Numerical simulation of critical particle size in asymmetrical deterministic lateral displacement

Microfluidics devices are widely used for particle separation. Deterministic Lateral Displacement (DLD) is a passive method for particle separation. DLD devices mainly separate particles based on their sizes. There are two main modes of movement in DLD arrays; the small particles move in a zigzag path, and the larger particles separate in the displacement mode. It is therefore important to estimate the critical particle size for the transition of modes before the fabrication of DLD devices. Asymmetry in the design of the arrays can affect the fluid behavior and the critical particle size. In this study, we investigate the effects of the asymmetry caused by changing the downstream gap size to the lateral gap size ratio on the fluid behavior and particle trajectories in DLD devices. We used two dimensional (2D) Finite Element Method (FEM) to study the variations in the flow lane's widths and combined the fluid analysis with structural mechanics to model the contact between the particles and the posts in DLD arrays. We simulated the spherical particles' trajectories with diameters ranging from 1.4 to 19.2 μm in circular post DLD arrays with a lateral gap size of 20μm. In contrast to the previous works, in these simulations, the effect of particle movement on the fluid flow profiles was considered. We evaluated the particle movement mode in seven different values of the downstream gap size to the lateral gap size ratio (ranging from 0.5 to 2) and eight different row shift fraction (ranging from 0.025 to 0.3). Our simulations showed that increasing the value of the downstream gap while the lateral gap is fixed increases the veering flow rate and width. By finding the particle with the largest diameter in the zigzag mode and the particle with the smallest diameter in the displacement mode, we estimated the critical particle diameter for each value of shift fraction in different values of the downstream gap to the lateral gap size ratio. Using these data, a curve was fitted for predicting the critical particle diameter in each ratio. Finally, a more general form of the formula for the critical particle diameter was proposed, which considers an extra parameter compared to the previous ones. The results of this study can lead to a better understanding of DLD devices' functions and, thus, save time and costs for better designs and experiments.