InterPore2026

Shear versus exponential stretching as drivers for mixing in porous media flows

20 May 2026, 15:35

1h 30m

Poster Presentation (MS09) Pore-Scale Physics and Modeling Poster

Speaker

Manuel Maeritz (University of Rennes 1)

Description

Solute mixing in porous media results from the interplay between molecular diffusion and the deformation of fluid parcels as they flow through the pore space. In three-dimensional porous media, fluid deformation is asymptotically governed by exponential stretching of fluid elements, induced by saddle points in the velocity field transverse to the mean flow direction (highlighted by black crosses in Fig. 1c). At early times, however, deformation may be dominated by liner elongations due to shear in direction longitudinal to the streamlines, induced by no-slip boundary conditions at grain surfaces. The shear inducing velocity field is illustrated in Fig. 1b, showing strong velocity heterogeneity in the cross section of the flow longitudinal to the mean flow direction. Early time deformation may play an important role for mixing and reaction as this regime is characterized by large concentration gradients. Yet, the relative contributions of exponential stretching and linear shear to fluid deformation and solute mixing remain poorly understood. Here, we address this question using numerical simulations of fluid deformation and mixing in body-centered cubic bead packs (the unit cell is presented in Fig. 1a), where the rate of exponential stretching can be varied with the direction of flow, while maintaining the same average shear rate. We quantify the deformation of elementary surfaces and their consequences on mixing through Lagrangian methods [1]. We show that shear not only dominates at early time but also induces a persistent excess of deformation with respect to pure exponential stretching. By expressing the deformation components in streamline coordinates [2], we derive approximate analytical expressions linking the different components of fluid deformation to shear, helicity and chaotic stretching. We discuss consequences for the mixing of solute sheets [1] and blobs [3], highlighting generic behaviors as well as fundamental differences between these two representations.