Multi-scale simulation techniques of fluid flow in porous media for paper-based microfluidics

SALAZAR BOVE, JOSELYNNE C.; TORO, SEBASTIÁN; KLER, PABLO A.

Congreso; III Brazil-Argentine Microfluidics Congress - VI Congreso de Microfluídica Argentina; 2022

In this work, multi-scale techniques for the determination of the effective permeability (Darcy’slaw) of porous materials with paper-like microstructures are studied and applied. The multi-scaletechnique is based on the definition of a representative volume element (RVE) of the materialto be modelled. In this case, the microstructure is built from connected channels where thefluid moves inside the void of the porous material (microscale). The fluid dynamic problem issolved under incompressible flow conditions in the Stokes regime, in order to calculate the effectivepermeability corresponding to that microstructure by imposing pressure gradients in the microscaleand subsequent numerical homogenization. This permeability is compared with experimentalresults for materials used in microfluidics such as Whatman paper #1 and Munktell, for whichappropriate micro-structure dimensions are sought in order to obtain a RVE. The technique wasalso validated by comparing the results obtained with DNS solutions (solution of the flow throughthe porous material on a single scale), with respect to solutions of the Darcy problem usingthe calculated effective permeability (numerical solution FE2). The limits of application of thismethodology and the modifications that should be made to the assumptions and formulations forappropriate flow modelling for paper-based microfluidic applications will be discussed.