Aggregation of bead-monolayers in flat microfluidic chambers - simulation by the model of porous media

In this paper, we for the first time simulate the process of hydrodynamic bead aggregation in a flat micro-fluidic chamber by a porous-media model in an iterative routine. This allows us to optimize the chamber design of our recently developed experimental method to form periodical monolayers from the flow of bead suspension. Periodical monolayers are advantageous for parallel assay formats since they enhance the mechanical rigidity of the aggregated pattern. This is important to avoid a spatial rearrangement along various steps of a read-out procedure which would impair the correlation between measurements. Furthermore, the monolayer formation guarantees the individual optical accessibility of all probe beads. By modelling the monolayers with porous media, we can drastically reduce the degrees of freedom in a two-phase, multi-particle problem. This way, we are able to compute stationary hydrodynamic flow patterns in the chamber. In order to simulate the complete filling process from these stationary solutions, we developed an iterative master routine which takes the transient aggregation pattern as the initial condition, then evaluates the placement of the newly introduced beads, and finally converts the points of aggregation into porous media.