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

M. I. Khodabocus, M. Sellier and V. Nock

Advances in Mathematical Physics, 2016, vol. 2016, issue 1

Abstract: 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.

Date: 2016
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https://doi.org/10.1155/2016/1234642

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2016:y:2016:i:1:n:1234642

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