Effective dispersion and separation resolution in continuous particle fractionation

Abstract

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, $$\mathbf {W}$$ , and a typically anisotropic dispersion tensor, $$\mathbb {D}$$ , 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, $$D_\mathrm{eff}$$ , which is primarily controlled by the projection of the dispersion tensor onto the direction orthogonal to $$\mathbf {W}$$ . 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 $$\mathcal {D}_\mathrm{eff}$$ can be orders of magnitude larger than the bare particle diffusivity.