Effective dispersion and separation resolution in continuous particle fractionation

Theoretical models and experiments suggest that the transport of suspended particles in microfluidics-based sorting devices can be modeled by a two-dimensional effective advection-diffusion process characterized by constant average velocity, , and a typically anisotropic dispersion tensor, , whose principal axes are slanted with respect to the direction of the effective velocity. We derive a closed-form expression connecting the effective transport parameters to separation resolution in continuous particle fractionation. We show that the variance of the steady-state particle concentration profile at an arbitrary cross-section of the device depends upon a scalar dispersion parameter, , which is primarily controlled by the projection of the dispersion tensor onto the direction orthogonal to . Numerical simulations of particle transport in a Deterministic Lateral Displacement device, here used as a benchmark to illustrate the practical use of the effective transport approach, indicate that sustained dispersion regimes typically arise, where the dispersion parameter can be orders of magnitude larger than the bare particle diffusivity.