Circulation and reaction enchancement of mass transport in a cavity

We numerically examine the mass transport into a fluid in the classical driven cavity problem and in the limit of large Péclet number, Pe. The species absorbed into the fluid is allowed to undergo a simple first-order chemical reaction. Two particular types of boundary conditions are imposed: a macroscopic gradient between the bottom and top surface and a zero-flux condition. We demonstrate that, in the absence of a chemical reaction and when a macroscopic gradient is present, mass transport into the liquid is enhanced due to a recirculation zone in the cavity which is connected to the top and bottom surfaces through two boundary layers. The corresponding enhancement is large and scales as Pe^1/2. In the presence of a chemical reaction with rate constant k, adsorption into the liquid is further enhanced with the flux at the top surface now scaling as k^1/2 for k≫Pe. However, for k=O(Pe), the chemical reaction removes the central spatially uniform concentration region from the cavity as well as the boundary layer at the bottom wall.