Dispersion controlled by permeable surfaces: surface properties and scaling

Abstract

Permeable and porous surfaces are common in natural and engineered systems. Flow and transport above such surfaces are significantly affected by the surface properties, e.g. matrix porosity and permeability. However, the relationship between such properties and macroscopic solute transport is largely unknown. In this work, we focus on mass transport in a two-dimensional channel with permeable porous walls under fully developed laminar flow conditions. By means of perturbation theory and asymptotic analysis, we derive the set of upscaled equations describing mass transport in the coupled channel–porous-matrix system and an analytical expression relating the dispersion coefficient with the properties of the surface, namely porosity and permeability. Our analysis shows that their impact on the dispersion coefficient strongly depends on the magnitude of the Péclet number, i.e. on the interplay between diffusive and advective mass transport. Additionally, we demonstrate different scaling behaviours of the dispersion coefficient for thin or thick porous matrices. Our analysis shows the possibility of controlling the dispersion coefficient, i.e. transverse mixing, by either active (i.e. changing the operating conditions) or passive mechanisms (i.e. controlling matrix effective properties) for a given Péclet number. By elucidating the impact of matrix porosity and permeability on solute transport, our upscaled model lays the foundation for the improved understanding, control and design of microporous coatings with targeted macroscopic transport features.

A reduced‐order model for chemical species transport in a tube with a constant wall concentration

“…Webster et al [15] also implemented the same methodology to address effective macroscopic transport parameters between parallel plates with constant concentration boundaries. The presented work can find applications in understanding the chemical reactive transport, [16] describing the transport in a conduit with solute stored in the porous matrix block, [9][10][11][12][13]17] and modelling of non-aqueous phase liquid (NAPL) dissolution. [18] However, the following main features make this study distinct from previous theoretical studies.…”

Causality and Bayesian Network PDEs for multiscale representations of porous media

“…with bandwidths h 1 and h 2 . Software DAKOTA [1] was used to automatize the process of computing the coefficients, basis functions, and truncation parameters appearing in (24). This approach is taken in [47] in the context of independent priors with the aim of computing Sobol' indices for global sensitivity analysis.…”

“…The simulation-assisted approach to the optimal design of porous meta-materials takes advantage of the availability of microscopic (pore-scale) and macroscopic (continuum or Darcy-scale) models, as well as of a bridge between the two provided by various upscaling techniques [52,51,24]. Such a bridge also facilitates analysis of both uncertainty propagation from the microscopic scale to the macroscopic scale and sensitivity of macroscopic material properties to the microscopic ones [47].…”

Rough or wiggly? Membrane topology and morphology for fouling control

“…Despite a number of studies have experimentally or analytically demonstrated the impact of morphological and topological alteration on, e.g., solute dispersion and fouling at the system (macro-) scale (Maruf et al 2013b;Battiato et al 2010;Griffiths et al 2013;Battiato & Rubol 2014;Rubol et al 2016;Ling et al 2016Ling et al , 2018, ROMs systems are still primarily optimized by trail and error. This is due to the lack of quantitative understanding of the impact of morphological and/or topological modifications on membrane fouling at prescribed operating conditions.…”