A multi-scale model for solute transport in a wavy-walled channel

Abstract

This paper concerns steady flow and solute uptake in a wavy-walled channel, where the wavelength and amplitude of the wall are comparable to each other but are much shorter than the width of the channel. The problem has two primary asymptotic regions: a core region where the walls appear flat at leading order and a wall region where there is full interaction between advection, diffusion and uptake at the wavy wall. For weak wall uptake, the effective uptake from the core is shown to increase with wall waviness in proportion to surface area, whereas for stronger wall uptake, it is found that the uptake from the core can be reduced as the wall amplitude increases. Conditions are identified under which this approximation is uniformly valid in a full channel flow, accounting for inlet conditions, and a comprehensive survey of the asymptotic distributions of solute both along and across the channel is provided. It is also shown how this multiscale approach can readily be extended to account for channel walls with multiple lengthscales of spatial variation.

Physical and geometric determinants of transport in fetoplacental microvascular networks

“…Characteristic parameters for various passively transported solutes. References (35)(36)(37)(38)(39)(40)(41)(42)(43)(44)(45)(46)(47)…”

“…When the diffusive capacity is low (µ • 1), radial diffusion over a long domain suppresses transverse concentration gradients. Following [46], we scale the axial coordinate by √ µ • and approximate the concentration profile as wellmixed, using…”

“…(S36) is no longer viable, as concentration boundary layers form in a corner region near the inlet of the tube. Instead the Lévêque approximation must be employed, which requires a transformation into the boundary layer coordinate system [37,46]. This allows us to recover the weakly flow-limited regime…”

Modelling crystal aggregation and deposition in the catheterised lower urinary tract

“…In the limit as A → ∞, the relative sizes of the diffusion, advection, and aggregation terms in the governing equations (2.7e-h) are the same for the four bulk concentrations (monomers, clusters, inhibitor particles and mass). Asymptotic analysis of similar advection-diffusiondeposition dynamics (but with no aggregation) can be found in references (Woollard et al 2008;Edwards 1999;Edwards et al 1999). We do not analyse the H ≈ 1 and H ≈ 0 cases; for these cases, the relative sizes of the advection, diffusion and aggregation terms are different for different bulk concentrations which leads to a significantly more complicated asymptotic solution structure, and is beyond the scope of this paper.…”

On the nonlinear convection-diffusion-reaction problem in a thin domain with a weak boundary absorption

“…The effects of the curved geometry and fluids microstructure on solute dispersion in pipe-like domains were investigated in [15,17]. Last but not least, let us also mention some contributions in the engineering literature as [7,19,22].…”