Moving boundaries crystal growth

Another approach to the problem of curved edges is based on a solution of Frank s equations in the case of moving boundaries by Mansfield [139], Figure 3.14 shows the ellipitical profile which would arise if the sides of a crystal sector move outwards with a constant velocity, h, which is of comparable size to the spreading rate, g. The magnitude of h is supposed to be determined by the growth rate of the adjoining dominant sector.10... 

Reid et al. [ 1.12] described the effect of 1 % addition certain polymers on the heterogeneous nucleation rate at-18 °C the rate was 30 times greater than in distilled, microfiltered water and at -15 °C, the factor was still 10 fold hogher. All added polymers (1 %) influenced the nucleation rate in a more or less temperature-dependent manner. However, the authors could not identify a connection between the polymer structure and nucleation rate. None the less it became clear that the growth of dendritic ice crystals depended on to factors (i) the concentration of the solution (5 % to 30 % sucrose) and (ii) the rate at which the phase boundary water - ice crystals moved. However, the growth was found to be independent of the freezing rate. (Note of the author the freezing rate influences the boundary rate). 

Denote boundary motion speed as u that may or may not depend on time. For crystal growth, the interface moves to the right with x = Xo>0. For crystal dissolution, the interface moves to the left with x = Xo<0. That is, u is positive during crystal growth and negative during crystal dissolution under our setup of the problem. The interface position can be found as... 

Mathematically, diffusive crystal dissolution is a moving boundary problem, or specifically a Stefan problem. It was treated briefly in Section 3.5.5.1. During crystal dissolution, the melt grows. Hence, there are melt growth distance and also crystal dissolution distance. The two distances differ because the density of the melt differs from that of the crystal. For example, if crystal density is 1.2 times melt density, dissolution of 1 fim of the crystal would lead to growth of 1.2 fim of the melt. Hence, AXc = (pmeit/pcryst) where Ax is the dissolution distance of the crystal and Ax is the growth distance of the melt. 

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