DISSOLUTION OR GROWTH OF SOLUBLE SPHERICAL OSCILLATING BUBBLES - THE EFFECT OF SURFACTANTS

A new theoretical formulation is developed for the effects of surfacta nts on mass transport across the dynamic interface of a bubble which u ndergoes spherically symmetric volume oscillations. Owing to the prese nce of surfactants, the Henry's law boundary condition is no longer ap plicable; it is replaced by a flux boundary condition that features an interfacial resistance that depends on the concentration of surfactan t molecules on the interface. The driving force is the disequilibrium partitioning of the gas between free and dissolved states across the i nterface. As in the clean surface problem analysed recently (Fyrillas and Szeri 1994), the transport problem is split into two parts: the sm ooth problem and the oscillatory problem. The smooth problem is treate d using the method of multiple scales. An asymptotic solution to the o scillatory problem, valid in the limit of large Peclet number, is deve loped using the method of matched asymptotic expansions. By requiring that the outer limit of the inner approximation match zero, the splitt ing into smooth and oscillatory problems is determined unambiguously i n successive powers of P--1/2, where P is the Peclet number. To leadin g order, the clean surface solution is recovered. Continuing to higher order it is shown that the concentration held depends on R(I)P(-1/2), where R(I) is the (dimensionless) interfacial resistance associated w ith the presence of surfactants. Although the influence of surfactants appears at higher order in the small parameter, surfactants are shown to have a very significant effect on bubble growth rates owing to the fact that the magnitude of R(I) is approximately the same as the magn itude of P-1/2 at conditions of practical interest. Hence the higher-o rder 'corrections' happen numerically to be of the same magnitude as t he leading-order, clean surface problem. This is the fundamental reaso n for major increases in the bubble growth rates associated with the a ddition of surfactants. This is in contrast to the case of a still, su rfactant-covered bubble, in which the first-order correction to the gr owth rate is of order R(I)P(-1) and presents a P--1/2 correction. Fina lly although existing experimental results have shown only enhancement of bubble growth in the presence of a surfactant the present theory s uggests that it is possible for a surfactant, characterized by weak de pendence of interfacial resistance on surface concentration, to inhibi t rather than enhance the growth of bubbles by rectified diffusion.