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

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.


Published in:
Computers & Fluids, 107, 272-284
Year:
2015
Publisher:
Elsevier
ISSN:
0045-7930
Keywords:
Note:
In hope to encourage research and collaboration in this field we provide an open-source version of our numerical code for free distribution and modification on the website http://lfmi.epfl.ch/ulambator
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 Record created 2014-12-08, last modified 2018-01-28

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