dL 2ФА (с — с,) G = dt Pyp(1/ke +1/k;) z kg(c – c.)' A(c – c,) 1/ke +1/k; dm/dt
Antibiotics like tetracycline may be crystallized by controlled cooling of an aqueous solution in a stirred tank to grow crystal seeds. Develop an expression for a cooling curve for a seeded batch crystallization conducted at constant supersaturation (neglecting nucleation). The expression is to give reactor temperature, T, as a function of time, t, in terms of the following system parameters: To = initial temperature, Tp=final product temperature, ms = mass of seed crystal, mp = mass of product crystal less the seed mass, G = linear crystal growth rate, Ls = seed crystal dimension, and Lp = product crystal dimension. In these circumstances, the change in solubility with time is balanced by crystal growth given in (17-23a). Assume a single crystal size, Ls, and a constant, linear growth rate, G, as given in (17-87). Neglect variation of solubility with temperature (dcs/dT) over small temperature ranges
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