3D FLUID DEFORMATION AND MIXING VIA A CONTINUOUS TIME RANDOM WALK

Abstract:

Fluid stretching and deformation as quantified by the fluid deformation gradient tensor directly controls mixing of diffusive species in both chaotic and non-chaotic, 2D and 3D flows at the pore- and Darcy scales. Indeed, recent advances [LeBorgne et. al. PRL, 110, 204501, 2013] in the prediction of mixing and scalar dissipation require the distribution of fluid deformation rates as quantitative inputs. However, these measures are often difficult to link to medium properties or statistical heterogeneity controls. To advance this problem, we present a novel Continuous Time Random Walk (CTRW) to model stochastic evolution of the 3D fluid deformation tensor in a Protean (streamline) coordinate frame. This approach allows topological constraints imposed by the flow kinematics to be naturally obeyed, and furthermore flow features that generate non-Fickian transport can be clearly elucidated. For simple flows, this framework allows the distribution of deformation rates (and hence mixing) to be expressed in terms of heterogenenity controls, and for more complex flows, this approach clearly identifies what flow features govern anomalous transport and how their statistics can be measured as model inputs.