdV=dPÞi
represent thermal expansivity and compressibility of the
ith component, respectively. Here, oxide volume, expansion and compressibility data are from Lange &
1358
HACK & THOMPSON
FLUID AND MELT PHYSICAL PROPERTIES
Carmichael (1990, table 3, p. 36) and data for H2O dissolved in melt are from Ochs & Lange (1999, p. 1316).
A P P E N D I X 2 : F O R M U L AT I O N O F
V I S C O S I T Y ( k) M O D E L S F O R
H Y D RO U S S I L I C AT E M E LT S A N D
C O N C E N T R AT E D ( S O L U T E B E A R I NG ) AQU EO U S F LU I D S
Viscosity variations for solute-bearing
aqueous fluids (immiscible with melt)
with PTX
Table A2.1: NaAlSi3O8 þ H2O fluid and melt viscosity
model coefficients [equation (A2.1)]
Fluid
Melt
lne A
9·69
8·85
Ba
2980
251190
Ca
874455
129602
Va
0
14·7 106
Best fit for NaAlSi3O8 þ H2O fluids with 0–58 wt % Alb
dissolved, and melts 0–8·4 wt % H2O.
These were obtained from the equation
ln mfluid ¼ ln A þ
Ba
Ca lnðXH2 O Þ PVa
þ
þ
RT
RT
RT
ðA2:1Þ
where A is a constant, XH2 O is mole fraction water, Ba and
Ca are activation energy parameters, and Va is the activation volume, R is the gas constant, P(ressure),
T(emperature). Here, XH2 O is calculated taking silicate
components on an eight oxygen basis. Units are Pa s, J, K
and
mol.
Coefficient
values
obtained
for
NaAlSi3O8 þ H2O fluids with 0^58 wt % Alb dissolved
are given in Table A2.1.
Viscosity variations for hydrous melt
(immiscible with fluid) with PTX
These were obtained from the equation
ln mfluid ¼ ln A þ
Ba
Ca lnð1 XH2 O Þ PVa
þ
þ
: ðA2:2Þ
RT
RT
RT
Coefficient values obtained for NaAlSi3O8 þ H2O melts
are given in Table A2.1. Units are Pa, s, J, K and mol.
Viscosity variations for multicomponent
solute-bearing aqueous fluids and melts
with PTX
These were obtained from the equation
X
n
n X
n
X
Ea,i PVa
Xi ln Am,i þ
oi,j Xi Xj
ln mf ¼
þ
þ
RT RT
i¼1
i¼1 j¼1
ðA2:3Þ
where Xi is mole fraction of the ith component, Am,i is a
constant, Ea,i is the activation energy and Va,i is the activation volume of the ith component, R is the gas constant,
P(ressure), T(emperature), and oi,j is a viscous interaction
parameter between solution components i and j. Here oi,j
was modelled as a constant independent of PT. Units are
Pa, s, J, K and mol. m^X is treated as a continuous solution.
This allows application to completely miscible PTX
regions and also immiscible fluid and melt (e.g. across a
solidus) because sub-/super-critical phases are separated
in X and therefore also in m. It should be noted that we
assume that silicate components are simple mineral-like
units on a constant oxygen basis, rather than oxide and
multi-oxide units on a variable oxygen basis.
Calibration
of
the
NaAlSi3O8 þ KAlSi3O8 þ
Si4O8 þ H2O model involved simultaneously fitting
melt viscosity data for dry Qtz, Alb, Ksp, and wet
Alb þ H2O, Alb þ Qtz þ H2O, Ksp þ H2O and hydrous
haplogranite (eutectic Qtz þ Alb þ Ksp þ H2O), and
taking m pure H2O ¼104 Pa s. End-member silicate
properties are given in Table A2.2, and viscous solution
interaction parameters are reported in Table A2.3.
The model fits 150 measurements with an average absolute
deviation of 0·34 log10(m, Pa s). Data sources
used: Dudziak & Franck (1966); Urbain et al. (1982);
Dingwell (1987); Persikov et al. (1990); Hess et al. (1995);
Dorfman et al. (1996); Schulze et al. (1996); Holtz et al.
(1999); Aude¤tat & Keppler (2004); Whittington et al.
(2004); and all data from Romano et al. (2001) except
one anomalously low m Ksp sample (K-713 containing
1·33 wt % H2O). The fit quality of our simple model is
comparable with other formulations (e.g. Giordano et al.,
2008a; Hui et al., 2009; Whittington et al., 2009a). Figure
A2.1 compares model viscosity with measured values.
There is evidence that increasing P decreases the m of
Alb melts (anhydrous: Kushiro, 1978; Brearley et al., 1986;
Suzuki et al., 2002; Behrens & Schulze, 2003; wet: Aude¤tat
& Keppler, 2004; Poe et al., 2006). Va for dry Alb is
20·5 2·7 (1s; 106 m3 mol1: Behrens & Schulze, 2003).
However, as data relevant to m dependence on P are compositionally limited (mostly dry Alb and lacking for other
components) we have set Va,i equal to zero. Thus, our
model may tend to overestimate m at elevated P. The current calibration for multicomponent NaAlSi3O8 þ
KAlSi3O8 þ Si4O8 þ H2O also tends to systematically
underestimate viscosity for anhydrous pure Alb and for
very H2O-poor melts, reflecting a difference in Ea,Alb in
this model (280 kJ, Table A2.2) and experimental estimates
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JOURNAL OF PETROLOGY
VOLUME 52
NUMBERS 7 & 8
kf rs rf
g
~vf ~vs ¼ f
mf
Table A2.2: SiO2 þ NaAlSi3O8 þ KAlSi3O8 melt viscosity model parameters [equation (A2.3)]
1
lne Am
Ea (kJ mol )
Qtz
12·1
515·8
Alb
11·3
280·4
Ksp
12·5
383·3
Table
A2.3: SiO2 þ NaAlSi3O8 þ KAlSi3O8 þ H2O
viscosity interaction parameters, oi,j [equation (A2.3)]
Qtz
26·8
Alb
9·5
Ksp
35·0
H2O
83·1
90·4
Qtz
Alb
Viscosity variations for hydrous mantle
melts (CaAl2Si2O8 þ CaMgSi2O6 þ H2O)
with PTX
These were obtained from the equation
B
T C
ðA3:1Þ
where ~v is velocity, subscripts refer to fluid or melt (f) and
solid (s), kf is the permeability of the solid, mf is fluid/melt
viscosity, f is interconnected porosity in the solid, r is
density and g is acceleration of gravity. Units are Pa, s, m
and kg.
Equation (A3.1) can be modified to express porous flow
through a cubic grain-pore model geometry [Turcotte &
Schubert, 2002, p. 402, equation (9-207)],
2 b f rs rf
g
ðA3:2Þ
~vf ~vs ¼ 24p
mf
where b is grain size and f is melt or fluid fraction, here
equivalent to porosity. Units are Pa, s, m and kg.
Fracture flow
31·2
(e.g. 357 kJ by Riebling, 1966; 414 kJ by Urbain et al., 1982;
488 kJ by Romano et al., 2001).
log10 mmelt ¼ A þ
JULY & AUGUST 2011
ðA2:4Þ
where A is a constant and parameters B and C are both
composition-dependent functions using multi-oxide units
on a variable oxygen basis for CaAl2Si2O8 þ
CaMgSi2O6 þ H2O melts as defined by Giordano et al.
(2008b, table 4, p. 208). Pressure is not included in this
Vogel^Fulcher^Tamman formulation, but could be added
as a separate term; for example, as in equation (A2.3).
A PPEN DI X 3: V ELOC IT I ES FOR
F L O W I N G H Y D RO U S S I L I C AT E
M E LT S A N D S O L U T E - B E A R I N G
AQU EO U S F LU I D S
Density and viscosity determine time^distance^mass
migration rates of natural fluids and melts.
Porous flow
Darcy’s Law provides one such description for flow in
porous media [Bird et al., 1960, p. 150, equations (4.J-1)^
(4.J-3)], here given for vertical fluid velocity,
Darcian fluid flux rates related to vertical parallel planar
fracture flow is given by [Norton & Knapp, 1977, p. 918,
equation (11)]
nfr d 3 rs rf
~qf ¼ g
ðA3:3Þ
12
mf
where ~qf is Darcian flux rate (m3 m2 s1), d is fracture
width (m), and nfr is the number of parallel fractures
per m2. ~vf ¼ ~qf =f and f ¼ nfr·d, so fluid velocity in parallel
vertical planar fractures is given by
2 d
rs rf
~vf ~vs ¼ g:
ðA3:4Þ
12
mf
It should be noted that equations (A3.2)^(A3.4) assume
that solid and fluid pressure are equal and thus that the
solid matrix deforms and collapses as fluid migrates. In
this study P equals lithostatic pressure.
It should be noted that the original Darcy equation was
formulated on the basis of a hydrostatic gradient.
Although relevant to high-permeability conditions, it is
not known if this equation also provides an adequate physical description of flow at the very low permeabilities
common to most metamorphic and mantle rocks (1018 to
1023; e.g. Brace, 1980) or of the extent to which bulk fluid
m, r properties also apply to surface-like fluid films between grains (see Appendix 4).
A P P E N D I X 4 : F L U I D P RO P E RT I E S
A L O N G G R A I N B O U N DA R I E S
C O M PA R E D W I T H B U L K F L U I D
Dissolution of silicate components in H2O tends to reduce
interfacial energies between fluid and grain boundaries,
thereby enhancing wetting behavior and so affecting migration through the rock matrix. This is an interesting
effect as it relates to solubility in the vicinity of the mineral
1360
HACK & THOMPSON
FLUID AND MELT PHYSICAL PROPERTIES
Fig. A2.1. Comparison of viscosity values [equation (A2.3), Table A2.2] for Si4O8(Qtz); KAlSi3O8(Ksp) þ H2O; NaAlSi3O8(Alb) þ H2O haplogranite (HPG) þ H2O experimental data and single-phase (continuous) solution model. The poor fit at high XH2O (low m) should be
noted; here the model gives much lower viscosity than measured, and smaller systematic underestimation of anhydrous Alb viscosity data.
surface and thus separate from bulk density and viscosity
in considerations of fluid migration. Low dihedral angles
occur where near-surface solute complexes in the fluid
may have some structural affinity with that of the solid
(Wanamaker & Kohlstedt, 1991). Fluids that generate
lower dihedral angles against minerals may more easily
penetrate along grain boundaries and thus be more
mobile. Surface tension is assigned a major role in some
models of metasomatic fluid migration above subducting
slabs (e.g. Mibe et al., 1999). For melts, the effects of wetting
are significant at smaller length-scales compared with
other physical factors in natural migration processes
(Stevenson, 1986; Riley & Kohlstedt, 1991).
A P P E N D I X 5 : k^ o C H A N G E S I N
T H E V IC I N I T Y OF C R I T IC A L
B E H AV I O U R
A water-saturated solidus for NaAlSi3O8 þ H2O occurs up
to c. 1·5 GPa where it vanishes at a critical end point
(according to Paillat et al., 1992; Stalder et al., 2000).
For Si4O8 þ H2O, the wet solidus upper critical end point
is at 1GPa (Kennedy et al., 1962; Newton & Manning,
2009). Up to this P there will be a step in m (as shown for
r) across the compositional gap between hydrous melt
and aqueous fluid. For fluid and melt the difference in m,
like r, diminishes with the difference in composition with
increasing P along the wet solidus to the critical end point.
The difference between fluid and melt has a much stronger control on m, r determined flow rates than compositional variations within either group. m, r values
approach each other towards critical points, which for
common rock compositions lie within the PT range of
these models (see Hack et al., 2007a, fig. 28, p. 172; those
workers suggested that critical points for granite, basalt,
and peridotite lie near 3·5 GPa and 7008C, 5·5 GPa and
10508C, and 10 GPa and 11008C, respectively). The locations of fluid/melt criticality in natural compositions are
not well established. In the vicinity of critical regions
larger than predicted, changes in X and physical properties
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JOURNAL OF PETROLOGY
VOLUME 52
(r, m) are expected for small changes in PT as shown for
SiO2 þ H2O (Fig. 3b). Figure 9 suggests the close proximity of fluid PT paths to critical phenomena in logarithmic
r^m space. Thus, further investigation in regions of vastly
enhanced solvent^solute interaction (e.g. complete melt^
fluid miscibility, near solidus fluids/melts, films along
grain boundaries) is warranted because the data will shed
light on natural fluid buoyancy and viscosity, and thus
bear upon migration velocities in many regions of
common geological concern.
A P P E N D I X 6 : O T H E R VO L AT I L E
COMPONENTS A N D EFFECTS ON
VISCOSITY AND DENSITY
Addition of volatiles tends to dilute and lower H2O activity
in fluids and as such volatiles can be practically viewed as
NUMBERS 7 & 8
JULY & AUGUST 2011
inert diluents. In turn, lowered aH2 O reduces mineral solubilities by an amount proportional to concentration of the
added volatile component (e.g. CO2: Walther & Orville,
1983; Newton & Manning, 2009). Because fluid m and r increase in proportion to silicate polymer concentrations in
solution, dilution caused by inert volatile components is expected to drive increased buoyancy and fluidity at the expense of decreased mass transport capacity. The proposed
variation in m, r of diluted fluids encourages faster flow
over longer length-scales in the PT gradients of the Earth’s
upper mantle. These kinds of dilute fluid are likely to be
associated with hydration and carbonation fronts more
than modal silicate metasomatism. In contrast, addition
of CO2 to melt tends to decrease dissolved H2O (e.g.
Dixon & Stolper, 1995, fig. 1, p. 1635) with the expected
effect of increasing viscosity and thus lowering melt
mobility.
1362