Time dependence of advection-diffusion coupling for nanoparticle ensembles

Abstract

Particle transport in fluids at micro-and nano-scales is important in many domains. As compared to the quiescent case, the time evolution of particle dispersion is enhanced by coupling: i) advection along the flow; and ii) diffusion along the associated velocity gradients. While there is a well-known, long-time limit for this advection-diffusion enhancement, understanding the short-time limit and corresponding crossover between these two asymptotic limits is less mature. We use evanescent-wave video microscopy for its spatio-temporal resolution. Specifically, we observe a near-surface zone of where the velocity gradients, and thus dispersion, are the largest within a simple microfluidic channel. Supported by a theoretical model and simulations based on overdamped Langevin dynamics, our experiments reveal the crossover of this so-called Taylor dispersion from short to long time scales. Studying a range of particle size, viscosity and applied pressure, we show that the initial spatial distribution of particles can strongly modify observed master curves for short-time dispersion and its crossover into the long-time regime.

Near-surface rheology and hydrodynamic boundary condition of semi-dilute polymer solutions

“…We have furthermore used the signal intensity distribution analyses of ref. [61,62], simultaneously fitting the distribution of intensities and velocity profiles and find good agreement with the slopes measured here, within 10% or so and not varying systematically with the imposed pressure.…”

Generalized Taylor dispersion for translationally invariant microfluidic systems

“…Beyond the examples studied here, many more remain to be investigated either analytically or numerically. In particular, the very compact form and generality of the results given here are ideally suited to predict Taylor dispersion in systems where the microscopic parameters such as the diffusion tensor and effective potential can be determined experimentally [19,21,22].…”

“…We pursue this parabolic diffusion model as it can be pushed through analytically, however we emphasize that Eq. ( 39) is straightforward to evaluate numerically for arbitrary complicated analytical expressions for D ⊥ (z) or indeed numerical [18] or experimental [19,21,22] data for D ⊥ (z).…”