The Path to Hydrodynamic Instability During Reactions at Liquid Interfaces: Comparison of Experimental Image Analysis Results and Simulations

Abstract

The photoreduction of Fe⁺³ to Fe⁺² which leads to patterns of photoproducts and to convections, was analysed by computerized image analysis of the concentration gradients along the vertical gravity axis, (perpendicular to the horizontal, covered, layer product). The observed time-evolution of the concentration profiles was analysed by modeling it with the actual photochemical reaction kinetics coupled to the diffusion of the components. Good agreement between experiments and simulations was obtained (see e.g., Fig. 4). The time evolution of the Rayleigh number of the reacting system was obtained by numerical solution of the appropriate one-dimensional reaction/diffusion equations, employing a recently developed Fast Fourier Transform algorithm. The calculated time for reaching the Rayleigh critical value of about 660 (two free boundaries) was in close agreement with the experimental value for the time of onset of convections (around 310 sec for both), and in agreement with the experimental system of a rigid cover (top) and a free liquid interface (bottom). It was also found that such a chemical reaction accelerates the evolution time of the hydrodynamic instability, compared to a double-diffusion system without a reaction.