Effect of non-uniform passive advection on A+B->C radial reaction-diffusion fronts 

Abstract

<p>The interplay between chemical and transport processes can give rise to complex reaction fronts dynamics, whose understanding is crucial in a wide variety of environmental, hydrological and biological processes, among others. An important class of reactions is A+B->C processes, where A and B are two initially segregated miscible reactants that produce C upon contact. Depending on the nature of the reactants and on the transport processes that they undergo, this class of reaction describes a broad set of phenomena, including combustion, atmospheric reactions, calcium carbonate precipitation and more. Due to the complexity of the coupled chemical-hydrodynamic systems, theoretical studies generally deal with the particular case of reactants undergoing passive advection and molecular diffusion. A restricted number of different geometries have been studied, including uniform rectilinear [1], 2D radial [2] and 3D spherical [3] fronts. By symmetry considerations, these systems are effectively 1D.</p><p>Here, we consider a 3D axis-symmetric confined system in which a reactant A is injected radially into a sea of B and both species are transported by diffusion and passive non-uniform advection. The advective field <em>v<sub>r</sub>(r,z)</em> describes a radial Poiseuille flow. We find that the front dynamics is defined by three distinct temporal regimes, which we characterize analytically and numerically. These are i) an early-time regime where the amount of mixing is small and the dynamics is transport-dominated, ii) a strongly non-linear transient regime and iii) a long-time regime that exhibits Taylor-like dispersion, for which the system dynamics is similar to the 2D radial case.</p><p>                                  <img src="https://contentmanager.copernicus.org/fileStorageProxy.php?f=gnp.ff5ab530bdff57321640161/sdaolpUECMynit/12UGE&app=m&a=0&c=360a1556c809484116c55812c8c06624&ct=x&pn=gnp.elif&d=1" alt="" width="299" height="299">                                                     <img src="https://contentmanager.copernicus.org/fileStorageProxy.php?f=gnp.671a6980bdff51231640161/sdaolpUECMynit/12UGE&app=m&a=0&c=c5a857c3fab835057e3af84001a91d15&ct=x&pn=gnp.elif&d=1" alt="" width="302" height="302"></p><p>                                                   Fig. 1: Concentration profile of the product C in the transient (left) and asymptotic (right) regimes.</p><p> </p><p>