Journal of Volcanology and Geothermal Research 107 (2001) 1±18
www.elsevier.nl/locate/jvolgeores
The yield strength of subliquidus basalts Ð experimental results
S.R. Hoover, K.V. Cashman*, M. Manga
Department of Geological Sciences, University of Oregon, Eugene, OR 97403, USA
Received 21 August 2000; revised 11 December 2000; accepted 11 December 2000
Abstract
Yield strength is an important property of particle±¯uid suspensions. In basaltic lavas that crystallize during ¯ow emplacement, the onset of yield strength may result in threshold transitions in ¯ow behavior and ¯ow surface morphology. However,
yield strength±crystallinity relations are poorly known, particularly in geologic suspensions, where dif®culties of experimental
and ®eld measurements have limited data acquisition in the subliquidus temperature range. Here we describe two complementary experimental approaches designed to examine the effect of particle shape on the low-shear yield strength of subliquidus
basalts. The ®rst involves melting cubes of holocrystalline basalt samples with different initial textures to determine the
temperature (crystallinity) at which these samples lose their cubic form. These experiments provide information on the
minimum crystal volume fractions (0.20 , f , 0.35) required to maintain the structual integrity of the cube. The second
set of experiments uses suspensions of corn syrup and neutrally buoyant particles to isolate the effect of particle shape on yield
strength development. From these experiments, we conclude that the shape is important in determining the volume fraction
range over which suspensions exhibit a ®nite yield strength. As anisotropic particles may orient during ¯ow, the effect of
particle shape will be controlled by the orientation distribution of the constituent particles. We ®nd that the so-called `excluded
volume' can be used to relate results of experiments on anisotropic particles to those of suspensions of spherical particles.
Recent measurements of yield strength onset in basaltic melts at crystal volume fractions near 0.25 are consistent with our
observations that crystal frameworks develop at low to moderate crystal volume fractions when crystals are anisotropic (e.g.
plagioclase). We further suggest that conditions leading to yield strength onset at low crystallinities include rapid cooling
(increased crystal anisotropy), heterogeneous nucleation (which promotes extensive crystal clustering and large cluster anisotropy) and static conditions (random crystal orientations). q 2001 Elsevier Science B.V. All rights reserved.
Keywords: lava rheology; yield strength; lava ¯ow morphology
1. Introduction
Lava ¯ows cool and crystallize as they move over
the surface of the earth. Crystallization, in turn, causes
rheological changes that affect both the velocity of the
¯ows and their style of emplacement (Grif®ths, 2000).
In Hawaii, these changes are most pronounced in
* Corresponding author. Tel.: 11-541-346-4323; fax: 11-541346-4692.
E-mail address: [email protected] (K. Cashman).
¯ows that move swiftly through open channels. Here
cooling is rapid during early stages of ¯ow, and resulting down-channel increases in ¯ow crystallinity cause
rheological changes that result in ¯ow thickening and
diminished ¯ow velocities (e.g. Lipman and Banks,
1987; Moore, 1987; Wolfe et al., 1988; Crisp et al.,
1994; Cashman et al., 1999). The rheology of suf®ciently dilute crystal-melt suspensions is Newtonian,
with a slightly higher shear viscosity than the particlefree ¯uid (Einstein, 1956). More concentrated suspensions can be non-Newtonian, exhibiting both yield
0377-0273/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved.
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S.R. Hoover et al. / Journal of Volcanology and Geothermal Research 107 (2001) 1±18
strength behavior and shear-thinning rheology
(Jeffrey and Acrivos, 1976). As non-Newtonian behavior will in¯uence ¯ow on both a micro- and macroscopic scale, accurate ¯ow emplacement models
require a thorough understanding of the rheology of
crystal-melt suspensions (e.g. Robson, 1967; Walker,
1967; Hulme, 1974; Dragoni and Tallarico, 1994;
Kilburn, 1996).
The properties of particle±¯uid suspensions are
governed in part by two limiting particle concentrations: the volume fraction of particles at which maximum packing is achieved (f m) and the minimum
volume fraction at which the suspension exhibits a
®nite yield strength (f c) (e.g. Krieger and Doherty,
1959; Wildemuth and Williams, 1984, 1985; Zhou et
al., 1995). Particle size, shape, and orientation distributions control both of these volume fractions,
although their effects are best documented for f m
(Larson, 1999). Theoretical values of f m for ordered
uniform spheres vary from a lower limit of 4/7 (cubic
closest packing) to an upper limit of 0.74 (hexagonal
closest packing). An increase in the particle size
distribution can lead to an increase in packing ef®ciency; for example, in a bidisperse suspension f m
can be as large as 0.85 (Yu and Standish, 1993). In
contrast, an increase in the anisotropy of individual
particles typically causes a decrease in packing ef®ciency (Onsager, 1949). A compilation of experimental studies by Blanc (1995) shows a decrease in the
volume fraction of ®bers (packed by vibrations) from
about 0.6 for ®bers with aspect ratios of 4, to 0.04 for
aspect ratios of 100. Orientational order permits
higher values of f m (Balberg, 1985), and affects the
relative shear viscosity of a suspension in both the
dilute (Batchelor, 1971) and semi-dilute (Shaqfeh
and Fredrickson, 1990) limits. For geological applications, f m is usually taken as 0.6, and shear viscosity is
assumed to increase with particle concentration
according to the Roscoe±Einstein equation (e.g.
Marsh, 1981; Pinkerton and Stevenson, 1992).
Yield strength (t y) development in suspensions is
less constrained, largely because of measurement
dif®culties (e.g. Kerr and Lister, 1991; Nguyen and
Boger, 1992). Yield strengths of crystal-melt suspensions have been measured in both the ®eld (Shaw et
al., 1968; Pinkerton and Sparks, 1978; Pinkerton and
Norton, 1995) and the laboratory (Shaw, 1969;
Murase and McBirney, 1973; Ryerson et al., 1988;
Lejeune and Richet, 1995; Pinkerton and Norton,
1995; Philpotts and Carroll, 1996). Although the
results have not been generalized into a predictive
model, it is clear that the onset of yield strength is
controlled by the volume fraction (f c) at which a
`touching framework' ®rst forms, and that f c is not
a constant. Here we examine yield strength development in viscous ¯uid±particle suspensions using
two different but complementary experimental
approaches. In the ®rst we determine f c in natural
basalts by melting basalt cubes until they lose their
cubic form. By comparing the melting behavior of
basalt samples with different initial crystal textures,
we establish relationships between f c and crystal
shape, spatial clustering and orientation distribution.
A second set of experiments utilizes corn syrup and
neutrally buoyant particles to isolate the effect of
particle shape on yield strength development. These
experiments complement a percolation-based numerical study of f c presented in a companion paper (Saar
et al., 2001).
2. Methods
2.1. Melting experiments
Following the approach of Philpotts and Carroll
(1996), we determine the minimum crystallinity
required for yield strength development by melting
cubes (1 cm 3) of basaltic lava until the cubic form
collapses. Two basalt samples from Hawai'i (one
0 0
a a and one pahoehoe) and one 0 a 0 a sample from
Lava Butte, OR, provide contrasting starting textures
(Fig. 1) in samples with similar compositions. Prior to
melting, 0 a 0 a samples from both Hawaii and Lava
Butte contained pyroxene and plagioclase crystals of
fairly uniform size (100±200 mm). Backscattered
electron (BSE) images show that pyroxene crystals
are near-equant in shape, and elongate plagioclase
crystals exhibit some preferred orientation (Fig. 1a
and c). In contrast, the interior of a small Hawaiian
pahoehoe toe has elongate plagioclase crystals
surrounded by ®ne-scale dendritic intergrowths of
plagioclase and pyroxene (Fig. 1b).
Samples are placed in a high-density graphite crucible and suspended in a furnace at temperatures
ranging from 1135 to 11608C for a minimum of 2
S.R. Hoover et al. / Journal of Volcanology and Geothermal Research 107 (2001) 1±18
3
Fig. 1. BSE images of samples used in the melting experiments. Scale bar is 200 mm long in all images; as gray scale levels vary between
images, phases are identi®ed separately for each image. (a) 0 a 0 a sample from Kilauea, HI. Dark gray crystals are plagioclase, light gray are
pyroxene, and white are Fe±Ti oxides. (b) Pahoehoe toe, Kilauea Volcano, HI. Black crystals are plagioclase, medium gray are pyroxene. Note
®ne scale dendritic intergrowths in this sample. (c) 0 a 0 a sample from Lava Butte, OR. Medium gray crystals are plagioclase, white are pyroxene,
black areas are void spaces.
hours (Table 1). Sample temperatures are accurate to
^58C. The bottom of each crucible has a 3/4 in. hole,
which allows molten samples to drain and quench in
water located at the base of the furnace. Oxygen fugacity is controlled by the graphite container, as
attempts to regulate the fugacity through the introduction of CO2 and H destroyed the crucible within 2±4
hours. The low fugacity resulting from use of a
graphite buffer may affect the melting conditions at
the cube surface, but we assume that the sample interior melts under conditions close to those of crystallization (QFM; e.g. Philpotts and Carroll, 1996).
Images of quenched samples are obtained using a
JEOL 6300 SEM operated at 10 keV accelerating
voltage, a beam current of 5 nA and a working
distance of 15 mm. BSE imaging allows two-dimensional characterization of sample textures using NIH
Image software.
2.2. Analog experiments
We use suspensions of corn syrup and particles to
perform analog experiments for determination of
yield strength. Corn syrup is diluted with water until
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S.R. Hoover et al. / Journal of Volcanology and Geothermal Research 107 (2001) 1±18
Table 1
Experimental conditions and results for melting of natural basalts. Temperatures are accurate to ^58C. Volume fractions (f ) of plagioclase
(f plag) and pyroxene (f px) were determined by image analysis of BSE images, and were determined only for those samples that could be used to
bracket f c
Flow type
Temperature
(8C)
Duration
(h)
Final shape
Pahoehoe
Pahoehoe
Pahoehoe
Pahoehoe
Pahoehoe
0 0
a a (Hawai'i)
0 0
a a (Hawai'i)
0 0
a a (Hawai'i)
0 0
a a (Hawai'i)
0 0
a a (Lava Butte)
0 0
a a (Lava Butte)
0 0
a a (Lava Butte)
1140
1145
1150
1155
1160
1140
1145
1150
1160
1132
1142
1150
31
10
18
31
2
19.5
5
3
5.25
18.75
15
2.5
Cubic
Cubic
Cubic w/melt
Cubic w/melt
All melt
Cubic w/melt
All melt
All melt
All melt
Cubic w/melt
Cubic w/melt
All melt
the mixture viscosity is 50±100 Pa s at room temperatures (similar to the viscosity of near-liquidus Hawaiian basalt), with a density of 1440 kg/m 3. Two
different populations of particles are used, spherical
(poppy seeds) and prismatic (wax). While neither
perfectly spherical (Fig. 2A) nor perfectly neutrally
buoyant (density r ˆ 1330 kg=m3 †; poppy seeds
provide a suf®ciently close approximation to both
characteristics to determine the behavior of suspensions of spherical particles. We create prismatic
neutrally buoyant particles by mixing melted paraf®n
wax with kaolin, shaving the cooled and solidi®ed
mixture, and sieving the shavings to obtain a uniform
grain size. The particles average 1 mm in length, and
have density of 1440 kg/m 3 and average aspect ratio
(length/width) of 3.4 (Fig. 2B). The particle size is
thus much smaller than the typical ®nal ¯ow thickness
of ,10 mm.
The experimental apparatus used is shown in Fig. 3.
Water pumped from a graduated cylinder into a sealed
container compresses a bag containing the corn syrup
suspension and extrudes it at a constant rate (21 g/
min) into a clear tank. The tank is covered (to prevent
dehyration of the corn syrup), and temperature and
effusion rate are held constant for all experiments,
while liquid:particle ratios are varied. To insure that
the ¯ow is controlled by the rheology of the suspension and not by a particle-free ¯uid layer at the ¯ow
base, experiments with suspensions of prismatic
f plag
f px
0.18
0.08
0.23
0.18
0.17
0.10
0.34
0.16
0.31
0.26
0.04
0.03
particles use both a smooth and a textured base.
After the pump is shut off, the extruded suspension
is allowed to spread. Flow height and radius are
recorded throughout extrusion. Three examples of
these measurements are shown in Fig. 4; a complete
description of the results can be found in Hoover
(1999).
For Newtonian ¯uids with constant physical properties and a ¯ow radius (R) that greatly exceeds ¯ow
height (H), the ¯ow radius is expected to increase with
time (t) as R / t 1/2 during active extrusion (constant
discharge), and as R / t 1/8 after extrusion ceases
(constant volume) (Huppert, 1982). Both spreading
regimes can be observed in our experiments with
particle-free corn syrup (Fig. 4). A balance of surface
tension and gravitational forces indicates that surface
tension will dominate only when the corn syrup is less
than 2 mm thick, assuming a surface tension of
0.08 N/m (Borhan and Pallinti, 1999). Continued
spreading of the particle-free corn syrup throughout
the duration of the experiment con®rms the absence of
surface tension in¯uence for the ¯ow dimensions of
our experiments.
If the ¯uid has a yield strength, spreading will stop
once the gravitational force driving ¯ow equals the
yield strength, as can be seen in the spreading behavior of the particle±¯uid suspensions (Fig. 4). Particlebearing experiments show R / t 1/8 for several hundred
seconds after active extrusion ceased, after which the
S.R. Hoover et al. / Journal of Volcanology and Geothermal Research 107 (2001) 1±18
Fig. 2. Binary images (collected from a petrographic microscope)
showing particles used in analog experiments. Scale bars are 1 mm
long in both images. (A) Poppy seeds. (B) Kaolin-wax shavings.
radius remains constant. Although spreading thus
appears to cease well before the end of each 2- to 3hour experiment, yield strengths inferred from
measurements of R/H should be considered maxima.
In the analog experiments, particle size does not
appear to in¯uence ®nal ¯ow thickness, as illustrated
by a comparison of f c and t y determined from experiments using particles of 0.5 and 1 mm (Hoover,
1999).
3. Results
3.1. Melting experiments
Starting materials for the melting experiments were
chosen to compare the relative strengths of networks
formed under different conditions of ¯ow emplace-
5
ment. Identical cubes of each sample are heated to,
and quenched at, temperatures from 11358C (Lava
Butte) or 11408C (Hawaiian samples) to as high as
11608C, at 58C intervals (Table 1). Over this temperature interval, all samples lose their structural integrity,
and the originally cubic forms collapses to melt blobs
(Fig. 5). Silicate melts do not wet graphite, and thus
melt will not be drawn from the cube (Philpotts et al.,
1998). Moreover, the surface tension of the basaltic
melt (,0.35 N/m) is suf®cient to prevent gravitational
melt drainage from the structure (,300 Pa for a 1 cm
cube) for pore spaces #1.2 mm in diameter. As the
spacing of crystals in both samples is an order of
magnitude smaller, loss of the cubic shape should
occur only with loss of the structural coherence of
the crystal network. As a corollary, the strength of
the crystal network at the point of collapse is
,300 Pa, thus the crystallinity at which structural
collapse occurs is the minimum required to obtain a
small, but ®nite, yield strength under pure shear
(simple gravity loading) conditions.
The three basalt samples respond differently to
heating. Both 0 a 0 a samples lose coherence at a lower
temperature (,11458C) than the pahoehoe sample,
which retains its shape until reaching almost
11608C. BSE images of the samples (Fig. 6) can be
used to evaluate sample textures just before and after
structural collapse (see also Table 1). Qualitatively,
both 0 a 0 a samples are characterized by equant pyroxene and partly aligned elongate plagioclase crystals of
fairly uniform size and spatial distribution (Fig. 6a, b,
e, f), although the two 0 a 0 a samples differ in the relative abundance of the two phases (Table 1). The
textural difference between pre- and post-collapse
samples is not dramatic, particularly in the Lava
Butte pair, and suggests that the framework responsible for the structural integrity of the cubic Lava Butte
sample involves a three-dimensional network of tabular plagioclase crystals. In contrast, the pre-collapse
pahoehoe sample (Fig. 6c) is dominated by spatially
heterogeneous clusters of plagioclase and pyroxene
crystals. These clusters disappear completely on
collapse (Fig. 6d), leaving isolated plagioclase-pyroxene clusters in a melt-dominated matrix.
Observed differences in failure temperature re¯ect
differences in the volume fraction of crystals (f ) in
pre- and post-collapse experiments (and thus bracketing values of f c), as the bulk composition of the
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S.R. Hoover et al. / Journal of Volcanology and Geothermal Research 107 (2001) 1±18
Fig. 3. Schematic diagram of experimental apparatus used for analog experiments. Water pumped from a graduated cylinder compresses a
plastic bag containing the suspension, forcing it upwards into a clear tank. A circular grid on the tank ¯oor and vertical grid on the tank wall
provide a reference for height (H) and radius (R) measurements.
Fig. 4. Radius vs time data for three analog experiments, one particle-free and two using prismatic particles (f indicated). Spreading
occurs as a function of t 1/2 (dotted lines) during active extrusion,
and as t 1/8 (dashed lines) during constant volume spreading, as
predicted by Huppert (1982). Note that while the particle-free
¯uid continues to spread during the entire duration of the experiment, particle-¯uid suspensions with f ˆ 0:11 and 0.18 stop
spreading (thus deviate from the t 1/8 curves).
samples is similar (Hoover, 1999). Also potentially
important are variations in particle shape between
different crystalline phases (Philpotts et al., 1998;
Saar et al., 2001). For this reason, we report two
values of f c Ð one based on the total crystallinity
(f c) and one based on the crystallinity of anisotropic
plagioclase crystals …fpc †: 0 A 0 a samples collapse at a
lower temperature than the pahoehoe sample. The
Hawaiian 0 a 0 a sample shows a large decrease in crystallinity between 1140 and 11458C, the temperatures
bracketing structural collapse. Resulting critical crystallinities are 0.57 . f c . 0.34, and 0:23 , fpc ,
0:18 (Table 1). The plagioclase-dominated Lava
Butte 0 a 0 a sample provides tighter constraints on the
minimum crystallinity of network formation, as the
11428C melting experiment …f ˆ 0:35† is very close
to collapse (Fig. 5c). Collapse occurs by 11508C …f ˆ
0:29†; yielding 0.35 . f c . 0.29 and 0:31 , fpc ,
0:26: In contrast, the initially dendritic pahoehoe
sample maintains its cubic form to a temperature
between 1155 and 11608C. Bracketing crystallinities
for this sample extend both f c and fpc to lower limits
than observed in the 0 a 0 a, with 0.35 . f c . 0.18 and
0:18 , fpc , 0:08 (Fig. 6c and d).
Qualitative descriptions of pre-collapse sample
textures are augmented by measurement of twodimensional plagioclase shape (minor and major
axes of the best-®t ellipse) and orientation, with the
S.R. Hoover et al. / Journal of Volcanology and Geothermal Research 107 (2001) 1±18
7
Fig. 5. Photographs of products of melting experiments. Basalt cubes were initially 1 cm per side. (a) Hawaiian 0 a 0 a at 11408C. (b) Hawaiian
0 0
a a at 11458C. (c) Hawaiian pahoehoe at 11558C. (d) Hawaiian pahoehoe at 11608C. (e) Lava Butte 0 a 0 a at 11328C. (f) Lava Butte 0 a 0 a at
11428C. (g) Lava Butte 0 a 0 a at 11508C.
goal of assessing the extent to which the anisotropic
plagioclase crystals play a role in network formation
(e.g. Philpotts et al., 1998). For crystals of uniform
shape, the mode of the frequency distribution of
minor/major axis ratios is the average short/intermediate axis ratio of the three-dimensional crystal population (Higgins, 1994). The average long/short axis ratio
may be estimated from the minimum minor/major
axis category (e.g. Hammer et al., 1999). Axis ratio
histograms show modes of 0.3±0.5 for all samples
(Fig. 7a, c and e), indicating that the crystals are tabular, with intermediate:short axis ratios of 2±3:1. The
small number of crystals with axis ratios ,0.2 indicates that long:short axis ratios are between 5:1 and
10:1. Near-equant crystals are relatively infrequent.
Crystal orientations (Fig. 7b, d and f; measured as
the angle between the apparent long axis direction
and the horizontal) show minimal alignment of plagioclase crystals except in the Hawaiian 0 a 0 a, where
crystals are moderately aligned at an angle approximately perpendicular to horizontal in Fig. 6a.
However, the variation among samples is not large,
and it appears that the orientation of individual crystals cannot explain the differences in fpc observed in
these samples (although this conclusion is quali®ed by
the lack of three-dimensional data).
In summary, while complete three-dimensional
characterization of our melting experiments is not
8
S.R. Hoover et al. / Journal of Volcanology and Geothermal Research 107 (2001) 1±18
Fig. 6. BSE images of melted samples. Scale bar is 100 mm in all images. Plagioclase crystals are dark gray, pyroxene crystals are medium gray
(Hawaiian samples) or white (Lava Butte samples), glass is light gray. (a) Hawaiian 0 a 0 a at 11408C. (b) Hawaiian 0 a 0 a at 11458C. (c) Hawaiian
pahoehoe at 11558C. (d) Hawaiian pahoehoe at 11608C. (e) Lava Butte 0 a 0 a at 11428C. (f) Lava Butte 0 a 0 a at 11508C.
S.R. Hoover et al. / Journal of Volcanology and Geothermal Research 107 (2001) 1±18
9
Fig. 7. Axis ratio (minor/major axis lengths) and long axis orientation histograms of plagioclase crystals in pre-collapse melting experiments.
(a) and (b) Hawaiian 0 a 0 a at 11408C. (c) and (d) Hawaiian pahoehoe at 11558C. (e) and (f) Lava Butte 0 a 0 a at 11428C.
possible, qualitative observations, together with twodimensional measurements of BSE images, suggest
the following minimum requirements for yield
strength development in basaltic lavas. In all samples,
we ®nd that the presence of anisotropic crystals or
crystal clusters allows yield strength development at
particle volume fractions less than 0.35. The pahoehoe toe shows the lowest bracketing values of f c,
with 0.35 . f c . 0.18 (Table 1). At f ˆ 0:35; the
sample contains connected clusters of plagioclase
and pyroxene crystals, which gives the sample a
more pronounced textural heterogeneity than indicated by measurement of the shape or orientation
characteristics of the individual crystals. The dissolution of most crystal clusters in the collapsed pahoehoe
samples suggests that these clusters (plagioclase 1
pyroxene) provide structural integrity in the precollapse sample. The Lava Butte sample contains
primarily plagioclase, and thus bracketing conditions
for framework formation are best approximated by the
10
S.R. Hoover et al. / Journal of Volcanology and Geothermal Research 107 (2001) 1±18
limiting plagioclase contents of 0:31 , fpc , 0:26:
Yield strength development in the Hawaiian 0 a 0 a
sample is less well constrained, as is the extent to
which plagioclase alone controls yield strength, but
f c is probably comparable to that of the Lava Butte
sample. f cof ,0.35 are similar to those measured by
Philpotts and Carroll (1996) and Philpotts and Dickson (2000) in slowly cooled samples from the interior
of ¯ood basalt lava ¯ows. However, Philpotts et al.
(1998) suggest that plagioclase alone is responsible
for framework formation in these samples. If plagioclase represents approximately half of the crystal
population, then the resulting fpc # 0:14 in the ¯ood
basalt samples is low relative to our measurements.
3.2. Analog experiments
Suspensions used in the analog experiments
contained from 0 to 0.50 volume fraction particles
(f ). As f increases, the ®nal ¯ow thickness increases
and the surface texture changes from smooth to rough.
The particle concentration at which these changes
occur is different for suspensions composed of spherical particles than for those containing prisms (Figs. 8
and 9). Suspensions of spherical particles retain a
smooth surface to concentrations of about 0.40, and
increase substantially in ®nal thickness at particle
concentrations of about 0.50. In contrast, suspensions
of prismatic particles develop a rough surface texture
at volume fractions of about 0.18, and the ®nal ¯ow
thickness increases substantially at particle concentrations of about 0.23. Prismatic suspensions containing
low particle volume fractions also show distinct alignment of particles in the direction of ¯ow.
We determine the yield strength (t y) of each
suspension from the ®nal height and radius of the
¯ow (Table 2) by assuming that ¯ow ceases when
the gravitational (buoyancy) force is balanced by
yield strength (e.g. Grif®ths and Fink, 1997), such that
ty ˆ C 0 gDrH 2 =R;
…1†
where Dr is the density difference driving spreading,
g is acceleration due to gravity, and C is a constant.
Following Blake (1990), we assume C 0 ˆ 0:32:
Calculated yield strengths are shown as a function
of particle concentration in Fig. 10. In all cases,
yield strength increases rapidly for f . f c. Curves
for suspensions of spherical and prismatic particles
are similar in form to simple exponential curves
(shown as solid and dashed curves in Fig. 10). Differences between t y for prismatic suspensions extruded
on smooth and textured bases are probably within the
measurement uncertainties.
4. Discussion
The experiments described here provide constraints
on the onset of yield strength in both natural basalts
and in simpler analog suspensions. The two types of
experiments are complementary. Natural samples
provide realistic crystal architectures, with both interpenetrating and isolated crystals of varying sizes,
shapes, and compositions. However, the textures are
dif®cult to quantify and the experiments are static (do
not involve ¯ow). Analog suspensions are well characterized, with particles of controlled sizes and shapes
and a simple ¯ow regime, but have isolated (rather
than interpenetrating) particles.
Here we use the melting experiments to estimate f c
in natural systems. Next, we quantify the effect of
variable particle shape on f c using the results of the
analog experiments, and introduce an invariant function based on the so-called `excluded volume'. We
show that our estimates of f c for different particle
shapes are consistent with those of ®eld (e.g. Pinkerton and Norton, 1995) and laboratory (e.g. Lejeune
and Richet, 1995; Pinkerton and Norton, 1995; Philpotts and Carroll, 1996) measurements, and also with
predictions of percolation theory (e.g. Garboczi et al.,
1995; Saar et al., 2001). Finally, we speculate about
the possible effects of different lava ¯ow emplacement regimes on the development of variable textures
and resulting yield strength behaviors.
4.1. Onset of yield strength in crystallizing basalt:
melting experiments
The melting experiments provide qualitative observations on the development of crystal frameworks in
basaltic lavas. 0 a 0 a samples, with uniform populations
of plagioclase and pyroxene crystals, lose structural
integrity at particle volume fractions of ,0.3. Before
structural collapse, the Hawaiian 0 a 0 a showed extensive interconnection of plagioclase and pyroxene
crystals, while after collapse the sample consisted of
isolated (in two-dimensional images; Fig. 6a and b)
S.R. Hoover et al. / Journal of Volcanology and Geothermal Research 107 (2001) 1±18
11
Fig. 8. Final ¯ow forms for analog experiments using poppy seeds. Volume fraction of solid particles (f ) shown for each image. Circular grid
underlying the ¯ows has a spacing of 1 cm.
plagioclase and pyroxene crystals. Loss of a crystal
network as the cause of collapse is less obvious in the
plagioclase-dominated Lava Butte samples (Fig. 6e
and f). However, the prevalence of highly anisotropic plagioclase crystals is likely to result in
intricate three-dimensional networks that may not
be visible in two-dimensional images (e.g. Philpotts
et al., 1998). Interconnected crystal networks also
appear to provide yield strength in the Hawaiian
pahoehoe, with an interconnected plagioclase 1
pyroxene network present in the highest temperature cubic sample (11558C; Fig. 6c) and absent in
the droplet-forming sample (11608C; Fig. 6d).
Although the precise crystallinity of network formation is not well established, bracketing crystallinities of 0.18 and 0.35 indicate yield strength
behavior at relatively low crystal volume fractions.
The melting experiments illustrate the importance of particle shape and clustering in determining the onset of yield strength. Both 0 a 0 a
samples lose structural coherence at crystal volume
fractions of ,0.30±0.35, while the pahoehoe sample
retains structural rigidity to somewhat lower crystallinities. These critical crystallinities are lower
than observed (Lejeune and Richet, 1995) or
assumed (Kerr and Lister, 1991) for magmatic suspensions containing spherical particles (where fc ˆ
0.4±0.5) and thus have been considered unusual
when observed in basaltic samples (e.g. Philpotts
and Dickson, 2000). Based on our observations, we
suspect that limiting crystal volume fractions of less
than 0.4 are common in melts that contain randomly
oriented anisotropic crystals. As crystal shape,
spatial heterogeneity, and orientation distribution
are controlled by cooling and ¯ow regimes that
accompany crystallization (e.g. Kouchi et al., 1986;
Sato, 1995; Manga, 1998), our results suggest that
f ± t y relations in lavas should re¯ect both the cooling and strain history. Finally, these experiments
illustrate the importance of both textural characterization (particularly crystal shape, orientation, and
spatial distribution) of natural and experimental
samples, and the importance of integrating sample
cooling and ¯ow histories into rheological models.
12
S.R. Hoover et al. / Journal of Volcanology and Geothermal Research 107 (2001) 1±18
Fig. 9. Final ¯ow forms for analog experiments using kaolin/wax shavings. Volume fraction of solid particles (f ) shown for each image.
Circular grid underlying the ¯ows has a spacing of 1 cm.
4.2. Effect of particle shape and concentration:
analog experiments
The effect of shape on the formation of particle
networks is most easily examined in the analog experiments, where particle shape and size are uniform, and
¯ow history is known. Two important observations can
be made about the results of our analog experiments
(Fig. 10). First, each set of experiments shows an
approximately exponential relationship between yield
strength and particle concentration. Second, the onset
of measurable yield strength occurs at lower particle
concentrations in suspensions of prisms than in suspensions of spheres. Each of these observations will be
discussed separately.
4.2.1. Yield strength models
The presence of a yield strength requires that a
touching framework of crystals exists across the entire
suspension, and that the framework is able to support
a small but non-zero stress (Kerr and Lister, 1991).
Although the existence of yield strength has been
questioned (e.g. Barnes and Walters, 1985; Barnes
1999), Blanc and van Damme (1995) note that ªtheoretically, nothing is against the very concept of yield
stress ¼ and that, in any case, it remains a useful
operational concept if the stresses do not vanish at
the smallest shear rates that one is able to apply or,
equivalently, at observation times compatible with the
experimentº. Empirical relationships describing yield
strength in particle suspensions are reviewed in
Pinkerton and Stevenson (1992); Zhou et al. (1995).
One convenient model is described by
f=fc 2 1
ty ˆ A
1 2 f=fm
1=p
…2†
(Wildemuth and Williams, 1984, 1985; Zhou et al.,
1995), where f c is the minimum particle concentration at which the suspension can sustain some (low)
external stress (the zero-shear yield strength), and f m
is volume concentration at which the yield strength
S.R. Hoover et al. / Journal of Volcanology and Geothermal Research 107 (2001) 1±18
13
Table 2
Height, radius, and calculated yield strength for all analog experimental data presented in Fig. 10
R (cm)
t y (Pa)
0.3
0.5
0.5
0.75
1.2
1.25
3.0
9.5
8.0
7.2
5.7
7.25
2.7
3.0
0.5
1.5
1.6
4.6
9.4
27
141
Prisms
Smooth base
9
11
14
15
18
23
0.5
0.75
0.75
1.25
1.0
1.5
7.3
10.0
5.75
5.9
6.0
4.0
1.6
2.6
4.5
12
7.6
25
Textured base
9
11
14
15
18
23
0.6
0.75
1.0
1.3
1.25
2.5
7.7
6.7
7.5
7.5
6.2
4.0
2.1
3.8
6.1
10
12
71
% particles
H (cm)
Spheres
17
25
28
33
40
45
50
approaches in®nity (will not deform continuously
under any applied stress). The constant A re¯ects the
total interparticulate cohesion, and p may re¯ect
the response of the aggregate to shearing. Eq. (2)
predicts a sharp increase in strength over a narrow
range in concentration, as commonly observed
experimentally (e.g. Blanc and van Damme, 1995;
Pinkerton and Norton, 1995; Fig. 10). Additionally,
by including the stress-dependent parameters A and
p, Eq. (2) permits the suspension architecture to
change with applied stress. Stress-dependence of
the suspension architecture provides a qualitative
explanation for the difference in measured yield
strength in a suspension after it has been at rest and
that measured during shear (e.g. Pinkerton and
Norton, 1995).
Here we relate our experimental data to Eq. (2),
noting that the data are insuf®cient to determine all
four variables (f c, f m, A, p) independently. For
spheres, our measurements indicate that f c , 0.25.
Using a maximum random loose packing for spheres
of 0.525 (Shapiro and Probstein, 1992), the yield
strength data for f . f c is consistent with p ˆ 1
Fig. 10. Yield strength measurements from analog experiments.
Open diamonds Ð kaolin/wax prisms extruded on smooth (nontextured) base. Solid diamonds Ð kaolin/wax prisms extruded on
textured base. Solid squares Ð poppy seeds extruded on smooth
(non-textured) base. Solid and dashed lines are exponential ®ts to
the yield strength data. Dotted lines are ®ts to the data using Eq. (2),
with p ˆ 1:
and A ˆ 5:3: p is thus within the range (0.5±2.0)
observed in concentrated suspensions (Zhou et al.,
1995). As discussed previously, A depends on a
number of properties and interparticle interactions,
and its absolute value is not meaningful for extrapolation to geological materials. Turning to the suspension
of prisms, we obtain the same value of p for fc ˆ
0:09: The yield strength data is now well described
by fm ˆ 0:28 and A ˆ 6:9: Comparing these two ®ts,
we note that not only are estimates of A similar, but
also that f c and f m differ by a factor of 2±3 in both
cases. This similarity suggests that a simple scaling
relationship may relate the two curves, although this
comparison is quali®ed by that observation that the ®t
parameters are quite sensitive to the choice of f c.
4.2.2. Effect of particle shape on f c
The observed reduction of both f c and f m
for anisotropic particles is well known, particularly
for ®ber suspensions (see review by Blanc, 1995).
Here we seek to generalize our experimental
results, and to relate our results to theoretical models,
through the use of an invarient function to relate t y,
f c and f m. In Saar et al. (2001) we provide a more
comprehensive discussion of these ideas and scaling
relationships.
14
S.R. Hoover et al. / Journal of Volcanology and Geothermal Research 107 (2001) 1±18
One way to view f c is as a percolation threshold
that de®nes the initial development of a connected
pathway of crystals across the suspending ¯uid. The
percolation threshold, pc, for overlapping (soft-core)
spheres is 0.29 (Pike and Seager, 1974) and is reduced
to 0.18 for non-overlapping (hard-core) spheres
(Powell, 1979). For comparison, in the analog experiments, where the dimpled shape of the poppy seeds
may allow partial overlap, f c t 0.25. The percolation
threshold decreases with increasing particle anisotropy for randomly oriented particles (Balberg 1985;
Garboczi et al., 1995; Saar et al., 2001), consistent
with the observed decrease of f c for prisms relative
to spheres in the analog experiments.
One of the relevant results of percolation theory
studies (e.g. Pike and Seager, 1974; Balberg, 1985)
and numerical simulations (e.g. Garboczi et al., 1995;
Saar et al., 2001) is that pc (and by analogy f c) scales
with the so-called excluded volume, Vex. The
excluded volume is the volume containing a particle
in which the center of a similar particle cannot be
placed without overlap of the particles. In a suspension of non-overlapping spheres, for example, Vex is
eight times the volume of each sphere.
In detail, for randomly positioned and parallelaligned particles, nc kVex l is independent of shape,
and also independent of the size distribution for
soft-core particles (e.g. Haan and Zwanzig, 1977;
Balberg et al., 1984a). Here n is the number of particles per unit volume (the subscript c denotes its value
at the percolation threshold), and kVex l is the mean
excluded volume of particles in the suspension. For
randomly oriented particles, nc kVex l is no longer a true
invariant, and varies by a factor of about two for all
particles shapes (Balberg, 1985). The variability of
nc kVex l is small, however, compared to the ordersof-magnitude variability of pc (Garboczi et al., 1995;
Saar et al., 2001).
If t y also scales with nkVex l then we should be able
to relate our two sets of t y(f ) measurements. To
compare results for non-spherical particles with
those for spheres, we can de®ne an `a' `effective'
volume fraction as
feff ˆ …kVex l=8V†f;
…3†
where V is the particle volume. f is the actual volume
fraction of the non-spherical particles and f eff is the
volume fraction of an equivalent object (here a sphere
with Vex ˆ 8V†: If we assume that the laths in the
analog experiments are randomly oriented rods with
a hemispherical cap of length L 1 W and width W,
Balberg et al. (1984b) showed that
kVex l ˆ …4p=3†W 3 1 2pW 2 L 1 …p=2†WL2 :
…4†
Note that for L @ W; kVex l=V is proportional to the
aspect ratio L=W; rather than to the volume of the
individual particles. Using Eqs. (3) and (4), and L ˆ
2:4W (Hoover, 1999), we calculate that feff ˆ 1:5f;
and use this to scale measured t y(f ) relations for
prismatic suspensions (Fig. 11). While this scaling
moves the curve for prismatic suspensions toward
that of spheres, it does not superimpose the curves
(i.e. kVex l does not appear to be a true invariant).
This discrepancy is probably the result of the reduction of nc kVex l by a factor of two for anisotropic particles with non-parallel orientations (Balberg 1985).
We can superimpose the curves shown in Fig. 10
using feff ˆ 2:2f (Fig. 11). As this constant is only
1.5 times greater than that predicted, it falls within
the anticipated factor-of-two range. Furthermore, as
noted in Section 4.2.1, fm ù 2fc ; an observation that
suggests that the linear scaling implied by Eq. (3) may
be a reasonable approximation over a wide range of f .
In summary, the dependence of t y on f observed in
our analog suspensions indicates that particle shape is
an important parameter in determining the volume
fraction range over which a suspension exhibits a
®nite yield strength. In real crystal-melt suspensions,
the exact effect of shape on t y is complicated by both
particle interpenetration and by particle orientation
distribution. The importance of the latter parameter
suggests that the ¯ow regime (and resulting particle
ordering) of a given suspension may play an important
role in de®ning the actual values of f c and f m applicable to a speci®c lava ¯ow.
4.3. Implications for basaltic lava ¯ows
This study was motivated by a relationship
observed between lava ¯ow surface morphology and
¯ow crystallinity, and particularly by the hypothesis
that threshold transitions in ¯ow surface morphologies may be explained by the onset of a yield strength
suf®cient to inhibit continuous ¯uid deformation
(Cashman et al., 1999). Results presented here support
this hypothesis, and provide a framework for relating
S.R. Hoover et al. / Journal of Volcanology and Geothermal Research 107 (2001) 1±18
Fig. 11. Scaled t y(f ) data for kaolin/wax prisms (open circles),
compared with actual measurements for poppy seeds (solid circles).
Scaling relations are given on ®gure, and are derived as described in
the text. Curves are exponential ®ts.
the rheology of basaltic lava ¯ows to ¯ow emplacement histories.
Abrupt changes in surface morphology commonly
accompany the down slope ¯ow of lava. Most obvious
is the transition from smooth (pahoehoe) to rough
( 0 a 0 a) surfaces that occurs during ¯ow through open
channels (e.g. Peterson and Tilling, 1980). This transition appears to coincide with a pronounced increase
in groundmass crystallinity (Cashman et al., 1999;
Polacci et al., 1999), and thus may result from the
onset of a yield strength suf®cient to resist shear stresses imposed by the ¯ow. Measurements of the crystal
content of quenched ¯ow surfaces may thus be used to
estimate limiting crystallinities for different ¯ow
surface types (Folley, 1999). Smooth pahoehoe may
form when f # 0:25; while 0 a 0 a may form when f $
0:35 (Fig. 12). These measurements thus allow a
conservative inference of 0:25 , fc , 0:35; which
coincides with estimates provided by our melting
experiments. If transitional ¯ow surfaces re¯ect
small but ®nite values of yield strength, then
measured crystallinities indicate f c as low as 0.15
in some samples.
Low estimated values of f c most likely re¯ect both
highly anisotropic crystal shapes and low degrees of
orientational order. Scaling of the analog experiments
illustrates the potential effect of increasing crystal
15
anisotropy on f c for randomly oriented crystals
(Fig. 13). Here f eff is calculated for different particle
aspect ratios using Eqs. (3) and (4). We use effective
values of fc ˆ 0:3 and fm ˆ 0:6 (the maximum crystallinity observed in ¯ow samples; Fig. 12) to estimate
the f range over which suspensions of different particle aspect ratios may exhibit yield strength behavior.
This simple model indicates that for a constant feff ˆ
0:3; actual values of f c will vary from 0.30 to 0.09 as
the particle axis ratio varies from 1:1 to 10:1. For the
same range in particle shapes, f m varies from 0.60 to
0.19 for a constant feff ˆ 0:6: For `typical' particle
aspect ratios of 3:1±5:1, 0.16 # f c # 0.22, and
0:32 # fm # 0:44; with the effect of each incremental increase in aspect ratio diminishing as the aspect
ratio increases. Extension of such a diagram to other
crystal shape orientations requires computer simulations, and is discussed in Saar et al. (2001).
These observations lead to some general predictions about yield strength development in basaltic
lavas. First, rapid cooling is more likely to generate
anisotropic crystal shapes than slow cooling (e.g.
Lofgren, 1980); rapid cooling may also promote
heterogeneous nucleation, and thus highly anisotropic
crystal clusters (as seen in the dendritic pahoehoe toe
sample, Fig. 6c). Both of these textural characteristics
should lead to yield strength onset at relatively low
crystallinities. However, sustained rapid cooling
requires suf®cient stirring to rupture surface crusts
(e.g. Crisp and Baloga, 1994); the hydrodynamic
effects of stirring in high velocity ¯ow will serve to
both break-up crystal clusters (increasing the apparent
nucleation rate, e.g. Kouchi et al., 1986) and increase
crystal alignment. Both processes will tend to increase
f c. Thus we expect that rapid cooling in a near-static
environment will produce the lowest values of f c,
while high ¯ow rates, with resulting high degrees of
orientational order, should produce higher values
of f c.
5. Conclusions
We have used both melting and analog experiments to examine the roles of crystal shape, spatial
distribution and orientation on yield strength development in crystal-melt suspensions. Most important
is our conclusion that crystal shape is an important
16
S.R. Hoover et al. / Journal of Volcanology and Geothermal Research 107 (2001) 1±18
Fig. 12. Groundmass crystallinity as a function of ¯ow type: pahoehoe, diamonds; transitional, circles; 0 a 0 a, squares; data from Folley
(1999). Also shown are interpretations of these data in the context of
parameters related to yield strength. Non-overlap of smooth pahoehoe and 0 a 0 a shown in dark gray, crystallinity of transitional ¯ow
samples shown in light gray. f c is bracketed by the low crystallinity
limits of these two ®elds.
parameter in determining the crystallinity over which
a crystal-melt suspension will exhibit yield strength
behavior. Flow dynamics may also be important, to
the extent that the dynamics of ¯ow controls the orientation distribution of anisotropic crystals, and changes
the suspension architecture through breakage of weak
crystal±crystal bonds. The use of the excluded
volume Vex to scale the results of our analog experiments was not entirely successful. Nevertheless, scaling by a simple factor related to Vex seems to be a
reasonable approach that may only require better
constraints on variations of kVex l with particle orientation distributions. Finally, our measurements
support earlier work indicating the onset of yield
strength behavior in natural basalts at moderate crystallinities (e.g. Shaw, 1969; Murase and McBirney,
1973; Pinkerton and Norton, 1995; Philpotts and
Carroll, 1996; Cashman et al., 1999). These results
are consistent with predictions of percolation theory
for the minimum particle volume fraction at which a
touching framework is ®rst created (e.g. Garboczi
et al., 1995; Saar et al., 2001). Based on these data,
together with the common occurrence of anisotropic
plagioclase crystals in basaltic lavas, we ®nd it
reasonable that basaltic lavas exhibit a ®nite yield
strength at moderate (0.15±0.4) crystal volume fractions. Conditions that promote low values of f c
Fig. 13. Comparison of actual and effective particle volume fractions (f ) calculated using Eqs. (3) and (4) for randomly oriented
rods with hemispherical caps (width W; total length L 1 W) for
different values of L. Shaded area illustrates actual f over which
a yield strength would be anticipated for limiting effective volume
fractions of fc ˆ 0:3 and fm ˆ 0:6:
include rapid cooling (increased crystal anisotropy), heterogeneous nucleation (increased spatial
clustering) and static conditions (random crystal
orientations). These results help to explain discrepancies among ®eld measurements, experimental
measurements, theoretical calculations and provide
a basis for linking emplacement conditions of
basaltic lava ¯ows with appropriate rheological
models.
Acknowledgements
The authors gratefully acknowledge the comments
and suggestions of Steve Blake and Tony Philpotts
that greatly improved the manuscript. We also thank
Martha Folley for her insight into the textures of
Hawaiian basalt ¯ows and for permission to use her
data in Figure 12, Dana Johnston for assistance with
the melting experiments, Dave Senkovitch for help
with myriad experimental details, and Ross Grif®ths
and Ross Kerr for discussions about the measurement
of yield strength. KVC acknowledges NSF support for
the work (EAR9508144 and 9902851).
S.R. Hoover et al. / Journal of Volcanology and Geothermal Research 107 (2001) 1±18
References
Balberg, I., 1985. Universal percolation-threshold limits in the
continuum. Phys. Rev. B 31, 4053±4055.
Balberg, I., Anderson, C.H., Alexander, S., Wagner, N., 1984a.
Excluded volume and its relation to the onset of percolation.
Phys. Rev. B 30, 3933±3943.
Balberg, I., Binenbaum, N., Wagner, N., 1984b. Percolation thresholds in the three-dimensional sticks system. Phys. Rev. Lett. 52,
1465±1468.
Barnes, H.A., 1999. The yield stress Ð a review or pi alpha v tau
alpha rho epsilon i-everything ¯ows? J. Non-Newtonian Fluid
Mech. 81, 133±178.
Barnes, H.A., Walters, K., 1985. The yield strength myth? Rheol.
Acta 24, 323±326.
Batchelor, G.K., 1971. The stress generated in a non-dilute suspension of elongated particles by pure straining motion. J. Fluid
Mech. 46, 813±829.
Blake, S., 1990. Viscoplastic models of lava domes. In: Fink, J.H.
(Ed.), Lava Flows and Domes. IAVCEI Proceedings in Volcanology, pp. 88±128.
Blanc, R., 1995. Order and disorder in ®ber suspensions. In: Guazzelli, E., Oger, L. (Eds.), Mobile Particulate Systems. Kluwer
Academic Publishers, Amsterdam, pp. 115±128.
Blanc, R., Van Damme, H., 1995. Rheology of pastes. In: Guazzelli,
E., Oger, L. (Eds.), Mobile Particulate Systems. Kluwer
Academic Publishers, Amsterdam, pp. 129±160.
Borhan, A., Pallinti, J., 1999. Breakup of drops and bubbles translating through cylindrical capillaries. Phys. Fluids 11, 2846±
2855.
Cashman, K., Thornber, C., Kauahikaua, J., 1999. Cooling and
crystallization of lava in open channels, and the transition of
pahoehoe lava to 0 a 0 a. Bull. Volcanol. 61, 306±323.
Crisp, J., Baloga, S., 1994. In¯uence of crystallization and entrainment of cooler material on the emplacement of basaltic 0 a 0 a lava
¯ows. J. Geophys. Res. 99, 11,819±11,832.
Crisp, J., Cashman, K.V., Bonini, J.A., Hougen, S.B., Pieri, D.,
1994. Crystallization history of the 1984 Mauna Loa lava
¯ow. J. Geophys. Res. 99, 7177±7198.
Dragoni, M., Tallarico, A., 1994. The effect of crystallization on the
rheology and dynamics of lava ¯ows. J. Volcanol. Geotherm.
Res. 59, 241±252.
Einstein, A., 1906. Eine neue Bestimmung der Molekuldimension. Ann. Phys. 19, 289±306 (English translation in Investigation on the Theory of Brownian Motion, Dover, New
York, 1956).
Folley, M., 1999. Crystallinity, rheology, and surface morphology
of basaltic lavas, Kilauea Volcano, Hawaii. M.Sc. Thesis,
University of Oregon, Eugene, 203 pp.
Garboczi, E.J., Snyder, K.A., Douglas, J.F., Thorpe, M.F., 1995.
Geometrical percolation threshold of overlapping ellipsoids.
Phys. Rev. E 52, 819±828.
Grif®ths, R.W., 2000. The dynamics of lava ¯ows. Ann. Rev. Fluid
Mech. 32, 477±518.
Grif®ths, R.W., Fink, J.H., 1997. Solidifying Bingham extrusions: a
model for the growth of silicic lava domes. J. Fluid Mech. 347,
13±36.
17
Haan, S.W., Zwanzig, R., 1977. Series expansion in a continuum
percolation problem. J. Phys. A 10, 1547±1555.
Hammer, J.E., Cashman, K.V., Hoblitt, R., Newman, S., 1999.
Degassing and microlite crystallization during the pre-climactic
events of the 1991 eruption of the Mt Pinatubo, Phillipines. Bull.
Volcanol. 60, 355±380.
Higgins, M., 1994. Numerical modeling of crystal shapes in thin
sections: estimation of crystal habit and true size. Am. Miner.
79, 113±119.
Hoover, S.R., 1999. Crystallinity and rheology of Hawaiian
basaltic lava ¯ows. M.Sc. Thesis, University of Oregon,
Eugene, 101 pp.
Hulme, G., 1974. The interpretation of lava ¯ow morphology.
Geophys. J. R. Astr. Soc. 39, 361±383.
Huppert, H.E., 1982. The propagation of two-dimensional and
axisymmetric viscous gravity currents over a rigid horizontal
surface. J. Fluid Mech. 121, 43±58.
Jeffrey, D.J., Acrivos, A., 1976. The rheological properties of
suspensions of rigid particles. AIChE J. 22, 417±432.
Kerr, R.C., Lister, J.R., 1991. The effects of shape on crystal settling
and the rheology of magmas. J. Geol. 99, 457±467.
Kilburn, C.J., 1996. Patterns and predictability in the emplacement
of subaerial lava ¯ows and ¯ow ®elds. In: Scarpa, C., Tilling, R.
(Eds.), Monitoring and Mitigation of Volcano Hazards.
Springer, Berlin, pp. 491±537.
Kouchi, A., Tsuchiyama, A., Sunagawa, I., 1986. Effect of stirring
on crystallization kinetics of basalt: texture and element partitioning. Contrib. Miner. Petrol. 93, 429±438.
Krieger, I.M., Doherty, T.J., 1959. A mechanism for non-Newtonian ¯ow in suspensions of rigid spheres. Trans. Soc. Rheol. 3,
137±152.
Larson, R.G., 1999. The Structure and Rheology of Complex Fluids.
Oxford University Press, Oxford, 663 pp.
Lejeune, A.-M., Richet, P., 1995. Rheology of crystal-bearing silicate melts: an experimental study at high viscosities. J.
Geophys. Res. 100, 4215±4230.
Lipman, P.W., Banks, N.G., 1987. Aa ¯ow dynamics, Mauna Loa,
1984. U.S. Geol. Surv. Prof. Pap. 1350, 1527±1567.
Lofgren, G.E., 1980. Experimental studies on the dynamic crystallization of silicate melts. In: Hargraves, R.B. (Ed.), Physics of
Magmatic Processes. Princeton University Press, Princeton, NJ,
pp. 487±551.
Manga, M., 1998. Orientation distribution of microlites in obsidian.
J. Volcanol. Geotherm. Res. 86, 107±115.
Marsh, B.D., 1981. On the crystallinity, probability of occurrence,
and rheology of lava and magma. Contrib. Miner. Petrol. 78,
85±98.
Moore, H.J., 1987. Preliminary estimates of the rheological properties of 1984 Mauna Loa lava. U.S. Geol. Surv. Prof. Pap. 1350,
1569±1588.
Murase, T., McBirney, A.R., 1973. Properties of some common
igneous rocks and their melts at high temperatures. Geol. Soc.
Am. Bull. 84, 3563±3592.
Nguyen, Q.D., Boger, D.V., 1992. Measuring the ¯ow properties of
yield stress ¯uids. Ann. Rev. Fluid Mech. 24, 47±88.
Onsager, L., 1949. The effects of shapes on the interactions of
colloidal particles. Ann. N.Y. Acad. Sci. 51, 627±659.
18
S.R. Hoover et al. / Journal of Volcanology and Geothermal Research 107 (2001) 1±18
Peterson, D.W., Tilling, R.I., 1980. Transition of basaltic lava
from pahoehoe to aa, Kilauea Volcano, Hawaii: ®eld
observations and key factors. J. Volcanol. Geotherm. Res. 7,
271±293.
Philpotts, A.R., Carroll, M., 1996. Physical properties of partly
melted tholeiitic basalt. Geology 24, 1029±1032.
Philpotts, A.R., Dickson, L.D., 2000. The formation of plagioclase
chains during convective transfer in basaltic magma. Nature
406, 59±61.
Philpotts, A.R., Shi, J., Brustman, C., 1998. Role of plagioclase
chains in the differentiation of partly crystallized basaltic
magma. Nature 395, 343±346.
Pike, G.E., Seager, C.H., 1974. Percolatant conductivity: a computer study I. Phys. Rev. B 10, 1421±1434.
Pinkerton, H., Norton, G., 1995. Rheological properties of basaltic
lavas at sub-liquidus temperature: laboratory and ®eld measurements on lavas from Mount Etna. J. Volcanol. Geotherm. Res.
68, 307±323.
Pinkerton, H., Sparks, R.S.J., 1978. Field measurements of the
rheology of lava. Nature 276, 383±385.
Pinkerton, H., Stevenson, R.J., 1992. Methods of determining the
rheological properties of magmas at sub-liquidus temperatures.
J. Volcanol. Geotherm. Res. 53, 47±66.
Polacci, M., Cashman, K.V., Kauahikaua, J.P., 1999. Textural characterization of the pahoehoe- 0 a 0 a transition in Hawaiian basalt.
Bull. Volcanol. 60, 595±609.
Powell, M.J., 1979. Site percolation in randomly packed spheres.
Phys. Rev. B 20, 4194±4198.
Robson, G.R., 1967. Thickness of Etnean lavas. Nature 216, 251±
252.
Ryerson, F.J., Weed, H.C., Piwinskii, A.J., 1988. Rheology of subliquidus magmas I Picritic compositions. J. Geophys. Res. 93,
3421±3436.
Saar, M., Manga, M., Cashman, K.V., Fremouw, S., 2001. Numer-
ical models of the onset of yield strength in crystal-melt suspensions. Earth Planet. Sci. Lett. in press.
Sato, H., 1995. Textural difference between pahoehoe and aa lavas
of Izu-Oshima volcano, Japan Ð an experimental study on
population density of plagioclase. J. Volcanol. Geotherm. Res.
66, 101±113.
Shapiro, A.P., Probstein, R.F., 1992. Random packings of spheres
and ¯uidity limits of monodisperse and bidisperse systems.
Phys. Rev. Lett. 68, 1422±1425.
Shaqfeh, E.S.G., Fredrickson, G.H., 1990. The hydrodynamic stress
in a suspension of rods. Phys. Fluids A 2, 7±24.
Shaw, H.R., 1969. Rheology of basalt in the melting range. J. Petrol.
10, 510±535.
Shaw, H.R., Wright, T.L., Peck, D.L., Okamura, R., 1968. The
viscosity of basaltic magma: an analysis of ®eld measurements
in Makaopuhi lava lake. Hawaii. Am. J. Sci. 266, 255±264.
Walker, G.P.L., 1967. Thickness and viscosity of Etnean lava ¯ows.
Nature 213, 484±485.
Wildemuth, C.R., Williams, M.C., 1984. Viscosity of suspensions
modeled with a shear-dependent maximum packing fraction.
Rheol. Acta 23, 627±635.
Wildemuth, C.R., Williams, M.C., 1985. A new interpretation of
viscosity and yield stress in dense slurries: coal and other irregular particles. Rheol. Acta 24, 75±91.
Wolfe, E.W., Neal, C., Banks, N.G., Duggan, T.J., 1988. Geological
observations and chronology of eruptive events. U.S. Geol.
Surv. Prof. Pap. 1463, 99.
Yu, A.B., Standish, N., 1993. A study of the packing of
particles with a mixture size distribution. Powder Technol. 76,
113±124.
Zhou, J.Z.Q., Fang, T., Luo, G., Uhlerr, P.H.T., 1995. Yield stress
and maximum packing fraction of concentrated suspensions.
Rheol. Acta 34, 544±561.