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Solidification of colloidal suspensions

Published online by Cambridge University Press:  24 April 2006

S. S. L. PEPPIN ,
J. A. W. ELLIOTT  and
M. GRAE WORSTER
S. S. L. PEPPIN
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
J. A. W. ELLIOTT
Affiliation:
Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Canada, T6G 2G6
M. GRAE WORSTER
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
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Abstract

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.

JFM classification

Complex Fluids: Colloids Phase change: Morphological instability
Type
Papers
Information
Journal of Fluid Mechanics , Volume 554 , 10 May 2006 , pp. 147 - 166
Copyright
© 2006 Cambridge University Press

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Supplementary material: File

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Peppin et al. supplementary movie

Movie 1. The movie shows the freezing of a 5 wt% montmorillonite clay suspension. The base of the cell is cooled to -3 0C.  All of the clay particles are excluded from the growing ice and a concentrated particle layer forms above the solidification front. The entire time-lapse movie represents 30 minutes of real time. The gradations at the top of the figure are in millimetres.

Download Peppin et al. supplementary movie(Video)
Video 3.2 MB

Peppin et al. supplementary movie

Movie 1. The movie shows the freezing of a 5 wt% montmorillonite clay suspension. The base of the cell is cooled to -3 0C.  All of the clay particles are excluded from the growing ice and a concentrated particle layer forms above the solidification front. The entire time-lapse movie represents 30 minutes of real time. The gradations at the top of the figure are in millimetres.

Download Peppin et al. supplementary movie(Video)
Video 7.5 MB

Peppin et al. supplementary movie

Movie 2. This movie again shows the solidification of a 5 wt% montmorillonite suspension. In this case the base of the cell has been cooled to -20 0C, and the rate of freezing is faster. The interface has become unstable, forming ice dendrites. The entire time-lapse movie represents 10 minutes of real time. The gradations at the top of the figure are in millimetres.

Download Peppin et al. supplementary movie(Video)
Video 3.4 MB

Peppin et al. supplementary movie

Movie 3. Freezing of a 50 wt% montmorillonite suspension. In this case the ice dendrites (darker regions) show strong side-branching and tip-splitting, and a polygonal pattern of ice forms in the clay. As the freezing rate slows down near the end of the movie, the top layer of clay is pushed upward by the growing ice. The blue region at the top is unfrozen water. The entire time-lapse movie represents 3 hours of real time.

Download Peppin et al. supplementary movie(Video)
Video 7.5 MB

Peppin et al. supplementary movie

Movie 3. Freezing of a 50 wt% montmorillonite suspension. In this case the ice dendrites (darker regions) show strong side-branching and tip-splitting, and a polygonal pattern of ice forms in the clay. As the freezing rate slows down near the end of the movie, the top layer of clay is pushed upward by the growing ice. The blue region at the top is unfrozen water. The entire time-lapse movie represents 3 hours of real time.

Download Peppin et al. supplementary movie(Video)
Video 6.3 MB