Deterministic Lateral Displacement (DLD): Finite element modeling and experimental validation for particle trajectory and separation

E. Pariset, J. Berthier, F. Révol-Cavalier, C. Pudda, D. Gosselin, F. Navarro, B. Icard, V. Agache
CEA Leti,

Keywords: deterministic lateral displacement (DLD), bioparticles, sample preparation, size-based separation


In biotechnology and biology, deterministic lateral displacement (DLD) arrays are used to separate particles based on their size, such as cells, bacteria, parasites and exosomes. DLD is very promising for sample preparation purposes as it enables sorting of nanometer to micrometer-sized label-free particles without altering their integrity (in case of biological species). It consists of aligned rows of shaped micro-pillars with a slant angle compared to the direction of the flow. The separation phenomenon is based on steric effects: particles larger than a critical size will be laterally displaced by the pillars whereas smaller particles will follow a global straight path. Models have been proposed in the literature to predict the critical sizes according to the geometry of the DLD arrays. However, these models are semi-empirical and do not cover all the possible pillar shapes and distributions. Here we present a finite element model to find the best separation geometries for different-shaped micro-pillars, using COMSOL finite element particle tracing module. The calculation is compared to the literature, and supported with experimental results with similar geometries. Here we demonstrate that COMSOL multiphysics can be used to model the separation in DLD arrays. First the hydrodynamics of the carrier fluid is computed and the Newton equation for each particle is solved. Our model also includes the steric exclusion effect from the DLD pillars on the particles thanks to the computation of the wall-particle distances. Here we show that the wall distance physics prevents particles from overlapping the pillars and correctly models the separation phenomenon in DLD arrays. The developed finite element model enables to evaluate the influence of the arrays geometrical parameters on the separation size, such as the pillars shape, orientation, inter-spacing and slant angle. In addition, the separation sizes are assessed experimentally with calibrated polystyrene spherical particles. This study shows that the separation sizes appear to be larger both numerically and experimentally when compared to the literature. Moreover, we demonstrate that the pillars orientation according to the flow direction has an impact on the separation size value. The approach presented here allows a reliable modeling of the separation limits experimentally observed with standard microparticles. From this study, the optimal pillars geometry can be chosen according to the desired separation size. This model could be the basis for a more ambitious study when adding both the effects of the steric hindrance between particles and the particle deformability in order to predict the behavior of more concentrated or biological samples in DLD arrays.