A study of the trapping and rejection of insoluble particles during the freezing of water

Morphological instability of a non-equilibrium ice–colloid interface

“…This suggests that k s → 1 for V V c . Experimental data indicate that for submicron hydrophilic particles, V c 10 μm s −1 (Cisse & Bolling 1971). In the present work, we consider freezing velocities much less than V c , so that the particles are completely rejected by the ice and k s = 0.…”

The interaction between a particle and an advancing solidification front

“…A best-"t line is shown running through each of the data sets. The di!erent symbols correspond to the following particle materials in water: (a) copper with G+10 K m\ [19], the best-"t line has a slope of !0.9; (b) copper with G+10 K m\ [19], slope !1.2; (c) tungsten with G+10 K m\ [19], slope !0.4; (d) latex with G+10 K m\ [20], slope !1.0; (e) latex with G+4; 10 K m\ [21], slope !0.6; (f) latex with G+1.8; 10 K m\ [22], slope !0.9; (g) nylon with G+200 K m\ [23], slope !1.1. The upward pointing triangles correspond to polystyrene particles in a succinonitrile melt with G+10 K m\ and a slope of !1.0 [24].…”

“…The predicted inverse relationship between < and R is consistent with the experimental data for most of these studies. The exceptions are the experiments with tungsten (data set c) [19] and one set of experiments with latex particles (data set e) [21] where the data is represented best by lines with slopes of !0.4 and !0.6, respectively. However, each of the best-"t lines through the remaining seven data sets has a slope near the predicted value of negative one.…”

“…Once again the particles used in these two studies were smaller than the critical radius given by Eq. (19). In addition, it should be Fig.…”

“…(19) so that the curvature of the phase boundary does not a!ect the "lm thickness. The thermomolecular pressure is directly proportional to the interfacial undercooling ¹ !¹ so that for arbitrary we can write…”