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On Marginal Stability Computation of Flow in a Rotating Cylindrical Annulus and Application to Protein Crystal Growth

Nelson J. Carrasquero, Daniel N. Riahi, Dambaru Bhatta


We consider the marginal linear stability of flow of fluid, which is a mixture of protein solution and an impurity, in a vertical cylindrical annulus. The system is rotating about the axis of the annulus with a constant angular velocity Ω. We also consider the system in the absence of rotation. We use particular boundary conditions, which are relevant for flow system during some growth stage of a cylindrical protein in a co-axial cylindrical container. We investigate particular model about the flow for both in the presence and absence of rotation and solve the corresponding marginal stability problem using a combined shooting and iterative methods. We find, in particular, dependence of the flow variables on the rotation rate and the flow excitation due to perturbations. In relations to the protein crystal-growth applications, certain types of perturbations with relatively smaller axial wavelength were detected to lead to beneficial flow excitation in the sense that impurity transport to the growing protein crystal is reduced.


Rotating Flow, Marginal stability, Annulus Flow, Convective Flow

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