The Effect of Surfactants on Bubble Growth

In the majority of publications devoted to research of diffusion growth of gas bubbles in a supersaturated solution, the coefficient of surface tension S is considered to be constant and the quantity of gas entering the bubble is determined by the diffusion flux of gas dissolved in the liquid at the bubble surface. In reality, the solution, for example, a natural hydrocarbon mixture, will always contain surfactants which, being adsorbed at the interface, reduce S on the one hand, and on the other hand, interfere with the transition of dissolved substance from the solution to the bubble. The effect of surfactants on the value of S is known [4). As to the influence of surfactants on the transition of gas from the dissolved state into the gaseous one, this effect is poorly studied. 

To examine the influence of surfactants on bubble growth, consider the following problem. A spherical gas bubble is placed in a binary solution, supersaturated at the given pressure and temperature. As a result, there emerges a diffusion flux toward the bubble surface. The process is accompanied by adsorption of a surfactant, which is present in the liquid, on the bubble surface. Assume that the process is diffusion-controlled, i.e. adsorption-desorption of surfactant molecules at the interface occurs sufficiently quickly. In such a case, the surface concentration of surfactant T may be taken equal to the equilibrium value [4]  

During the adsorption of surfactant molecules on the gas-liquid interface, a monomolecular layer is formed. At low surface concentrations of the surfactant 

One noteworthy attempt to take into account the effect of the surfactant film at the bubble surface on the rate of diffusion growth was made in [5]. It is based on the assumption that the intensities of substance transfer through a surface free from surfactants and through a surface covered by a surfactant are characterized by different diffusion factors. The proposed model introduced a number of parameters, whose determination requires extensive experimental work that involves different surfactants. 

The considered process is described by the following system of equations  

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