AMADEus Seminar - Pr. Francisco J. Valdès-Parada - Wednesday 12 april 2017 - 4:00 pm ENSAM (Amphi La rochefoucault Liancourt)

ABSTRACT

 In many transport processes in multiscale systems, there is a separation in both time and length scales that allows treating transport processes at the microscale to be quasi-steady with respect to their macroscale counterparts. In the particular case of porous media, there is a need for an equation that may describe all the dynamics of the effective diffusion coefficient. At the moment, approximate expressions, applicable separately at the early, pre-asymptotic and quasi-steady stages, are available but no expression has been reported for the entire time range. In this talk we use the method of volume averaging to describe such dynamics by systematically upscaling information from the pore-scale. By solving ancillary closure problems in both simple and random geometries in periodic unit cells, we were able to make predictions about the effective diffusivity dynamics. In addition, solution of the closure problems in homothetic 2D and 3D unit cells leads to an approximate analytical solution, which, under some conditions, is in agreement with those resulting from periodic unit cells. The second part of the talk is about an extension of the first part to dispersion in porous media. In this case, we find it more convenient to first transform the formulation to the Laplace domain, and subsequently to the frequency domain. In this way, the dynamics of the dispersion coefficient are studied. The upscaled model in the frequency domain is validated with direct numerical simulations at the pore-scale showing good agreement as long as the assumptions and constraints imposed are met. Extensions and on-going work are also discussed.