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Numerical simulation reveals velocity and film thickness distributions in low-Reynolds two-phase tube flow, highlighting mechanisms governing microscale capillary transport.
A finite element solution to the steady-state problem of an inviscid bubble flowing at low Reynolds number in a cylindrical tube occupied by a second viscous phase was obtained. Interfacial tension forces were balanced against the viscous and pressure forces in order to locate the position of bubble-liquid interface. Velocities, pressures, and film thicknesses were obtained as a function of the capillary number. Specific applications of these results include the description of multiphase flow in tubes and porous media, and blood cell movement in small capillaries. The numerical results are compared with published theories and experiments.
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Shen et al. (1985) studied this question.
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