Numerical Simulation of Particle Transport in a Drift Ratchet

The directed transport of microparticles depending on their size is the basis for particle sorting methods that are of utmost importance in, for example, life sciences. A drift ratchet is a Brownian motor that allows for such a directed transport. Hereby, the particle motion is induced by a combination of the Brownian motion and asymmetries stemming, for example, from the domain's geometry, electrical fields, or transient pressure boundary conditions. We simulate a particular drift ratchet which consists of a matrix of pores with asymmetrically oscillating diameter wherein a fluid with suspended particles is pumped forward and backward, and where the particles' long-term transport direction depends on their size. Thus, this setup allows for continuous and parallel particle separation, which has been shown experimentally. However, for a deeper understanding and for an optimized parameters' choice, further investigations, i.e., simulations, are necessary. In this paper, we present first results achieved with our parallel three-dimensional simulation codes applied to a still simplified scenario. This simplification is necessary to isolate different phenomena (e.g., asymmetries and Brownian motion) to check their relevance for the particle transport. The simulation codes are based on (adaptive) Cartesian grids in combination with finite volume and finite element discretizations. Cartesian grids allow for a very efficient implementation of the solver algorithms and an efficient balanced parallelization via domain decomposition. The achieved simulation results show the effectiveness of our approach and give some strong hints on a directed particle transport already with the simplified model we used here.