Chaotic Mixing in Three Dimensional Porous Media

Abstract

Under steady flow conditions, the topological complexity inherent to all random 3D porous media imparts complicated flow and transport dynamics. It has been established that this complexity generates persistent chaotic advection via a three-dimensional (3D) fluid mechanical analogue of the baker's map which rapidly accelerates scalar mixing in the presence of molecular diffusion. Hence pore-scale fluid mixing is governed by the interplay between chaotic advection, molecular diffusion and the broad (power-law) distribution of fluid particle travel times which arise from the non-slip condition at pore walls. To understand and quantify mixing in 3D porous media, we consider these processes in a model 3D open porous network and develop a novel stretching continuous time random walk (CTRW) which provides analytic estimates of pore-scale mixing which compare well with direct numerical simulations. We find that chaotic advection inherent to 3D porous media imparts scalar mixing which scales exponentially with longitudinal advection, whereas the topological constraints associated with 2D porous media limits mixing to scale algebraically. These results decipher the role of wide transit time distributions and complex topologies on porous media mixing dynamics, and provide the building blocks for macroscopic models of dilution and mixing which resolve these mechanisms.

36 pages

References in corpus (1)

• Permeability of porous materials determined from the Euler characteristic

Cited by in corpus (12)

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• A Primer on the Dynamical Systems Approach to Transport in Porous Media
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• A Unified Theory for Chaotic Mixing in Porous Media: from Pore Networks to Granular Systems
• The influence of finite size particles on fluid velocity and transport though porous media
• Is Chaotic Advection Inherent to Heterogeneous Darcy Flow?
• The impact of clogging on the transfer dynamics of hydraulic networks