Vertical shear affects chemical front speed in thin-layer flows

The dynamics of a chemical reaction in a flow can be described through the motion of a front which divides reacted from unreacted regions. These fronts advance because of the production of new reaction product and are advected by flow, so we expect the front velocity to be the vector sum of a constant chemical velocity and the flow velocity, consistent with the Eikonal equation. However, in previous quasi-two-dimensional experiments we measured chemical velocities many times larger than expected, and they seemed to increase with flow velocity. Vertical shear explains the discrepancy, even in the absence of out of plan flow such as from Ekman pumping. We present simulations using the Eikonal equation and accounting for shear, resulting in a close match to chemical velocities measured in our experiments. We also show that adding a lubrication layer reduces shear and makes experimental measurements of chemical velocity match two-dimensional theory more closely. Compensating for vertical shear may allow more accurate identification of the flow structures which cause other advection-reaction-diffusion phenomena like extinction.