Dynamic equilibrium model for stable nano- and micro-bubbles partly covered with hydrophobic material

Abstract

In the dynamic equilibrium model, a bubble is only partly covered with hydrophobic material in contrast to the skin model that a bubble is completely covered with organic material. On the surface of the hydrophobic material in water, gas is highly concentrated due to the presence of depletion layer. Then, gas diffuses into a bubble near the peripheral edge of the hydrophobic material, which may balance with the gas diffusion out of a bubble from the other part of the uncovered bubble surface due to the higher internal gas pressure than the partial pressure of gas dissolved in the liquid water by the Laplace pressure. In the present study, not only the condition of the mass balance but also that of stability is numerically calculated. The results have indicated that a nanobubble could be stable when the fraction of the surface coverage by the hydrophobic material is more than 0.5 in water both supersaturated and under-saturated with gas (air). In slightly degassed water, a microbubble could be stabilized when the fraction of the surface coverage is on the order of 10-4 or less. These bubbles could play an important role in underwater acoustics as well as in acoustic cavitation.