Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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.

4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
2
The categories of this paper are: math
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess