Computing Stationary Free-Surface Shapes in Microfluidics

by M. Schindler, P. Talkner, & P. Hanggi arXiv.org E-print Archive, 25 Nov 2005 We propose a Finite-Element algorithm to compute free capillary surface shapes that are significantly deformed. The algorithm is thoroughly explained by physical as well as mathematical arguments. We show that it is robust in the sense that it yields the correct surface shape starting with quite different ones, without the need for re-meshing at the boundary. The errors of the computed shape's curvature are shown to be extremely small, at least an order of magnitude less than one percent in two accuracy tests. Our variational approach, formulated in arbitrary curved coordinates allows to substantiate the numerical observation that only a second-order approximation suffices for the free surface discretisation. Finally, we present a comparison of our numerical results with an experimentally observed droplet. Read more