Starting concentration profile, boundary layer

Simple Analytical Models. To derive simple analytical models for horizontal reactors, two flow simplifications have been used boundary layer similarity models and film theory (see Table 3 in reference 212). In these treatments, a constant concentration shape is assumed from the start of the deposition zone or from an axial position after the initial concentration profile development zone. Thereafter, the shape stays constant, with only the absolute magnitude of the concentration changing with axial position. 

The calculated concentration profiles in a KC1 solution-anion exchange membrane boundary layer at different times after the start of a constant current of density 5 ma. per sq. cm. are plotted in Figure 5. The diffusion coefficient of KC1 in the solution was taken as 2.0 X 10—5 sq. cm. per second and the thickness of the diffusion layer as 0.03 cm. 

In both, layer and suspension crystallization solid material forms from the melt starting with a nucleus through which a solid/liquid interface is created. As crystallization proceeds the mass of solidified substance steadily increases which causes the interface to move. The impurity components remaining in the melt thereby enrich in front of the solid/liquid interface, forming a concentration boundary layer. The concentration profile in this boundary layer changes as the interface advances which is in literature referred to as moving boundary problem. ... 

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