Slug Self-Propulsion in a Capillary Tube Mathematical Modeling and Numerical Simulation

Abstract EN

A composite droplet made of two miscible fluids in a narrow tube generally moves under the action of capillarity until complete mixture is attained.

This physical situation is analysed here on a combined theoretical and numerical analysis.

The mathematical framework consists of the two-phase flow phase-field equation set, an advection-diffusion chemical concentration equation, and closure relationships relating the surface tensions to the chemical concentration.

The numerical framework is composed of the COMSOL Laminar two-phase flow phase-field method coupled with an advection-diffusion chemical concentration equation.

Through transient studies, we show that the penetrating length of the bidroplet system into the capillary tube is linear at early-time regime and exponential at late-time regime.

Through parametric studies, we show that the rate of penetration of the bidroplet system into the capillary tube is proportional to a time-dependent exponential function.

We also show that this speed obeys the Poiseuille law at the early-time regime.

A series of position, speed-versus-property graphs are included to support the analysis.

Finally, the overall results are contrasted with available experimental data, grouped together to settle a general mathematical description of the phenomenon, and explained and concluded on this basis.