Rapid multiplex patterning through conformally-mapped microfluidic flows*

The simultaneous manipulation of many microscale particles is challenging but essential to fundamental biophysical studies. Such a task is typically realized through multiple traps, or local direct fields incorporated with a feedback mechanism, leading to potential perturbations on particles and delayed responses associated with the feedback-control loop. Here, we achieve this goal by utilizing the uniformity of flow fields in micro-manipulation, realizable through a 3D microfluidic channel obeying symmetry principles. We show that any imperfection in symmetry can be amended by deforming a testing flow pattern to match the desired one. We demonstrate that this restored symmetry can be extended to any manipulation pattern through conformal mapping, which is differentiable along the entire path. These conformally-mapped flows can thus be used to entrain multiple microparticles into smooth and rapid patterns, with their accuracies as high as submicron scales, without any need of real-time feedback. We also extend such robust flow controls to the manipulation of Brownian particles and living microorganisms.