  Microfluidics provides a powerful and versatile technology to accurately
control spatial and temporal conditions for cell culturing and can therefore be
used to study cellular responses to gradients. Here we use Lattice Boltzmann
methods (LBM) to solve both the Navier-Stokes equation (NSE) for the fluid and
the coupled convection-diffusion equation (CDE) for the compounds that form the
diffusion-based gradient. The design of a microfluidic chamber for
diffusion-based gradients must avoid flow through the cell chamber. This can be
achieved by alternately opening the source and the sink channels. The fast
toggling of microfluidic valves requires switching between different boundary
conditions. We demonstrate that the LBM is a powerful method for handling
complex geometries, high Peclet number conditions, discontinuities in the
boundary conditions, and multiphysics coupling.
