Controls on microstructural features during solidification of colloidal suspensions

Abstract

We present a mathematical model of the directional freezing of colloidal suspensions. Key ingredients of the model are the disjoining forces between the colloidal particles and the solidified suspending fluid, flow of the suspending fluid towards the solidification front through an accumulating layer of particles, and flow through microscopic films of unfrozen liquid separating particles from the freezing front. Our model predicts three different modes of solidification leading to different microstructures: dendritic formations; laddered structures of ice spears and lenses; a frozen fringe, from which transverse ice lenses can form. It explains why different researchers have reported the existence of ice lensing with and without the pre-existence of frozen fringes. Our quantitative predictions 1 are encapsulated within a universal, dimensionless phase diagram showing which microstructure is to be expected under which operating conditions, and we show that these predictions are consistent with previous experimental studies as well as new experiments that we present here.

The effect of solidification direction with respect to gravity on ice-templated TiO2 microstructures

“…Consequently, the particle collision rate is increased further; i.e., particles are provided with an increased number of aggregation opportunities. A combination of fluid motion-induced particle redistribution and orthokinetic aggregation (and consequent enhanced sedimentation) may have effectively increased the particle fraction at the base of the suspension prior to the commencement of solidification and may be a contributing factor for why the model developed by You et al [41] accurately predicts the dendritic structures observed here for downward and horizontal solidification, but not the structures observed for upward solidification. If our hypotheses posed here are correct, the particle volume fraction at the interface would be higher than that predicted by the model (over the course of solidification); this would lead to increased values of D/(1+Φ) while F remained unchanged; i.e., in terms of Fig.…”

“…Ice lensing is studied in a variety of fields, e.g., geology (frost heaves [80]), food engineering [81], and cryobiology [82]. Although various hypotheses have been proposed to explain their development [41,[83][84][85][86][87][88], most of the ice-templating literature attributes ice lens formation to particle engulfment, rather than particle rejection, at the solidification interface [2,[37][38][39][40]. During directional solidification, particles are first rejected by the advancing solid/liquid interface before they are incorporated within interdendritic space.…”

“…Phase diagram after Ref [41]. showing predicted ice-templated morphologies, including: dendrites (blue), ice spears (red), and ice banding (grey) based on solidification and suspension parameters.The Darcy coefficient (D), film coefficient (F), and (Φ), are given by Eqs.…”

Directional freezing of binary colloidal suspensions: a model for size fractionation of graphene oxide

“…This force is the result of the temperature gradient and is of the van der Waals type 13,14,16 . For large particles and fast freezing speed, the dynamics is governed by the balance of the disjoining force and the hydrodynamic force.…”

Stability of ice lenses in saline soils

“…While it is known that frost heave (the uplift of the soil surface in winter) is caused by the formation of ice lenses, the physical mechanisms governing their initiation and growth have yet to be fully explained (O'Neill 1983;Rempel 2010;Peppin & Style 2013;Wettlaufer 2019). In soils with a high clay content, ice lenses can become non-planar, forming complex polygonal and reticulate vein structures (Taber 1929;Mackay 1974;Arenson et al 2006;Peppin, Elliott & Worster 2006;Deville 2013;El Hasadi & Kodadadi 2015;Wang et al 2016;Xu et al 2016;You, Wang & Worster 2018b). In addition, most soils and colloidal suspensions contain dissolved solutes in the pore fluid, which significantly influence the freezing process (Hallet 1978;Chamberlain 1983;Arenson et al 2006;Pekor 2014;Schollick et al 2016;Wang et al 2016;You et al 2018a;Ginot et al 2019).…”