PNNL

Abstract

Permeable and porous coated surfaces are common in natural and engineered systems and exhibit features that significantly deviate from their smooth impermeable counterparts. Even though flow and transport above such surfaces may be significantly affected by the surface topology, e.g. its porosity and permeability, the connection between the surface characteristics and their impact on macroscopic solute transport is still 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 both the set of upscaled equations describing mass transport in the coupled channel-porous matrix system and an analytical expression relating the dispersion coefficient and the surface properties, namely porosity and permeability. Our analysis shows that the impact of surface coatings topology on macrodispersion strongly depends on the magnitude of P´eclet number, i.e. on the interplay between diffusive and advective mass transport. The study provides a rigorous basis to relate matrix permeability to dispersion coefficient in coupled channel-matrix systems and gives quantitative guidelines for the design of porous/micro-patterned surfaces. The analysis also shows the possibility of controlling macrodispersion by either active (i.e. changing the operating conditions) or passive mechanisms (i.e. designing the pore geometry of the matrix) in the appropriate range of P´eclet numbers. 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.