Numerical modeling of two-fluid Taylor-Couette flow with deformable capillary liquid-liquid interface

A two-fluid Taylor-Couette flow with a deformable interface separating two liquid layers is studied numerically by a combination of the finite volume and level set methods. Effect of the interfacial tension is accounted for. It is shown that if the layers are infinitely long, there exist stable steady states with Taylor vortices of finite strength and finite deformations of the interface. On the other hand, if the length of the layers is finite and no-slip conditions are imposed at the edges, the liquid-liquid interface becomes unstable near the edges. Data from the literature and experimental data acquired in the present work are used for comparison with the numerical predictions. A qualitative agreement between the experimental and numerical observations of this instability is obtained. The results are of potential importance for development of bioseparators employing Taylor vortices for enhancement of mass transfer of a passive scalar (say, a protein) through the interface.