Numerical Study of Quantifying Diffusion Effects on Deterministic Lateral Displacement at the Nanoscale

Nanoparticles in biomedical applications require precise sorting and enrichment, extending deterministic lateral displacement (DLD) to the nanoscale, however, remains limited due to the dominant influence of diffusion. At such scales, Brownian motion blurs the deterministic critical diameter, causing an uncertainty region where displacement and zigzag modes coexist. In this study, a two-dimensional finite-element model that couples fluid dynamics, solid mechanics, and stochastic Brownian forces is constructed, for the first time, to investigate nanoscale DLD. Simulation results indicate that diffusion exerts its strongest influence near zero-velocity points, causing deterministic displacement trajectories to transform into zigzag mode. Based on first-passage theory, the zero-crossing time of the Y-direction velocity is introduced as a dynamic measure of Brownian influence. By defining a threshold for the relative growth of zero-crossing time, a quantitative method to determine the width and boundaries of the uncertainty region is proposed. This numerical approach provides a new perspective for understanding diffusion-induced mode transitions and offers design guidelines for the development of reliable nanoscale DLD systems.