Influence of heat losses on nonlinear fingering dynamics of exothermic autocatalytic fronts

Across traveling exothermic autocatalytic fronts, a density jump can be observed due to changes in composition and temperature. These density changes are prone to induce buoyancy-driven convection around the front when the propagation takes place in absence of gel within the gravity field. Most recent experiments devoted to studying such reaction-diffusion-convection dynamics are performed in Hele–Shaw cells, two glass plates separated by a thin gap width and filled by the chemical solutions. We investigate here the influence of heat losses through the walls of such cells on the nonlinear fingering dynamics of exothermic autocatalytic fronts propagating in vertical Hele–Shaw cells. We show that these heat losses increase tip splittings and modify the properties of the flow field. A comparison of the differences between the dynamics in reactors with respectively insulating and conducting walls is performed as a function of the Lewis number LeLe, the Newton cooling coefficient αα quantifying the amplitude of heat losses and the width of the system. We find that tip splitting is enhanced for intermediate values of αα while coarsening towards one single finger dominates for insulated systems or large values of αα leading to situations equivalent to isothermal ones.