Devising and characterizing a non-perturbative manipulator in 3D microfluidic channels

Thanks to the lack of inertia of fluids, hydrodynamic forces in the Stokes regime, such as a microscale flow, are products of only flow pattern geometry. Consequently, an object entrained in a microfluidic flow cannot sense any variations if the surrounding flow remains uniform such that it is strain-free. This concept thus suggests the capacity of a microfluidic device for non-perturbative manipulations, which has not been fully explored. Here, we investigate the capability of such non-perturbative manipulations in a microscope-compatible 3D microfluidic device having vertically offset channels converging on a middle chamber. Using symmetry arguments, we illustrate a minimum of 6 channels are necessary to realize microscale manipulations along arbitrary directions, completely strain-free at the chamber center. By introducing two independent strain rate tensor invariants for characterizing flow perturbation, we demonstrate a finite volume with substantially low strain rate can be achieved around the strain-free center and can thus enable effectively non-perturbative manipulation over a spatial scale much greater than the size of the manipulated objects. We also fabricated such a microfluidic device and demonstrated its non-perturbative manipulation capabilities in experiments.