Effect of non-uniform passive advection on A+B->C radial reaction-diffusion fronts&#160;
Authors: Comolli Alessandro , De Wit Anne , Brau Fabian 
Published: March 2021

&lt;p&gt;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-&gt;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.&lt;/p&gt;&lt;p&gt;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 &lt;em&gt;v&lt;sub&gt;r&lt;/sub&gt;(r,z)&lt;/em&gt; 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.&lt;/p&gt;&lt;p&gt;&amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &lt;img src=&quot;https://contentmanager.copernicus.org/fileStorageProxy.php?f=gnp.ff5ab530bdff57321640161/sdaolpUECMynit/12UGE&amp;app=m&amp;a=0&amp;c=360a1556c809484116c55812c8c06624&amp;ct=x&amp;pn=gnp.elif&amp;d=1&quot; alt=&quot;&quot; width=&quot;299&quot; height=&quot;299&quot;&gt;&amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160;&lt;img src=&quot;https://contentmanager.copernicus.org/fileStorageProxy.php?f=gnp.671a6980bdff51231640161/sdaolpUECMynit/12UGE&amp;app=m&amp;a=0&amp;c=c5a857c3fab835057e3af84001a91d15&amp;ct=x&amp;pn=gnp.elif&amp;d=1&quot; alt=&quot;&quot; width=&quot;302&quot; height=&quot;302&quot;&gt;&lt;/p&gt;&lt;p&gt;&amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160;Fig. 1: Concentration profile of the product C in the transient (left) and asymptotic (right) regimes.&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;References:&lt;/p&gt;&lt;p&gt;[1] L. G&amp;#225;lfi, Z. R&amp;#225;cz, Phys. Rev. A 38, 3151 (1988);&lt;/p&gt;&lt;p&gt;[2] F. Brau, G. Schuszter, A. De Wit, Phys. Rev. Lett. 118, 134101 (2017);&lt;/p&gt;&lt;p&gt;[3] A. Comolli, A. De Wit, F. Brau, Phys. Rev. E, 100 (5), 052213 (2019).&lt;/p&gt;