Numerical simulations of a buoyant autocatalytic reaction front in tilted Hele-Shaw cells

We present a numerical analysis of solutal buoyancy effects on the shape and the velocity of autocatalytic reaction fronts, propagating in thin tilted rectangular channels. We use two-dimensional (2D) lattice Bathnagar-Gross-Krook (BGK) numerical simulations of gap-averaged equations for the flow and the concentration, namely a Stokes-Darcy equation coupled with an advection-diffusion-reaction equation. We do observe stationary-shaped fronts, spanning the width of the cell and propagating along the cell axis. We show that the model accounts rather well for experiments we performed using an Iodate Arsenous Acid reaction propagating in tilted Hele-Shaw cells, hence validating our 2D modelization of a three-dimensional problem. This modelization is also able to account for results found for another chemical reaction (chlorite tetrathionate) in a horizontal cell. In particular, we show that the shape and the traveling velocity of such fronts are linked with an eikonal equation. Moreover, we show that the front velocity varies nonmonotonically with the tilt of the cell, and nonlinearly with the width of the cell.