J. Phys. Chem. C 2010, 114, 20141–20145
20141
Growth of Bubbles by Rectified Diffusion in Aqueous Surfactant Solutions Thomas Leong, Shuhui Wu, Sandra Kentish,* and Muthupandian Ashokkumar* School of Chemistry and Department of Chemical and Biomolecular Engineering, The UniVersity of Melbourne, VIC 3010, Australia ReceiVed: August 16, 2010; ReVised Manuscript ReceiVed: October 13, 2010
Bubbles grow by the rectified diffusion process in an acoustic field. While there is a thorough understanding of this process for the air-water system, only limited experimental data is available in the literature for aqueous solutions containing surfactants. In order to expand the experimental database, we have determined the bubble growth rate by the rectified diffusion process in aqueous solutions containing sodium dodecyl sulfate (SDS) at various concentrations. Compared to water, the growth rate is higher in SDS solutions. The addition of 0.1 M sodium chloride to SDS results in a further enhanced growth rate at lower bulk concentrations of the surfactant. These results suggest that the surface loading of surfactant molecules plays a key role in enhancing the growth rate, likely due to an increase in the mass transfer resistance during the compression phase of the bubble oscillations. This is supported by results for the growth rates determined for dodecyl trimethylammonium chloride with the growth rate for a given equilibrium surface concentration higher than that of SDS. The experimentally determined bubble oscillation amplitudes for both surfactants decline relative to that of water, consistent with previously published models. Introduction The basis of many applications of ultrasound is acoustic cavitation, the formation, growth, and collapse of microbubbles,1 resultant from pressure fluctuations that occur in an applied sound field. These bubbles can undergo a range of different behaviors.2 They dissolve, coalesce, or leave the system entirely. Bubbles can also grow in size over many acoustic cycles, through a process known as rectified diffusion. This behavior is well-understood for simple air-water systems, and models have been developed to predict the bubble motion3-6 and rectified diffusion growth.7,8 Less understood is the cavitation behavior of bubbles in complex solutions containing surface active materials such as alcohols and surfactants. Improving the fundamental understanding of bubble dynamics in the presence of such species is important for many sonoprocessing applications in industry. Processes such as ultrasonic emulsification and polymerization, for example, utilize surface active species to influence not just the bubble behavior, but the critical product criteria such as size distribution and product stability. To date, models developed for rectified diffusion in the presence of surfactants at various ultrasonic frequencies significantly underestimate the growth rate measured in experiments. This is because there is no simple correlation between the rate of growth and the surface activity of the species introduced into solution. Another reason for the lack of understanding is the difficulty of isolating the effect of rectified diffusion in a sound field when many bubbles are present, as the effect of coalescence additionally serves to grow bubbles.9 Indirect evidence on the role of rectified diffusion in multibubble systems and the effect of surface active solutes has been documented by Ashokkumar and co-workers.2,10,11 However, direct experimental studies of rectified diffusion in the presence of surfactants remain limited. Initial experiments were conducted by Crum in 1980.12 However, these utilized an indirect method * To whom correspondence should be addressed. E-mail: sandraek@ unimelb.edu.au (S.K.),
[email protected] (M.A.).
for measuring bubble size based on bubble buoyancy. Further, only a commercial surfactant, Photoflo, was utilized, which made it difficult for results to be related to any fundamental surfactant parameters. This was followed by the work of our group,13 which measured the growth rate of a single bubble in solutions of the anionic surfactants sodium dodecyl sulfate (SDS) and sodium dodecyl benzenesulfonate (SDBS). Both studies12,13 showed that the rate of bubble growth significantly exceeded that expected from consideration of surface tension effects alone. A number of reasons have been postulated for this increase in diffusion rate. Crum12 speculated that it could arise from enhanced acoustic streaming. Fyrillas and Szeri14 built a sophisticated mathematical model based on the premise that the surfactant layer added to the mass transfer resistance of air flowing in and out of the bubble and that this was the cause of the more rapid growth. Other workers15-19 describe the effects of insoluble surface layers around bubbles using the principles of interfacial rheology. In this case, the surface active species is described in terms of a monolayer with interfacial tension and interfacial viscosity, both of which are a function of the two-dimensional surface concentration (surface excess; Γ) at the air/water interface. The surface excess in turn is an inverse function of bubble radius (Γ∝ R-2). These workers15-19 have shown that a surface layer of polymer or surfactant can impart additional resistance to the movement of the interface and so substantially reduce the amplitude of bubble oscillation in tension and compression. They offer no explanation as to how such amplitude reduction can result in rectified diffusion. However, it is possible that asymmetrical behavior caused by variations in interfacial viscosity could result in similarly asymmetrical behavior in the mass transfer of gas into and out of the bubble and thus potentially result in rectified diffusion. The focus of this paper is to present new data for rectified diffusion growth of bubbles in surfactant solutions. The aim is to clarify the mechanism responsible for the increased growth rate of bubbles in the presence of charged surfactants. Thus,
10.1021/jp107731j 2010 American Chemical Society Published on Web 11/04/2010
20142
J. Phys. Chem. C, Vol. 114, No. 47, 2010
Leong et al.
Figure 1. The experimental setup for the single bubble rectified diffusion experiments.
the present study not only expands the database of previous work but also provides a fundamental understanding of the rectified diffusion process.
Interfacial tension was measured by the Wilhemy plate method using an Analite 2141 surface tension meter. This data was used to calculate equilibrium surface excess concentrations (Γ) using the Gibbs isotherm.20
Experimental Details Experiments used two surfactants, SDS (VWR international, purity >99%) and dodecyl trimethylammonium chloride (DTAC; TCI Japan, purity >99%). Sodium chloride was supplied by Merck Germany (NaCl, purity >99.5%). All solutions were made up in Milli-Q water (Millipore 0.22 µm pore size, conductivity
