Analysis of models for two solution crystal growth problems

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Two diffusive solution crystal growth models are considered in which transport is governed by small parameters. The first is a simple model describing precipitant-driven solution crystal growth; the second describes a hanging drop evaporation configuration used for protein crystallization. Both contain components with widely differing diffusivities, the ratio being ϵ. The second system also has a small density ratio ϱ between the two contacting phases. Asymptotic scaling methods are used to show that in the first problem, the precipitant concentration remains uniform to O(√ϵ), while in the second, the drop concentrations remain uniform to O(ϱ/√ϵ) if ϱ ≪ √ϵ and the vapor concentrations remain uniform to O(√ϵ/ϱ) if √ϵ ≪ ϱ. The latter result implies that the drop will rema in effectively well mixed when ϱ ≪ √ϵ, but that sharp gradients will develop in the drop when √ϵ ≪ ϱ. An example is given to indica te that for certain proteins, sharp concentration gradients may develop in the drop during evaporation, while under the same conditions, the concentrations of other proteins remain uniform.