Solidification of colloidal suspensions

We present a mathematical model of the unidirectional solidification of a suspension of hard-sphere colloids. Similarity solutions are obtained for the volume fraction and temperature profiles ahead of a planar solidification front. The highly nonlinear functional dependence of the diffusion coefficient on the volume fraction gives rise to a range of behaviours. For small particles, Brownian diffusion dominates and the system behaviour is reminiscent of binary-alloy solidification. Constitutional supercooling occurs at the interface under certain conditions, leading potentially to an instability in the shape of the interface. For larger particles, Brownian diffusion is weak and the particles form a porous layer above the interface. In this case constitutional supercooling reaches a maximum near the surface of the layer, and the porous medium itself is potentially unstable. In stable systems there exists the possibility of secondary nucleation of ice.

[1]  Andrew I. Cooper,et al.  Aligned two- and three-dimensional structures by directional freezing of polymers and nanoparticles , 2005, Nature materials.

[2]  M. Worster,et al.  Pressure and relative motion in colloidal suspensions , 2005 .

[3]  M. Grae Worster,et al.  Premelting dynamics in a continuum model of frost heave , 2004, Journal of Fluid Mechanics.

[4]  P. Monteiro,et al.  Observations of ice lens formation and frost heave in young Portland cement paste , 2003 .

[5]  H. Modarress,et al.  Equation of state for hard-spheres , 2003 .

[6]  K. Muldrew,et al.  Measurement of freezing point depression of water in glass capillaries and the associated ice front shape. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Kunio Watanabe.  Relationship between growth rate and supercooling in the formation of ice lenses in a glass powder , 2002 .

[8]  Daan Frenkel,et al.  Suppression of crystal nucleation in polydisperse colloids due to increase of the surface free energy , 2001, Nature.

[9]  Stephen H. Davis,et al.  Theory of Solidification , 2001 .

[10]  M. Mizoguchi,et al.  Water and Solute Distributions near an Ice Lens in a Glass-Powder Medium Saturated with Sodium Chloride Solution under Unidirectional Freezing , 2001 .

[11]  M. Mizoguchi,et al.  Ice configuration near a growing ice lens in a freezing porous medium consisting of micro glass particles , 2000 .

[12]  R. Zernicke,et al.  Cryobiology of articular cartilage: ice morphology and recovery of chondrocytes. , 2000, Cryobiology.

[13]  M. Worster,et al.  The interaction between a particle and an advancing solidification front , 1999 .

[14]  R. A. Flores,et al.  Dynamics of solidification in 2% corn starch-water mixtures : Effect of variations in freezing rate on product homogeneity , 1996 .

[15]  Y. Roos.  Phase Transitions in Foods , 1995 .

[16]  V. Starov,et al.  Concentrated dispersions of charged colloidal particles: Sedimentation, ultrafiltration and diffusion , 1993, Colloids and Surfaces A: Physicochemical and Engineering Aspects.

[17]  John F. Brady,et al.  Brownian motion, hydrodynamics, and the osmotic pressure , 1993 .

[18]  A. M. Meirmanov,et al.  The Stefan Problem , 1992 .

[19]  W. Kurz,et al.  Fundamentals of Solidification , 1990 .

[20]  P. Pusey,et al.  Phase behavior of dispersions of hard spherical particles , 1990 .

[21]  H. Huppert.  The fluid mechanics of solidification , 1990, Journal of Fluid Mechanics.

[22]  S. Kinosita,et al.  Segregated ice growth on a microporous filter , 1989 .

[23]  W. Russel,et al.  Disorder-to-Order Transition in Settling Suspensions of Colloidal Silica: X-ray Measurements , 1989, Science.

[24]  R. Jackson,et al.  The resolution of shocks and the effects of compressible sediments in transient settling , 1988, Journal of Fluid Mechanics.

[25]  J. M. Rallison.  Brownian diffusion in concentrated suspensions of interacting particles , 1988, Journal of Fluid Mechanics.

[26]  M. Worster.  Solidification of an alloy from a cooled boundary , 1986, Journal of Fluid Mechanics.

[27]  H. Huppert,et al.  Dynamic solidification of a binary melt , 1985, Nature.

[28]  Kevin O'Neill,et al.  Exploration of a Rigid Ice Model of Frost Heave , 1985 .

[29]  Sam R. Coriell,et al.  Oscillatory morphological instabilities due to non-equilibrium segregation , 1983 .

[30]  L. V. Woodcock.  GLASS TRANSITION IN THE HARD‐SPHERE MODEL AND KAUZMANN'S PARADOX * , 1981 .

[31]  G. Batchelor,et al.  Brownian diffusion of particles with hydrodynamic interaction , 1976, Journal of Fluid Mechanics.

[32]  D. Simatos,et al.  The physical state of water at low temperatures in plasma with different water contents as studied by differential thermal analysis and differential scanning calorimetry. , 1975, Cryobiology.

[33]  K. E. Starling,et al.  Equation of State for Nonattracting Rigid Spheres , 1969 .

[34]  J. C. Brice,et al.  The Growth of Crystals from the Melt , 1967 .

[35]  D. Uhlmann,et al.  Interaction Between Particles and a Solid‐Liquid Interface , 1964 .

[36]  W. G. Hoover,et al.  Fifth and Sixth Virial Coefficients for Hard Spheres and Hard Disks , 1964 .

[37]  W. Mullins.  Stability of a Planar Interface During Solidification of a Dilute Binary Alloy , 1964 .

[38]  B. Chalmers,et al.  Freezing of Liquids in Porous Media with Special Reference to Frost Heave in Soils , 1958 .

[39]  W. Kuhn,et al.  Freezing point depression of gels produced by high polymer network , 1955 .

[40]  E. M.,et al.  Statistical Mechanics , 2021, Manual for Theoretical Chemistry.

[41]  S. Taber,et al.  Frost Heaving , 1929, The Journal of Geology.

[42]  J. Gibbs.  On the equilibrium of heterogeneous substances , 1878, American Journal of Science and Arts.

[43]  M. Mizoguchi,et al.  MICROSCOPIC OBSERVATION OF ICE LENSING AND FROST HEAVE IN GLASS BEADS , 1998 .

[44]  Lawrence F. Shampine,et al.  The MATLAB ODE Suite , 1997, SIAM J. Sci. Comput..

[45]  Salvatore Torquato,et al.  Computer simulations of dense hard‐sphere systems , 1996 .

[46]  W. Russel,et al.  An asymptotic description of transient settling and ultrafiltration of colloidal dispersions , 1989 .

[47]  L. Rosenhead.  Conduction of Heat in Solids , 1947, Nature.