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arXiv · 1411.2728

Boundary elements method for microfluidic two-phase flows in shallow channels

Mathias Nagel·François Gallaire
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Abstract

In the following work we apply the boundary element method to two-phase flows in shallow microchannels, where one phase is dispersed and does not wet the channel walls. These kinds of flows are often encountered in microfluidic Lab-on-a-Chip devices and characterized by low Reynolds and low capillary numbers. Assuming that these channels are homogeneous in height and have a large aspect ratio, we use depth-averaged equations to describe these two-phase flows using the Brinkman equation, which constitutes a refinement of Darcy's law. These partial differential equations are discretized and solved numerically using the boundary element method, where a stabilization scheme is applied to the surface tension terms, allowing for a less restrictive time step at low capillary numbers. The convergence of the numerical algorithm is checked against a static analytical solution and on a dynamic test case. Finally the algorithm is applied to the non-linear development of the Saffman-Taylor instability and compared to experimental studies of droplet deformation in expanding flows.

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Mathias Nagel, François Gallaire. 2014-11-11. Boundary elements method for microfluidic two-phase flows in shallow channels. https://doi.org/10.1016/j.compfluid.2014.10.016

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