Inertia and scaling in deterministic lateral displacement

The ability to separate and analyze chemical species with high resolution, sensitivity, and throughput is central to the development of microfluidics systems. Deterministic lateral displacement (DLD) is a continuous separation method based on the transport of species through an array of obstacles. In the case of force-driven DLD (f-DLD), size-based separation can be modelled effectively using a simple particle-obstacle collision model. We use a macroscopic model to study f-DLD and demonstrate, via a simple scaling, that the method is indeed predominantly a size-based phenomenon at low Reynolds numbers. More importantly, we demonstrate that inertia effects provide the additional capability to separate same size particles but of different densities and could enhance separation at high throughput conditions. We also show that a direct conversion of macroscopic results to microfluidic settings is possible with a simple scaling based on the size of the obstacles that results in a universal curve.