Investigation of pressure balance in proximity of sidewalls in deterministic lateral displacement

Deterministic lateral displacement (DLD) is a popular technique for the size-based separation of particles. A key challenge in the design of DLD chips is to eliminate the fluid flow disturbance caused by channel sidewalls intersecting with pillar matrix. While there are numerous reports attempting to mitigate this issue by adjusting the gaps between pillars on the sidewalls and the closest ones residing on the bulk grid of DLD, there are only a few works that also configure the axial gap of pillars adjacent to the accumulation sidewall. Herein, we study various designs numerically to investigate the effects of geometrical configurations of sidewalls on the critical diameter and first stream flux fraction variations across the channel. Our results show that regardless of the model used for the boundary gap profile, applying a pressure balance scheme can improve the separation performance by reducing the critical diameter variations. In particular, we found that for a given boundary gap distribution, there can be two desired parameter sets with relatively low critical diameter variations. One is related to sufficiently low lateral resistance of interface unit cells next to the accumulation sidewall, while the other one emerges by reducing the axial resistance of the interface unit cells to an appropriate extent. This work should pave the way for designing DLD systems with improved performance, which can be critically important for applications such as the separation of rare cells, among others, wherein target species need to be concentrated into as narrow a stream as possible downstream of the device to enhance purity and the recovery rate simultaneously.