Dynamics of miscible interfaces and the effects of Korteweg stresses

Miscible flows in vertical capillary tubes are investigated by axisymmetric numerical simulations for a variety of viscosity and density ratios, and at different dimensionless flow and injecting net flow. For naturally buoyant flow, the simulations indicate a strong effect of the viscosity ratio on the flow. Different viscosity ratios are seen to lead to either a continuously rising finger, or to a sequence of bubbles that pinch off from the main finger. The influence of the Peclet number is seen to depend on the viscosity ratio. For the moderate viscosity contrast, and at relatively low values of Pe, the tendency for the bubbles to pinch off from the main finger is somewhat impeded by the effects of diffusion. At large Pe values, the tendency towards bubble generation is more pronounced. Furthermore, the effects of Korteweg stresses and non-vanishing divergence are addressed. A positive Korteweg stress constant results to a faster and more pointed finger, and a negative constant leads to a slower and blunter finger. The effect of divergence is found to be small. For the flows with injection, both the influences of Korteweg stresses and divergence are insignificant to the finger tip velocity for large Peclet number.