Fluid deformation in isotropic Darcy flow

The deformation of fluid elements governs many processes in porous media, including the transport, dispersion and mixing solutes, chemical reactions colloidal particles. Recently, it has been shown that even strongly heterogeneous steady three-dimensional (3-D) Darcy flow with isotropic hydraulic conductivity admits only constrained kinematics. This is due to its inherently helicity-free nature, as velocity everywhere orthogonal vorticity. property precludes braided streamlines instead a pair coherent 3-D streamfunctions, cannot wander freely throughout domain. In this study, we consider impact these kinematic constraints upon at scale. We show condition corresponds an streamline coordinate system, which use derive ab initio continuous time random walk framework for deformation. find combined intermittent nature shear events leads limited algebraic growth, stretching ranging from sublinear superlinear behaviour. Fluid remarkably similar two-dimensional (2-D) flow, structure fundamentally same two superposed 2-D flows. These results have implications understanding transport provide basis quantification flow.