A simulation method for particle migration in microfluidic spirals with application to small and medium particle concentrations

This paper treats the separation of particles in microchannels relevant to biological and industrial process engineering. To elucidate the mechanisms creating uneven distribution of particles over the cross section, simulations are conducted with the particles being geometrically resolved and coupled to the fluid by an immersed-boundary method. In a first step, the method is validated for particle focusing in straight channels. Beyond validation, new information not previously available is reported for these cases. Next, an efficient approach is presented to simulate the motion of particles in spiral ducts of small curvature by means of a well-controlled set of approximate equations. It is applied here to situations with spherical particles and validated with reference data for inertial migration in curved channels achieving good agreement. The simulation data provide new rich information on the details of the separation process concerning migration time, particle positioning in the cross section, streamwise particle spacing, and velocity field of the continuous phase. For concentrations smaller than 1%, three different focusing modes are observed: single position, two symmetric positions, and periodic trajectories oscillating between two focusing points. Another set of results is obtained with particle concentrations up to 10% in a curved channel. Here, the spatial distribution of particles is determined in a statistical sense and related to the mean flow of the continuous phase. While focusing is reduced with increasing particle concentration, the distribution of particles is found to be still far from uniform up to the investigated concentration level.