An analytical model for plug flow in microcapillaries with circular cross section

Plug flow in microcapillaries or microchannels offers significant advantages for the development of microfluidic applications and recently triggers many interests and studies. Recirculation is formed within liquid plugs due to the presence of interfaces. This paper presents an analytical model to investigate the recirculation flow and the flow resistance in microcapillaries with circular cross section. A fourth order partial differential equation is used to model the Stokes flow within the liquid plug. The results of the flow field show that the flow pattern is affected by the plug length. The flow resistance is determined through the force balance of the liquid plug. The comparison of the flow field and the flow resistance from the analytical model and the experiments shows good agreement.

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► An 2D analytical model for flow fields in liquid plugs is proposed.
► The flow resistance is obtained and validated against experimental results.
► Recirculating vortices in plugs are influenced by the plug length.
► Two contributors to flow resistance, friction and surface tension, are identified.
► Short plugs experience high values of plug resistance coefficient.