Capillary instability driven by a permeability gradient

Viscous fingering, the phenomenon associated with the Saffman- Taylor instability, occurs when a low viscosity fluid penetrates a fluid of higher viscosity. Surface tension generally acts to stabilize the interface of the two fluids. In this work, we study a new surface-tension-induced instability that is driven by a permeability gradient. The instability is even revealed when a fluid of higher viscosity penetrates a fluid of lower viscosity (stable in the Saffman-Taylor sense). This capillary instability is demonstrated in a microfluidic setup composed of two symmetric channels that linearly increase in width, rather than the traditional Hele-Shaw cell. The conditions necessary to achieve this instability are studied. In particular, we determined a critical capillary number below which the instability occurs. The effect of viscosity ratio and permeability gradient are also examined.