Slug Self-Propulsion in a Capillary Tube Mathematical Modeling and Numerical Simulation (2016)
AuthorsKhodabocus MI, Sellier M, Nock Vshow all
© 2016 M. I. Khodabocus et al.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.
CitationKhodabocus MI, Sellier M, Nock V (2016). Slug Self-Propulsion in a Capillary Tube Mathematical Modeling and Numerical Simulation. Advances in Mathematical Physics. 2016. 1-16.
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ANZSRC Fields of Research09 - Engineering::0915 - Interdisciplinary Engineering::091504 - Fluidisation and Fluid Mechanics
01 - Mathematical Sciences::0105 - Mathematical Physics