Calculating the motion of highly confined, arbitrary-shaped particles in Hele-Shaw channels

摘要

We combine theory, numerical calculations, and experiments to accuratelypredict the motion of anisotropic particles in shallow microfluidic channels,in which the particles are strongly confined in the vertical direction. Weformulate an effective quasi-two-dimensional description of the Stokes flowaround the particle via the Brinkman equation, which can be solved in a timethat is two orders of magnitude faster than the three-dimensional problem. Thecomputational speedup enables us to calculate the full trajectories ofparticles in the channel. To test our scheme, we study the motion ofdumbbell-shaped particles that are produced in a microfluidic channel using`continuous flow lithography'. Contrary to what was reported in earlier work(Uspal et al., Nature communications 4 (2013)), we find that the reorientationtime of a dumbbell particle in an external flow exhibits a minimum as afunction of its disk size ratio. This finding is in excellent agreement withnew experiments, thus confirming the predictive power of our scheme.