Manipulation of instabilities in core-annular flows using a deformable solid layer

The stability of core-annular flow (CAF) of two immiscible fluids surrounded by a soft, deformable solid layer is analyzed to examine the role of solid deformability on the interfacial instabilities in the CAF, using both low-wavenumber asymptotic analysis and numerical solutions by considering axisymmetric perturbations. For CAF in a rigid tube, two qualitatively distinct mechanisms due to capillary forces and viscosity stratification destabilize the interface between the two fluids. We show using a low-wavenumber analysis that the deformability of the solid layer has a stabilizing effect when the more viscous liquid is in the annular region, while it is destabilizing when the less viscous fluid is in the annular region. When the more viscous fluid is in the annulus, our numerical results demonstrate that by tuning the shear modulus of the solid layer, it is possible to maintain a stable core-annular flow(otherwise unstable in a rigid tube), where perturbations with all wavelengths are stable. For the same configuration, when the radius of the core fluid becomes small, we also find that it is possible to restrict the length scale of the instability to a small band of wavelengths. When the less viscous fluid is in the annulus, we show that the CAF (otherwise stable in a rigid tube) could be destabilized by solid deformability. Both these predictions, viz., suppression or enhancement of instability of the liquid-liquid interface by wall deformability could be potentially exploited in microfluidic drop formation applications that seek to control and manipulate the instability of the interface. (C) 2013 American Institute of Physics. [http://dx.doi.org/10.1063/1.4788712]