Advection-dominated transport past isolated disordered sinks: stepping beyond homogenization.
Proc Math Phys Eng Sci
; 478(2262): 20220032, 2022 Jun.
Article
en En
| MEDLINE
| ID: mdl-35756879
ABSTRACT
We investigate the transport of a solute past isolated sinks in a bounded domain when advection is dominant over diffusion, evaluating the effectiveness of homogenization approximations when sinks are distributed uniformly randomly in space. Corrections to such approximations can be non-local, non-smooth and non-Gaussian, depending on the physical parameters (a Péclet number Pe, assumed large, and a Damköhler number Da) and the compactness of the sinks. In one spatial dimension, solute distributions develop a staircase structure for large Pe , with corrections being better described with credible intervals than with traditional moments. In two and three dimensions, solute distributions are near-singular at each sink (and regularized by sink size), but their moments can be smooth as a result of ensemble averaging over variable sink locations. We approximate corrections to a homogenization approximation using a moment-expansion method, replacing the Green's function by its free-space form, and test predictions against simulation. We show how, in two or three dimensions, the leading-order impact of disorder can be captured in a homogenization approximation for the ensemble mean concentration through a modification to Da that grows with diminishing sink size.
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Bases de datos:
MEDLINE
Tipo de estudio:
Prognostic_studies
Idioma:
En
Revista:
Proc Math Phys Eng Sci
Año:
2022
Tipo del documento:
Article
País de afiliación:
Reino Unido