Viscous potential flow analysis of capillary instability with heat and mass transfer through porous media

The capillary instability of the cylindrical interface separating two viscous and incompressible fluids through porous medium is studied using viscous potential flow theory, when there is heat and mass transfer across the interface. The fluids are considered to be viscous and incompressible with different kinematic viscosities. A dispersion relation that accounts for the growth of axisymmetric waves is derived and stability is discussed theoretically as well as numerically. Stability criterion is given in terms of critical value of wave number. Various graphs have been drawn to show the effect of various physical parameters such as heat transfer capillary number, viscosity ratio, permeability and porosity on the stability of the system. It has been observed that porous media and heat transfer both have stabilizing effect while porosity has destabilizing effect on the stability of the system.