Lubrication Force Saturation Matters for the Critical Separation Size of the Non-Colloidal Spherical Particle in the Deterministic Lateral Displacement Device

Abstract

Deterministic lateral displacement (DLD) is a popular technique for separating micro-scale and nano-scale particles continuously. In this paper, an efficient three-dimensional fictitious domain method is developed for the direct numerical simulation of the motion of a non-colloidal spherical particle in the DLD device (i.e., cylinder array), based on substantial modification of our previous FD method. A combination of the fast Fourier transformation (FFT) and a tri-diagonal solver is developed to efficiently solve the pressure Poisson equation for a DLD unit with a shifted periodic boundary condition in the streamwise direction. The lubrication force correction is adopted in the fictitious domain method to correct the unresolved hydrodynamic force when the particle is close to the cylinder with the gap distance below one mesh, and the lubrication force is assumed to saturate at a smaller critical gap distance as a result of the surface roughness effect. The proposed method is then employed to investigate the effect of the critical gap distance of the lubrication force saturation on the motion mode (i.e., separation size) of the particle in the DLD device. Our results indicate that the lubrication force saturation is important to the particle critical separation size, and a smaller saturation distance generally makes the particle more prone to the zigzag mode.