Key points are not available for this paper at this time.
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 travelling waves in the brain. Compared with steady flow, pulsations enhance the effective diffusivity and solute drift which scale quadratically with the wave amplitude, and depend on the ratio of wave-induced to bulk-flow-induced Péclet numbers, Pec/ Peb. 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 Pec/ Peb O (1), and shuttle dispersion which enhances diffusivity due to oscillatory solute transport for Pec/ Peb O (1). The pulsations also induce an effective solute drift, that scales quadratically with the wave amplitude and linearly with Pec/ Peb. 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, normalised by its value in steady flow, is O (10^3) and the mean enhancement in effective solute drift is -O (1). Physiological mechanisms such as frequency-dependent wave amplitude, and approximately constant wave velocity across brain travelling waves, may diminish the enhancement magnitudes. The research presents a generalised framework for quantifying dispersion in spatiotemporally varying annular conduits and improves our understanding of perivascular solute transport.
Sarkar et al. (Tue,) studied this question.