Numerical analysis of flow anisotropy in rotated-square deterministic lateral displacement devices at moderate Reynolds number

Deterministic lateral displacement (DLD) is a microfluidic method for accurately separating particles by size or deformability. Recent efforts to operate DLD devices in the inertial, rather than in the Stokes flow regime, have been hindered by a loss of separation efficiency and difficulty predicting the separation behavior. One factor contributing to these problems is the onset of inertia-induced flow anisotropy where the average flow direction does not align with the direction of the pressure gradient in the device. We use the lattice-Boltzmann method to simulate two-dimensional flow through a rotated-square DLD geometry with circular pillars at a Reynolds number up to 100 for different gap sizes and rotation angles. We find that anisotropy in this geometry is a nonmonotonous function of Reynolds number and can be positive or negative. This finding is in contradiction to the naive expectation that inertia would always drive flow along the principal direction of the pillar array. Anisotropy tends to increase in magnitude with gap size and rotation angle. By analyzing the traction distribution along the pillar surface, we explain how the change of the flow field upon increasing inertia leads to the observed trends of anisotropy. Our work contributes to a better understanding of the inertial flow behavior in ordered cylindrical porous media, and it might contribute to improved DLD designs for operation in the inertial regime.