Processing of immiscible metallic alloys by
rheomixing process
Z. Fan, S. Ji, and J. Zhang
Mixing immiscible alloys has been a long standing challenge to both materials scientists and processing engineers.
Despite great efforts made worldwide, including extensive space experiments, no casting techniques so far can
produce the desirable fine and uniform dispersed microstructure. Based on extensive experience in mixing immiscible
organic liquids offered by the polymer processing community, the authors have successfully developed a rheomixing
process for mixing immiscible alloys. The rheomixing process utilises first the intensive shear stress-strain field
offered by a twin screw extruder to create a fine homogeneous liquid dispersion within the miscibility gap and then
the viscous force offered by a semisolid slurry at a temperature below the monotectic temperature is used to
counterbalance the gravitational force and the Marangoni effect. A laboratory scale rheomixer has been designed
and constructed to realise this two step mixing strategy. The Ga – Pb and Zn – Pb systems were selected to
demonstrate the principles of rheomixing. The experimental results showed that the rheomixing process developed is
capable of creating a fine and uniform microstructure from immiscible alloys. This paper describes the rheomixing
process in detail and the preliminary experimental results on rheomixing in the Ga – Pb and Zn – Pb systems are
discussed.
MST/4664
The authors are in the Wolfson Centre for Materials Processing, Brunel University, Uxbridge, Middx UB8 3PH, UK
([email protected]). Manuscript received 22 March 2000; accepted 6 November 2000.
# 2001 IoM Communications Ltd.
Introduction
A large number of liquid alloys, such as Al – Bi, Al – In, Al –
Pb, Ga – Pb and Zn – Pb, exhibit limited miscibility, i.e., the
binary phase diagrams show a miscibility gap which
represents the equilibrium between two liquids of different
compositions. As shown schematically in Fig. 1, the binary
phase diagrams of such systems typically contain a
monotectic reaction at TM, an eutectic reaction at TE and
a miscibility gap (MCE) with a maximum temperature TC.
Those systems, often referred as the immiscibles, are
characterised by their unique thermodynamic features,
such as positive deviation from the Raoult’s law and
large positive enthalpy of mixing.1 The thermophysical
properties of the relevant immiscible systems2 are summarised in Table 1.
The immiscible systems have great potential applications
in advanced bearing systems, electrical contacts and superconducting devices.3 Unfortunately, it has not yet been
possible to produce those alloys by casting techniques.1,4
During the early stage of the cooling process of a
homogeneous liquid, the frequently encountered large
density difference between two liquids leads to a rapid
spatial separation by gravity force, resulting in a two-layer
structure, the heavier one at the bottom and the lighter one
at the top of the crucible. The sedimentation velocity
increases as the square of the droplet radius, therefore, large
droplets settle much more rapidly than small ones.5 When
droplets of different sizes and thus different sedimentation
velocities collide, they coagulate to form even larger
droplets which settle even more rapidly. Owing to this
phenomenon, no casting process under terrestrial conditions has yet been able to produce the desired dispersion
microstructure, even when extremely high solidification
rates were achieved.1 These systems have gained renewed
interest as a result of materials research in space in the
1980s.3 Many tests were carried out during space experiments to achieve an appropriate phase distribution under
microgravity conditions. The results, however, were rather
disappointing, because even under microgravity conditions
ISSN 0267 – 0836
a coarse phase separation occurred.4 After intensive
theoretical and experimental investigation, the origin of
the coarse demixing in outer space was found to be
Marangoni motion of the droplets, which is on Earth
superimposed on gravity driven sedimentation (Stokes’
motion) and often hidden behind its action.6
The Lorentz force, induced by a magnetic field perpendicular to the electrical current, was first used to counterbalance the gravity force.7,8 The method uses the effect that
magnetic and electrical fields excited in the melt have
selective ability to affect the decomposed liquid alloy
depending on their conductivity. This effect allows the
creation of a situation in which the Lorentz forces
compensate for the difference in gravity. However, the
alloys cast by this method were extremely inhomogeneous.9
In addition to Lorentz force, high energy ultrasonic
vibration has also been applied to avoid coagulation and
to disperse the minor phase.10 It was found that the
maximum quantity of Pb which can be homogeneously
dispersed in Al using this method was less than 10 wt-%.
More recently, a new strip casting process and a planar flow
casting technique have been developed in Germany.11,12 In
both processes, an artificial temperature gradient was
created to introduce a controlled Marangoni motion,
which was intended to counterbalance partially the
gravity-driven Stokes’ motion. Unfortunately, the experimental results were unsatisfactory, Pb was found to
concentrate in the middle of the strip.
Based on the extensive experience in processing of
immiscible organic liquids by twin screw extrusion offered
by the polymer processing community,13,14 a novel
rheomixing process has been developed recently in our
laboratory.15 This rheomixing process utilises first an
intensive shear stress – strain field provided by a twin
screw extruder to create a fine and homogeneous liquid
dispersion within the miscibility gap and then the viscous
force offered by a semisolid slurry at a temperature below
TM to counterbalance the gravity force and the Marangoni
effect. In this paper the rheomixing process is discussed and
the authors’ experimental results on the rheomixing of the
immiscible Ga – Pb and Zn – Pb alloys are described.
Materials Science and Technology
July 2001 Vol. 17
837
838 Fan et al. Processing of immiscible metallic alloys by rheomixing process
1 Schematic phase diagram of an immiscible A – B
binary system
The mixing strategy
When an initially spherical Newtonian liquid droplet of
radius r and a viscosity g9 is suspended in another
Newtonian liquid of a viscosity g and subjected to shear
stresses, it deforms and then breaks up into smaller droplets.
Taylor16 extended the work of Einstein17 on dilute
suspensions of solid spheres in a Newtonian liquid, to a
dispersion of a single Newtonian liquid droplet in another
Newtonian liquid, subjected to a well defined deformation
field. He concluded that the degree of deformation of the
droplet at low stresses in a uniform shearing flow can be
expressed by two dimensionless parameters, the capillary
number k and the viscosity ratio l
2g_cr
s
g’
:
l~
g
k~
:
:
:
:
:
:
:
:
:
:
:
:
:
:
ð1Þ
:
:
:
:
:
:
:
:
:
:
:
:
:
:
ð2Þ
.
where s is the interfacial tension between two liquids and c
is the shear rate. It is clear from the above equations that the
droplet deformation is a result of balancing the interfacial
tension force (tending to keep the droplet spherical) with the
viscous force (tending to elongate the droplet). When the
interfacial tension force can no longer balance the viscous
force, the deformation becomes unstable and the droplet
will burst. The parameter describing the critical conditions
for droplet breakup is the critical capillary number, kcrit.
Droplets can only break up when kwkcrit. In addition, it has
been confirmed by experiment that breakup of liquid
droplet is easiest when the viscosity ratio falls within
0.3vlv1.5 (Ref. 14).
During mixing the dispersed phase progressively breaks
up until a minimum drop diameter is reached.18 This
minimum drop size was found to be related not only to the
breakup process but also to the shear-induced coalescence
by droplet collision in two-phase liquids with a volume
fraction less than the percolation threshold (usually
0.158).19 The coalescence can be accelerated by the same
factors that favour the drop breakup, i.e. high shear rate
and reduced viscosity ratio. Therefore, the minimum
droplet size under given shear mixing conditions is a
dynamic balance between two opposite processes, droplet
breakup and coalescence.
It is well known that the interfacial tension between
immiscible metallic liquids is very small, being a few tens of
mN/m (Ref. 20), and that the viscosity ratio is close to 1
(Ref. 21). According to the above analysis, a fine and
uniform liquid suspension is expected under high shear
mixing conditions. However, it should be pointed out that
such a fine liquid suspension will become unstable and will
demix rapidly under the effect of Stokes’ and Marangoni
motions once the shear deformation field is removed. In
order to achieve the desired fine and uniform dispersion in
the solid state, the fine liquid suspension has to be stabilised
throughout the subsequent solidification process.
Although the rheological behaviour of semisolid metals
needs further investigation, it is clear that the viscosity of a
semisolid slurry increases exponentially with the volume
fraction of the solid phase and decreases dramatically with
the increase of shear rate and shearing time.22,23 This means
that the viscosity of a semisolid slurry can be controlled
effectively by choosing the proper processing conditions,
such as temperature and shear rate. This offers us an useful
means to stabilise the fine liquid dispersion obtained by high
shear mixing. For a particular alloy composition at a given
temperature below TM, a fixed volume fraction of the solid
phase forms in the liquid matrix, which will increase the
viscosity of the matrix to such a level that the gravity force
exerted on the liquid droplet will be counterbalanced by the
viscous force from the liquid matrix.
Based on the above analysis, the following two step
strategy is proposed for mixing the immiscibles, as
illustrated schematically in Fig. 2.
Creation of a fine liquid dispersion by high shear
mixing An artificial shear stress – strain field is applied
continuously to the immiscible system during the cooling
of a homogeneous liquid from a temperature above TC.
This shear mixing action is so extensive that it can
override the demixing actions resulted from both Stokes’
and Marangoni motions. Consequently, a fine and
homogeneous liquid dispersion is created at a
temperature above TM.
Stabilisation of the fine liquid dispersion Although the
fine liquid dispersion created by high shear mixing
action will slow down substantially the demixing process
by both Stokes’ and Marangoni motions, it is still
unstable and will demix once the deformation field is
removed. However, the fine liquid dispersion can be
further stabilised by shearing it at a temperature below
TM to create a semisolid slurry, the viscosity of which is
high enough that both Stokes’ and Marangoni motions
Table 1 Thermophysical properties* of some immiscible systems2
Alloy (A – B)
rA, g cm23
rB, g cm23
aA (XA~0.5)
aB (XB~0.5)
DHmix, cal/g atom{ (XB~0.5)
TC,‡C
TM,‡C
Al – Pb
Al – In
Al – Bi
Ga – Pb
Zn – Pb
2.7
2.7
2.7
5.93
7.14
11.34
7.30
9.80
11.34
11.34
0.942
0.872
0.964
…
0.978 (XZn~0.22)
0.988
0.802
0.756
…
0.845 (XPb~0.78)
2236
1365
1708
…
3590 (XZn~0.22)
1566
875
1037
610
798
659
639
657
312.5
417.7
*a activity.
{1 cal/g atom~4.184 J mol21.
Materials Science and Technology
July 2001 Vol. 17
Fan et al. Processing of immiscible metallic alloys by rheomixing process 839
a initial stabilisation: creation of a fine L2 dispersion in L1; b further stabilisation: formation of primary solid phase in L1 through a
monotectic reaction; c monotectic solidification of L1 and eutectic solidification of L2
2 Schematic illustration of two step strategy to achieve fine and homogeneous dispersion from immiscible alloys
1: drive motor; 2: gear box; 3: water cooling to drive shaft; 4:
end cap; 5: feeder; 6: heating element; 7: cooling channel; 8:
barrel; 9: die; 10: die cavity; 11: short assembly; 12: outlet
valve; 13, 14: thermocouples; ; 15: base; 16: mounting unit
3 A schematic illustration of constructed laboratory
scale twin screw rheomixer
can no longer produce coarse separation. Further
stabilisation of the fine liquid dispersion can also be
achieved by introduction of fine and insoluble solid
particles at a temperature above TM.
Rheomixing process
Twin screw extrusion compounding, usually for polymer
processing, offers both high shear dispersive mixing action
and positive displacement pumping action. It is an ideal
process to perform the above two separate functions in a
single equipment.
A demonstrator rheomixing machine with closely intermeshing, self-wiping and co-rotating twin screws, has been
designed and constructed based on the principles described
in the previous section, as illustrated schematically in Fig. 3.
It consists of a liquid metal feeder, a high shear twin screw
extruder, a shot assembly, and a central control system. The
16 mm screws have a specially designed screw profile to
achieve high shear rate and to enhance the positive
displacement pumping action. The maximum rotation
speed is 1000 rev min21, which corresponds to a shear
rate of 4082 s21 in the gap between the tip of the screw flight
and the barrel. The extruder has a series of heating and
cooling elements dispersed along the length of the extruder,
forming two heating/cooling zones. The maximum barrel
temperature is currently 500‡C. The temperature control of
each individual zone is achieved by balancing the heating
and cooling power input by a central control unit, giving
rise to a control accuracy of ¡1 K.
The fluid flow pattern in a closely intermeshing, selfwiping, and co-rotating twin screw extruder is quite
a figure of eight flow pattern in screw channels24; b stretching,
folding, and reorienting processes during takeover of materials
25
from one screw to the other
4 Schematic illustrations of flow pattern in closely
intermeshing, self-wiping and co-rotating twin screw
extruder
characteristic. Extensive study by the polymer processing
community has confirmed that the fluid moves in figure of
eight motions around the periphery of the screws,24 and the
figure of eight moves from one pitch to the next one,
forming a figure of eight shaped helix and pushing the fluid
along the axial direction of the screws, as illustrated
schematically in Fig. 4a. This is referred as a positive
displacement pumping action. In this continuous flow field,
the fluid undergoes cyclic stretching, folding, and reorienting processes. This is shown schematically in Fig. 4b with
respect to the streamlines during the take over of the
materials from one screw to the other one. In consideration
of the much lower viscosity of liquid metals, or even
semisolid metals, compared with that of the polymer melt,
the intensity of turbulence inside the barrel should be very
high. In addition, Fig. 4b also indicates that the fluid is
subjected to a cyclic variation of shear rate due to the
continuous change of the gap between screw and the barrel.
The lowest shear rate is found at the gap between the root of
a screw flight and the barrel. The highest possible shear rate
is offered by the intermeshing regions between two screws if
there is a leakage path, although the exact shear rate can not
be calculated because of the complexity of the screw
geometry. The intermediate shear rate is found in the gap d
between the tip of a screw flight and the barrel surface,
which is given by the following equation26
D
{2
: : : : : : : : : : : ð3Þ
c_ ~Np
d
where D is the screw diameter and N is the screw rotation
speed. Therefore, the fluid flow in a closely intermeshing,
self-wiping, and co-rotating twin screw extruder is charMaterials Science and Technology
July 2001 Vol. 17
840 Fan et al. Processing of immiscible metallic alloys by rheomixing process
acterised by high shear rate and high intensity of turbulence.
It is these flow characteristics which make the intermeshing
twin screw extruder an ideal mixing device for realising the
two step strategy proposed in the section on ‘The mixing
strategy’ above for rheomixing of the immiscible alloys.
The rheomixing process starts from feeding liquid metal
at a temperature above the miscibility gap from a heated
crucible into the extruder barrel through the liquid metal
feeder. The liquid metal is rapidly cooled into the miscibility
gap in the first part of the twin screw extruder while being
mechanically sheared by the co-rotating twin screws,
converting the liquid alloy into a fine liquid suspension,
wherein the minor liquid phase is finely dispersed in a liquid
matrix. Further cooling and shearing the liquid suspension
to a temperature below TM will allow the formation of a
semisolid slurry with a predetermined volume fraction of
the solid phase dictated by accurate temperature control.
The semisolid slurry is then injected at a high velocity into a
mould cavity. The fully solidified casting is finally released
from the mould. All these procedures are performed in a
continuous cycle and controlled by a central control system.
The selection of the semisolid formation temperature is
crucial. The viscosity of the semisolid slurry at the selected
temperature should be high enough to counterbalance the
gravitational force on the liquid droplet by the viscous
force, and low enough to keep suitable fluidity for mould
filling.
It is also possible to shear the immiscible system at a
temperature just a few degrees above TM to create a fine
liquid suspension, which is then directly injected into the
mould cavity for solidification. In addition, fine solid
particles (e.g. alumina powder) may be fed into the
rheomixer at the same time with liquid metal, forming a
semisolid slurry at a temperature above TM. The slurry is
then injected into the mould cavity for solidification.
5 Secondary electron SEM image showing microstructure of rheomixed Ga – 10 wt-%Pb alloy
Experimental and results
Two immiscible systems, Ga – Pb and Zn – Pb, were chosen
as model immiscible systems to demonstrate the rheomixing
process because of their relatively low monotectic temperature and large density difference. The relevant thermophysical properties of the Ga – Pb and Zn – Pb systems are
listed in Table 1.
High purity Ga (99.99%) and industrially pure Pb and Zn
(99.8%) were used as the starting materials for preparation
of the immiscible alloys. A charge of 70 cm3 of alloy with a
predetermined composition for each run was melted in a
resistance furnace at a temperature well above its immiscible
temperature. In order to obtain chemical homogeneity, the
duration of melting was for 30 min with occasional
mechanical stirring. The rheomixer was then set at a
predetermined temperature (usually just above the monotectic temperature) and rotation speed (800 rev min21 in
this case) before the homogeneous alloy melt was fed into
the rheomixing machine. After mixing for 1 minute, the
barrel temperature was then set just below the monotectic
temperature to create a semisolid slurry. The time at this
temperature was 20 s. The mixed alloy slurry was finally
tapped into ice-water by opening the valve located at the
end of the extruder. For the present work, the shot sleeve
and die was not used.
For microstructural examination, solidified alloy samples
were cut and cold mounted in a transparent epoxy resin.
The mounted samples were carefully polished using a
standard metallographic technique. The morphology and
phase distribution in the specimens were examined optically
and by Jeol 840 scanning electron microscope.
As a result of water quenching, the Ga – Pb alloy
obtained had an irregular shape. Specimens for microMaterials Science and Technology
July 2001 Vol. 17
6 Microstructure of rheomixed Zn – 40 wt-%Pb
bright particles are Pb and dark matrix is Zn
alloy:
structural examination were cut from the bottom of the
alloy blocks. Figure 5 shows a secondary electron image of
the Ga – 10 wt-%Pb alloy produced by the rheomixing
process. Fine and spherical Pb particles of 5 – 10 mm in
diameter (bright phase) are distributed uniformly in the Ga
matrix (dark phase).
Based on the carefully selected rheomixing conditions, a
high volume fraction of solid Zn phase was formed at a
temperature below its monotectic temperature. This high
volume fraction of solid can ensure the high viscosity of the
semisolid slurry. Consequently, the rheomixed Zn – Pb alloy
can be obtained in rod form, being 5 mm in diameter and
20 – 70 mm in length. A secondary electron image of the
rheomixed Zn – 40 wt-%Pb alloy is shown in Fig. 6. Using
EDX analysis, the bright phase was identified as Pb and the
dark phase was Zn phase. Figure 6 shows that Pb particles
with an average diameter of 40 mm are uniformly dispersed
in a Zn matrix.
Discussion
STABILITY OF A SINGLE DROPLET IN A
VISCOUS LIQUID
The movement of a single liquid droplet of radius r in
another liquid driven by both gravity and interfacial tension
is well understood. The velocity of Stokes’ motion US can be
Fan et al. Processing of immiscible metallic alloys by rheomixing process 841
expressed as5
US ~
2gDr(gzg’) 2
r
3g(2gz3g’)
:
:
:
:
:
:
:
:
:
:
ð4Þ
and the velocity of Marangoni motion UM is given by27
dT ds 2 k
dx dT
UM ~
r
: : : : : : : : ð5Þ
ð2kzk’Þð2gz3g’Þ
where k and k9 denote the conductivity of the liquid matrix
and the liquid droplet, respectively.
During the rheomixing process, the semisolid slurry can
be considered as a suspension, in which solid particles are
dispersed in a liquid matrix. For the convenience of
theoretical treatment, the three phase slurry will be treated
as liquid droplet dispersed in a semisolid matrix. The
viscosity of the semisolid matrix can be effectively
controlled by varying the volume fraction of the solid
phase, which in turn is dictated by the mixing temperature.
If the viscosity of the matrix is high enough to counterbalance both Stokes’ motion and Marangoni motion, the
droplet will be stabilised in the slurry. As discussed in the
previous section, the temperature gradient of the alloy
inside the rheomixer is negligibly small due to the high
intensity of turbulent flow created by the twin screw
extruder, i.e., dT/dx#0. Therefore, Marangoni effect can be
omitted during the rheomixing process. Below the monotectic temperature TM, solid phase is formed through the
monotectic reaction. In the case of the Ga – Pb system, Pb
will be the solid phase. For a solid particle moving in a
liquid, the velocity of Stokes motion can be calculated by
the following equation28
US ~
2gr2 Dr
9g
:
:
:
:
:
:
:
:
:
:
:
:
: ð6Þ
According to Stefanescu et al.,29 the viscosity of a
suspension can be expressed by the following equation
g~g0 ½1z2:5VP (T)z10:05VP2 (T)
:
:
:
:
:
:
ð7Þ
where VP(T) is the volume fraction of solid particles at
temperature T, g0 is the viscosity of the liquid matrix, which
is a function of temperature and can be expressed in an
Arrhenius-type equation
g0 ~c exp (E=RT)
:
:
:
:
:
:
:
:
:
:
:
ð8Þ
where c and E are constants and R is the ideal gas constant.
Using the lever rule and assuming the average slope of line
FE in Fig. 1 is m, the volume fraction of the solid phase can
be calculated as
c0 rl
Vp (T)~
: : : : : : ð9Þ
rp Sz DT
m zc0 (rl {rp )
where c0 is the alloy composition, DT is the temperature
difference between TM and T, and S is the alloy composition
of the matrix at TM in Fig. 1. Using the above equations, it
is possible to estimate the effect of particle size and
temperature on the Stokes’ motion. Figure 7 shows the
calculated velocity of the Stokes’ motion of the Pb particles
in the Ga – 10 wt-%Pb system as a function of r and T.
For the calculation, the parameters S, m, c, and E in the
above equations were taken as 94.8 wt-%, 3834.6 K,
4.35961025 Pa s and 0.955 kcal mol21 (1 kcal mol21~
4.184 kJ mol21) respectively. In Fig. 7, the velocity of
Stokes’ motion increases with the increase in temperature
on both sides of the monotectic temperature. The velocity
changes abruptly at the monotectic temperature, as a result
of the formation of the solid phase through monotectic
reaction. Compared with the effect of temperature, the
effect of particle size is significant on the velocity of Stokes’
motion. Under a gravity field, larger particles travel at a
much faster velocity than smaller particles do. This explains
7 Calculated velocity US of Stokes’ motion of Pb
particles in Ga – 10 wt-%Pb system as function of
temperature and particle size
why fine liquid droplets (or solid particles) have to be
achieved before casting to ensure a homogeneous microstructure.
MICROSTRUCTURAL EVOLUTION
The mechanism of microstructural evolution for both alloys
can be summarised as follows. When the liquid alloy is fed
into the rheomixer, the melt cools quickly to the barrel
temperature set by the control system, which is usually just
above TM. At the same time, the melt separates rapidly into
two immiscible liquids through nucleation and growth of
liquid droplets. Under the extensive shear mixing action
created by the twin screws, the liquid droplets will keep a
fine particle size, as a result of the dynamic equilibrium
between two opposite processes, coagulation and breakup
of liquid droplets. The final size of liquid droplets will be
dictated by the intensity of shear mixing action and the
thermal physical properties of the system, such as viscosity,
interfacial tension, etc. When the melt reaches a temperature below the monotectic temperature, a solid phase will
form from one of the liquid phases through the monotectic
reaction. The solid phase will be Pb in the Ga – Pb system,
and Zn in the Zn – Pb system. At this temperature, the alloy
is in semisolid state. The viscosity of the semisolid slurry is
determined by the solid volume fraction, which in turn is a
function of temperature. By careful selection of the
processing temperature, the viscous force should be high
enough to counterbalance the gravity force. Consequently,
the alloy system is stabilised for the final solidification of the
remaining liquid, normally by an eutectic reaction at a lower
temperature.
So far a new technology, rheomixing, has been presented
for processing immiscible metallic alloys together with some
preliminary experimental results on rheomixing of the Ga –
Pb and Zn – Pb systems. Further studies are being carried
out at the authors’ laboratory along two parallel directions.
One aspect is the further development of rheomixing
technology for processing Al based immiscible systems for
bearing applications. The other aspect is fundamental
investigation into the thermodynamics and kinetics of
phase separation and the solidification behaviour of
immiscible alloys under a high shear rate and a high
intensity of turbulence.
Summary
In order to create a homogeneous microstructure from
immiscible alloy systems, a two step strategy was proposed.
Materials Science and Technology
July 2001 Vol. 17
842 Fan et al. Processing of immiscible metallic alloys by rheomixing process
In the first step, the initial stabilisation is achieved by
applying an intensive shear stress – strain field to create a
fine homogeneous liquid dispersion at a temperature above
TM. In the second step, a fine liquid dispersion is further
stabilised by shearing it at a temperature below TM to create
a semisolid slurry, the viscosity of which is high enough that
both Stokes’ and Marangoni motions can no longer
produce coarse separation. Based on this two step strategy,
a rheomixing process has been successfully developed, and a
laboratory scale rheomixer was designed and constructed to
demonstrate the rheomixing principles. A high shear mixing
action offered by a closely intermeshing, self-wiping, and
co-rotating twin screw extruder was used in the rheomixing
process. The flow pattern in the twin screw extruder was
characterised by a high shear rate and a high intensity of
turbulence. The experimental results on rheomixing of the
immiscible Ga – Pb and Zn – Pb systems have demonstrated
that the rheomixing process is capable of creating fine and
uniform dispersed microstructures from immiscible systems.
Acknowledgements
Financial support from Ford Motor Co. and PRISM
(Lichfield, UK) is gratefully acknowledged. Professor M. J.
Bevis, Wolfson Centre for Materials Processing, Brunel
University is also thanked for his helpful discussions and
encouragement.
References
1. r. n. singh and f. sommer: Rep. Prog. Phys., 1997, 60, 57 – 150.
2. r. hultgren, r. l. orr, p. d. anderson, and k. k. kelley:
‘Selected values of the thermodynamic properties of binary
alloys’; 1973, Metals Park, OH, ASM.
3. b. predel, l. ratke, and h. frederikson: in ‘Fluid science and
materials science in space’, (ed. H. U. Walter), 517; 1987,
Berlin, Springer-Verlag.
4. l. ratke and s. diefenbach: Mater. Sci. Eng., 1995, R15, 263 –
347.
Materials Science and Technology
July 2001 Vol. 17
5. a. lavich: ‘Physicochemical hydrodynamics’; 1962, Engelwood
Cliffs, NJ, Prentice-Hall.
6. j. legros, a. sanfeld, and m. velarde: in ‘Fluid science and
materials science in space’, (ed. H. U. Walter), 83; 1987, Berlin,
Springer-Verlag.
7. o. v. abramov, j. m. gelfat, s. i. senin, m. z. sorkin, and j. ju.
kuckina: Phys. Chem. Mater. Treat. (USSR), 1981, 3, 47.
8. d. uffelmann, l. ratke, and b. feuerbach: in ‘Immiscible
liquid metals and organics’, (ed. L. Ratke), 239; 1993,
Oberursel, DGM Informationsgesellschaft.
9. f. sommer: Z. Metallkd, 1996, 87, 11.
10. v. o. abramov, o. v. abramov, f. sommer, and d. orlov: Mater.
Lett., 1995, 23, 17.
11. b. prinz and a. romero: in ‘Immiscible liquid metals
and organics’, (ed. L. Ratke), 244; 1993, Oberursel, DGM
Informationsgesellschaft.
12. t. berrenberg and p. r. sahm: Z. Metallkd, 1996, 87, 187.
13. t. p. vainio, a. harlin, and j. v. seppala: Polym. Eng. Sci.,
1995, 35, 225.
14. l. a. utracki and z. h. shi: Polym. Eng. Sci., 1992, 32, 1824.
15. z. fan, m. j. bevis, and s. ji: PCT Patent GB00/03552, UK
Patent Office, London, 24 September 1999.
16. g. i. taylor: Proc. R. Soc., (London), 1932, A138, 41.
17. a. einstein: Ann. Phys. (Leipzig), 1906, 19, 289.
18. a. p. plochocki, s. s. dagli, and r. d. andrews: Polym. Eng.
Sci., 1990, 30, 741.
19. c. m. roland and g. g. a. bohm: J. Polym. Sci. B, Polym. Phys.,
1984, 22, 79.
20. m. merkwitz, j. wise, k. thriemer, and w. hoyer: Z. Metallkd.,
1998, 89, 247.
21. t. iidi and r. i. l. guthrie: ‘The physical properties of liquid
metals’, Clarendon Press, Oxford, 1988.
22. m. c. flemings: Metall. Trans. A, 1991, 22A, 957 – 981.
23. d. h. kirkwood: Inter. Mater. Rev., 1994, 39, 173 – 189.
24. r. erdmenger: Chem. Ing. Tech., 1964, 39, 175.
25. h. e. h. meijer and j. m. h. janssen: in ‘Mixing and
compounding of polymers’, (ed. I. Manas-Zloczower and Z.
Tadmor), 85; 1994, Cincinnati, OH, Hanser Publishers.
26. c. rauwendaal: ‘Polymer Extrusion’, 3rd edn; 1985. Cincinnati, OH, Hanser Publishers.
27. n. young, j. goldstein, and m. block: J. Fluid Mech., 1959, 6,
350.
28. d. j. shaw: in ‘Introduction to colloid and surface chemistry’,
4th edn, 22; 1992, Oxford, Butterworth-Heinemann.
29. d. stefanescu, a. moitra, a. s. kacar, and b. k. dhindaw:
Metall. Trans. A, 1990, 21A, 231.