Colloidal mushy layers

M. Grae Worster,S.S.L. Peppin,J.S. Wettlaufer

doi:10.1017/jfm.2020.863

Abstract

Highlights

The freezing of colloidal and nano suspensions is of increasing importance in composite materials science, Earth and planetary science, cryobiology, microfluidics, food engineering and chromatography (Rempel 2010; Qian & Zhang 2011; Deville 2013; Henderson et al 2013; Pawelec et al 2014)
Comparing the result for R = 5 nm with that for R = 25 nm, we see that the region of unfrozen colloid χ increases with R for sufficiently large R, which implies that the regions of segregated ice within the mushy layer occupy a smaller volume fraction
We have extended the mathematical modelling of freezing colloidal suspensions from the cases of planar interfaces (Peppin et al 2006; You et al 2018) to situations in which mushy layers form comprising segregated ice and unfrozen colloid

Summary

Introduction

The freezing of colloidal and nano suspensions is of increasing importance in composite materials science, Earth and planetary science, cryobiology, microfluidics, food engineering and chromatography (Rempel 2010; Qian & Zhang 2011; Deville 2013; Henderson et al 2013; Pawelec et al 2014). Intricate microstructures can form during the freezing of colloidal suspensions (figure 1b–d) but with a greater variety of patterns, including dendrites aligned with the thermal gradient (figure 1b), lenses perpendicular to the thermal gradient (figure 1c) and polygonal structures (figure 1d) Some of these structures, the dendritic ones, arise from morphological instability of the interface between frozen solvent (ice) and unfrozen solution or colloidal suspension (Peppin, Worster & Wettlaufer 2007; El Hasadi & Kodadadi 2015) but others form by regelative processes within partially frozen colloid (O’Neill & Miller 1985; Rempel, Wettlaufer & Worster 2004; Anderson & Worster 2012). We consider only hard-sphere interactions between the colloidal particles, though cohesion between particles can be an important influence on microstructural evolution

Phase diagram

Relative motion in colloidal suspensions

Fickian formulation

Darcy formulation

Migration of clusters

Particle flux in a colloidal mushy layer

Formation of a colloidal mushy layer at a cooled boundary

A simple model

Conclusions