Symmetry-Protected Stressless Microfluidics*

Flows under spatial confinement have often been regarded as possessing nonuniform structures accompanied by deformations and rotations. Symmetries of the system can however provide a powerful tool to both understand and manipulate the structure of the flow. Here, we studied flows confined by three-dimensional (3D) microfluidic devices with polyhedral symmetries. We show that all characteristic flows following an Octahedral symmetry can be classified into strain-full and strain-free groups, corresponding to distinct subgroups of the Octahedral symmetry group. Interestingly, the strain-free group of flow modes corresponds to uniform flow in arbitrary directions, which suggest exploiting them for 3D stress-free manipulations of flows. To demonstrate the robustness of these symmetry-protected flows, we built a microfluidic device with these symmetries and successfully realized stress-free manipulations by entraining several microparticles in the bulk fluid and forcing them to follow a variety of parallel and identical, user-specified 3D paths.