PMID: 23030879Oct 4, 2012

Impact of structured heterogeneities on reactive two-phase porous flow

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Daniel Reeves, Daniel H Rothman

Abstract

Two-phase flow through heterogeneous media leads to scale-free distributions of irregularly shaped pockets of one fluid trapped within the other. Although reactions within these fluids are often modeled at the homogeneous continuum scale, there exists no current framework for upscaling from the pore scale that accounts for the complex and scale-free geometry of the bubbles. In this paper, we apply a linear-kinetics reaction-diffusion model to characterize the steady-state chemical environment inside the irregular pockets. Using a combination of theory and invasion-percolation simulations, we derive scaling laws describing the distribution of diffusion times within bubbles. We show that chemical concentrations within the bubbles are determined by the Laplace transform of the entire distribution of diffusion times from each location. This serves as a means to compute average concentrations of reactant within a bubble of unique geometry and size. Furthermore, the overall system size imposes upper bounds on the distribution of bubble sizes, thereby imposing a system-size dependence on the statistics and average concentrations. These conclusions have profound implications for continuum models of porous reactive flow, where kinetic a...Continue Reading

References

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Citations

Mar 21, 2015·Proceedings. Mathematical, Physical, and Engineering Sciences·Yossi Cohen, Daniel H Rothman

Related Concepts

Body Fluids
Environment
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Chemicals
Blood Flow
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