Mixing and Bimolecular Reactions in Heterogeneous Porous Media Flows
Transport, Mixing and Reactions
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This book addresses the coupling of a bimolecular transformation reaction with bounded rectilinear and spatially heterogeneous subsurface flows. It is shown that due to the action of local dispersion, at large time, the cross covariance budget is characterized by a balance between its rate of production and dissipation. This results in deriving a formula for effective reaction rate given by _eff [1+2 D_ij (( lnC_1) ( x_i ))(( lnC_2) ( x_j )) ] that accounts for the influence of concentration microstructure and small-scale mixing on the macroscopic bimolecular kinetics. For rectilinearly varyin...
This book addresses the coupling of a bimolecular transformation reaction with bounded rectilinear and spatially heterogeneous subsurface flows. It is shown that due to the action of local dispersion, at large time, the cross covariance budget is characterized by a balance between its rate of production and dissipation. This results in deriving a formula for effective reaction rate given by _eff [1+2 D_ij (( lnC_1) ( x_i ))(( lnC_2) ( x_j )) ] that accounts for the influence of concentration microstructure and small-scale mixing on the macroscopic bimolecular kinetics. For rectilinearly varying flows, a theoretical bound (using variational calculus) on dissipation time scale ( ) is shown to be a tight bound. The formulation for reaction macro-kinetics developed here provides a way to represent the influence of reactant concentration microstructure in large-scale descriptions of reactive transport. The book should be useful to Theoretical Physicists, Theoretical Chemists, Mathematical Modelers, Computational (or Numerical) Modelers, Hydrogeologists, Turbulence enthusiasts, Civil, Chemical and Environmental Engineers.
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