Algorithm to implement unsteady jump boundary conditions within the lattice Boltzmann method.

An algorithm is proposed to implement unsteady jump boundary conditions in the lattice Boltzmann method (LBM). This is useful for dealing with problems of mass transfer across membranes that exhibit resistance and discontinuity in concentration. The algorithm is simple to implement into an existing LBM-based code that computes diffusion and advection of a solute. Analytical solutions are recovered in the limiting case of a planar membrane. When combined with the immersed boundary method, the algorithm can handle moving deformable boundaries that adopt arbitrary geometries. Simulations of controlled solute release from stationary rigid and moving deformable particles are given as a proof of concept.