Acceleration of reaction fronts by hydrodynamic instabilities in immiscible systems

We are studying the propagation of a reaction front in an immiscible liquid-liquid system under the condition of a mass transfer across the interface accompanied by a neutralization reaction. The system, when placed in a vertical Hele-Shaw cell, shows a buoyancy-driven cellular structure penetrating into the aqueous bulk solution. By tilting the Hele-Shaw cell to the horizontal position, the penetrative convection vanishes in favor of a planar reaction front. At higher acid concentrations this reaction-diffusion state is replaced by a Marangoni convection interacting with the front propagation. We show that the scaling behavior of the reaction front position, x(f), with time shows a characteristic crossover. In the long-time limit all systems obey x(f) similar to t(0.49 +/- 0.02) and differ only in the timespan needed to enter this diffusion-controlled state. For an intermediate time all reaction-diffusion systems display a x(f) similar to t(1.50 +/- 0.06) law. Both convection types observed in the system operate at Damkohler numbers, Da similar to 0.1, and lead to an acceleration of the front propagation by at least a factor of four. The influence of the Marangoni convection is even stronger at the beginning due to the higher flow velocities, v similar to 0.2 mm/s. However, Marangoni convection rapidly relieves the driving concentration gradients. Therefore, the buoyancy-driven convection wins the competition with respect to the front acceleration for intermediate and long times. (c) 2006 Elsevier Ltd. All rights reserved.