Session A25: Bubbles: Collapse I

Shock wave interactions in single-bubble collapse near a corner

Damage to neighboring surfaces due to repeated bubble collapse is one of the most important consequences of cavitation, which can be found in a multitude of hydraulic systems. A number of experimental studies have been conducted to predict the dynamics of re-entrant jets as well as bubble migration in a corner. However, the temperatures and pressures during the collapse have yet to be investigated. In this study, we quantify the effects of bubble-boundary interactions on the bubble dynamics and the temperatures/pressures produced by the collapse of a single bubble near two perpendicular rigid surfaces. For this purpose, we use an in-house, high-order accurate shock- and interface-capturing method to solve the 3D compressible Navier-Stokes equations for gas/liquid flows. The non-spherical bubble dynamics are investigated, and the subsequent pressure and temperature fields are characterized based on the relevant parameters entering the problem: geometry, stand-off distances from each surface, driving pressure. We demonstrate that bubble-boundary interactions amplify/reduce pressures and temperatures produced during the collapse and increase the collapse time and the non-linearity of the bubble displacement, depending on geometric parameters.   

The role of compressibility and vorticity in the collapse of a bubble near a rigid boundary

Cavitation-bubble collapse is known to cause structural damage in a variety of industrial applications such as naval hydrodynamics and turbomachinery. The concentration of energy and shock emission during the non-spherical collapse is expected to depend on the liquid compressibility, and possibly the vorticity produced during the process. Thus, a better understanding of role of compressibility and vorticity is essential to predicting cavitation erosion. In this study, we compare direct simulations to potential flow calculations to extract the effects of compressibility and vorticity on the collapse of a gas bubble near a rigid boundary. The 3D compressible Navier-Stokes are solved in the gas and liquid using a high-order shock- and interface-capturing scheme; potential calculations are conducted using a boundary integral method. We observe a delay between the two approaches, attributed to the differences in the pressure fields at early times due to compressibility effects. Nevertheless, bubble morphologies are similar for most of the collapse, with discrepancies visible only in the last stage of collapse. The vorticity evolving during the collapse may plays a role on the bubble dynamics at this stage.   

Collapse of individual bubbles near rigid boundaries

Cavitation happens in a variety of applications ranging from naval hydrodynamics to biomedical ultrasound. The inertial collapse of cavitation bubbles concentrates energy into a small volume, and is capable of producing high pressures and temperatures and emitting radially propagating shock waves. One important consequence of such phenomenon is structural damage to neighboring objects following repeated collapse of cavitation bubbles. In order to provide a better understanding of this problem, we perform high-resolution numerical simulations of the inertial collapse of individual bubbles near rigid surfaces by solving the three-dimensional compressible Navier-Stokes equations for gas/liquid systems. By considering the collapse of a single bubble as well as a bubble pair near a rigid surface, we explain that the bubble-boundary and/or bubble-bubble interactions can affect the energy concentration, give rise to the kinetic energy of non-converging motions, and break the symmetry of the collapse that modify the pressures and temperatures thereby produced. The results are used to investigate the non-spherical bubble dynamics and characterize the pressure and temperature fields based on the relevant parameters entering the problem: initial stand-off distance, distance and angle between the two bubbles, and driving pressure This work was supported by ONR grant N00014-12-1-0751 under Dr. Ki-Han Kim.   

The diameters and velocities of the jet droplets produced after bubble bursting

Here we provide a theoretical framework revealing that the radius $R_d$ of the top droplet ejected from a bursting bubble of radius $R_b$ can be expressed as $R_d=0.22\,R_b\,\left(1-\left(\frac{Oh}{Oh'_c}\right)^{1/2}\right)$ for $Oh\leq Oh'_c\simeq 0.03$ and $Bo\leq 0.1$ with with $Oh=\mu/\sqrt{\rho R_b\sigma}\ll 1$ the Ohnesorge number, $Bo=\rho g R_b^2/\sigma$ the Bond number and $\rho$, $\mu$ and $\sigma$ the liquid density, viscosity and surface tension coefficient respectively. This prediction, which agrees very well with both experimental data and numerical simulations for all the values of $Oh$ and $Bo$ investigated, can be particularized to express the diameters of the jet droplets produced from the bursting of sea bubbles with radii $R_b\leq 1$ mm, with implications in marine aerosol production. The velocities of the first drops ejected are also expressed as a function of $Oh$ and $Bo$, being this initial drop velocity largely reduced by air drag at tiny distances $\sim R_b$ above the interface. We find that the ratio between the radius of curvature at the tip of the jet and the jet radius controls the growth of capillary instabilities, a fact explaining why no droplets are ejected from the tip of the fast Worthington jet for values of $Oh$ slightly larger than $Oh'_c$.   

Bubble formation and collapse on the ridge and groove of a solid surface

The dynamics of a single bubble collapsing near a ridge-patterned structure are investigated experimentally to find how the ridge pattern affects the damage on structure by the collapsed bubble. When a bubble formed by sparking electrodes in water collapses above the ridge of the structure, a bubble-splitting jet or a structure-ward collapse with strong reentrant jet occurs depending on the geometry of the structure surface. The boundary which divides the two collapse modes is derived theoretically using a potential flow model, and it is in excellent agreement with experimental results. Meanwhile, when a bubble collapses above the groove of the structure, water flows entrained from the tops of neighboring ridges collide with each other before reaching the bottom of the groove. Because part of the kinetic energy is dissipated in the form of a pressure wave by the collision, the strength of the bubble reentrant jet, which is a major cause of cavitation erosion, is expected to reduce accordingly. The effect of the reentrant jet on surface erosion is confirmed by our simple test for damage assessment.   

Non-Newtonian bubbles: dynamics of colloidal film rupture

A Newtonian soap bubble ruptures on the timescale of milliseconds, and this rupture grows at a constant rate [1]. Inspired by recent work [2] where films with high surfactant concentration developed crack-like instabilities during rupture, we investigate whether soap films with colloidal particles (\textasciitilde 1 micron) show similar behavior. We rupture a flat film containing surfactant and colloidal spheres using a needle and record it with a high-speed camera at 83,000 frames per second. By varying colloidal volume fraction, we can access a wide range of non-Newtonian behavior. We find that rupturing colloidal films exhibit a wide variety of instabilities, and their occurrence is sensitive to film thickness. We systematically study film rupture dynamics as a function of film thickness and colloidal volume fraction. Surprisingly, the rupture opens at a constant rate even at high colloidal volume fraction, but this rate is significantly slower than the Culick velocity. [1] F. E. C. Culick, Journal of Applied Physics(1960), \quad [2] Petit, P., Le Merrer, M., {\&} Biance, A., Journal of Fluid Mech(2015)