Cavitation dynamics of surface nanobubbles
Dockar, Duncan Alexander
Cavitation is the fluid phenomenon where a bubble of gas or vapour can spontaneously form in a liquid in response to a local drop or variation in pressure. Unlike bubbles formed from other types of processes such as boiling, cavitation bubbles can become highly unstable due to their sensitivity to fluctuations in pressure. These cavitation bubbles can very rapidly expand many orders of magnitude in size, in what is sometimes referred to as “explosive” growth; when they collapse, they often release a high-speed liquid jet, which can lead to pitting and erosion if directed onto a solid surface. Cavitation is a problem often encountered in engineering, such as in turbomachinery, where the repeated formation and collapse of these bubbles can cause major structural damage. More recently, engineers have aimed to exploit the high-speed jet dynamics during cavitation bubble collapse for novel applications at the nano to microscale, such as in surface cleaning, diagnostics and cancer treatment. Around 20 years ago, spherical-cap shaped nanoscale bubbles were found to be able to exist long-term on solid substrates under certain experimental conditions. These newly discovered “surface nanobubbles” were of scientific interest as their resistance to dissolution seemed to contradict previous Epstein-Plesset theory on the general unstable diffusive equilibrium of bubbles. They were confirmed to be diffusively stable if the surrounding liquid was supersaturated with dissolved gas, and the substrate had surface heterogeneities, such as roughness or chemical patterning, such that the bubble’s three-phase contact line was pinned to the substrate. This contact line pinning resulted in a constant contact radius (CCR) mode of growth unique to surface nanobubbles, where the radius of curvature would begin to decrease during expansion, contrary to the radial growth typically found in spherical bubbles. Surface nanobubbles initially seemed to provide a convenient explanation for the heterogeneous nucleation of cavitation bubbles. However, early experiments found that they did not respond as expected to pressure drops intended to induce cavitation growth. Most of the classical analyses for cavitation assume a spherical bubble immersed in an infinite liquid. This results in models which are mathematically simple and usually suitable for most applications, however, surface nanobubbles have a spherical cap shape and typically grow with a pinned contact line, and so the classical spherical bubble models were found not to be suitable for these cases. The research in this thesis investigates the cavitation dynamics of pinned surface nanobubbles using Molecular Dynamics (MD) simulations. The cavitation threshold for unstable growth, the growth rate and oscillation dynamics, and finally the collapse of pinned surface nanobubbles are simulated and investigated further here. Results are compared to the corresponding classical spherical bubble equations, and improved models are proposed, where appropriate, to account for their different observed cavitation dynamics. Most of the surface nanobubbles’ unique behaviour arises from their pinned mode of growth. The surface tension contribution across the liquid-gas interface (the Laplace pressure) is found to increase during growth of the surface nanobubble due to the CCR mode of growth, which is the opposite effect to spherical bubbles. Surface nanobubbles are found to be able to resist pressures many mega-Pascals (MPa) lower than that predicted by the classical Blake threshold equation for unstable growth of spherical bubbles. A new model is derived to more accurately predict this cavitation threshold for surface nanobubbles, which captures their spherical cap shape and pinned growth. The proposed model suggests that the smallest surface nanobubbles can be resistant to pressures as low as −28 MPa. Critical discussions are also made on experimental findings that suggested that 300 nm bubbles were resistant to pressures of −6 MPa. The classical Rayleigh-Plesset equation for spherical bubbles is modified to be more suitable for surface nanobubbles, accounting for their spherical cap shape and Laplace pressure variation, which could accurately predict their growth rate and oscillation dynamics. The natural frequency of surface nanobubbles is also found through linearised analyses of this newly derived growth rate model. The proposed natural frequency is compared to other models for bubbles, such as the classical Minnaert frequency, and was found to be better at capturing the surface nanobubble’s oscillation dynamics. The MD simulation set-up is also critically examined for accurately modelling the pressure variations acting on the surface nanobubbles. The surface nanobubbles are found to collapse less violently than spherical bubbles, since the cavitation jets have less time to develop before impacting the solid surface. Despite the collapsing surface nanobubbles causing less damage, the resulting pit shapes were found to be similar to the pit shapes from spherical bubble collapse, with the perimeters of the pits typically scaling with the maximum bubble size before collapse. The internal gas phase is found to decelerate the jet formation, and reduce the resulting damage, through comparisons to the collapse of vapour bubbles. No toroidal rebounding bubbles were observed in the collapsing surface nanobubbles, which is a common occurrence in spherical bubble collapse, as the jets do not flow outward from the impact centre after impact on the substrates. The findings presented here should provide an improved understanding for the design of microfluidic engineering processes where the cavitation dynamics of pinned surface nanobubbles are to be utilised.