Numerical Analysis On Circular Particle In Deterministic Lateral Displacement Devices Using IB-LBM

Particle separation is the key step in biomedical process. Recently, deterministic lateral displacement (DLD) device is highly recommended for particle separation because of its high efficiency and simple structures. Aiming to numerically investigate the interplay between the separating particles and the flow, the immersed-boundary-lattice-Boltzmann method (IB-LBM) and the spring model of circular particle for liquid-structure simulation were employed in this study. The simulations provide effective critical size for separations in cylindrical, rectangular, I-shaped, hexagonal and octagonal DLD arrays. It is found that all these non-circular pillar shapes lead to smaller critical sizes. Specifically, critical sizes for rectangular and I-shaped arrays are the smallest and those for hexagonal and octagonal arrays are between the critical sizes of cylindrical and rectangular devices. Moreover, by adding a shape factor into the traditional empirical formula by Davis, a new formula is proposed to estimate the critical size of any DLD microfluidic arrays with convex-shaped pillars for spherical particle separation. The ratio of sub-channel widths is found to play an important role in reducing the critical sizes. Furthermore, the simulations are taken to investigate the effects of viscosity and stiffness on deformable and circular particles in DLD devices. It is found that in the cylindrical arrays with the same structures and displacements, if particle’s bending stiffness Kb and viscosity contrast X, are small, the effective size of the circular particle becomes larger and the travelling mode of the particle changes from zigzag (ZZ) to lateral displacement (LD). On the other hand, the effective size of a larger circular particle becomes even larger and keeps going on LD mode. Thus, viscosity contrast and particle stiffness can change the particles’critical sizes as well as traveling mode to some extent. The key factors for separation are still particle diameter, gap size and lateral gradient. By measuring the changes of the particle maximum length and the capillary number, it is found that small capillary number leads to less deformability and smaller effective size. Thus, the circular particle with small capillary number tends to go into zigzag mode.The simulation results deepen our understanding towards DLD separation and pave a valuable way toward designing high-performance DLD microfluidic arrays.