Enhanced Taylor-Aris dispersion in slender pulsatile annular channels: Implications for perivascular solute transport

We derive expressions for the long-time effective dispersion coefficients of a solute in a slender annular channel with a spatiotemporally pulsating inner boundary. The problem is motivated by transport in perivascular spaces (PVSs) that are subjected to pulsations induced by traveling waves in the brain. Compared to steady flow, pulsations enhance the effective diffusivity and solute drift which scale quadratically with the wave amplitude, and depends on the ratio of wave-induced to bulk-flow-induced Péclet numbers, ${\text{Pe}}_c/{\text{Pe}}_b$ . The mean enhancement in diffusivity can be decomposed into a bulk-flow-induced contribution and two wave-induced corrections: entropic slowdown, which reduces diffusivity due to solute lodging in the constrictions, for ${\text{Pe}}_c/{\text{Pe}}_b\lesssim 𝒪\left(1\right)$ , and shuttle dispersion which enhances diffusivity due to oscillatory solute transport for ${\text{Pe}}_c/{\text{Pe}}_b\gtrsim 𝒪\left(1\right)$ . The pulsations also induce an effective solute drift, that scales quadratically with the wave amplitude and linearly with ${\text{Pe}}_c/{\text{Pe}}_b$ . The effective dispersion coefficients are sensitive to the annular cross-sectional area ratio with narrower geometries yielding stronger enhancements. For a representative murine PVS geometry subjected to pulsations under delta wave parameters, the mean enhancement of diffusivity, normalized by its value in steady flow, is $𝒪\left({10}^3\right)$ and the mean enhancement in effective solute drift is $-𝒪\left(1\right)$ . Physiological mechanisms such as frequency-dependent wave amplitude, and approximately constant wave velocity across brain traveling waves may diminish the enhancement magnitudes. The research presents a generalized framework for quantifying dispersion in spatiotemporally varying annular conduits and improves our understanding of perivascular solute transport.