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.
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
Record created on 2014-12-08, modified on 2016-08-09