Axial Dispersion of Brownian Colloids in Microfluidic Channels

Particles in non-uniform flow fields undergo an enhanced axial dispersion compared to diffusion in the absence of flow. Qualitatively, axial dispersion is enhanced by flow because particles diffuse across streamlines and advect at rates different from the average velocity, resulting in a net spreading relative to the mean. Taylor and Aris first calculated the asymptotic form of this dispersion coefficient for point-like tracer particles in a cylindrical tube under the assumptions that the particles diffuse isotropically and explore all streamlines of the flow field uniformly. Colloidal dispersions, especially under confined flow, exhibit markedly different behavior due to their finite size and particle-particle and particle-wall hydrodynamic interactions.

We present a complete theoretical framework for the axial dispersion of a Brownian colloidal suspension confined in a parallel plate channel, extending the Taylor-Aris treatment to particles with diameters comparable to the channel width. The theoretical model incorporates the effects of confinement on the colloid distribution, corrections to the velocity profile due to the effects of colloid concentration on the suspension viscosity, and position-dependent anisotropic diffusivities. We test the theoretical model using explicit-solvent molecular dynamics simulations that fully incorporate hydrodynamic correlations and thermal fluctuations, and obtain good quantitative agreement between theory and simulations. We find that the non-uniform colloid structuring that arises in confinement due to excluded volume between the colloids and channel walls significantly impacts the transport properties of the suspension. The developed model should prove useful in many applications involving the axial dispersion of colloids, including extracting diffusion coefficients from microfluidic experiments and modeling the transport of colloids in geological fractures.