Model for the growth and the oscillation of a cavitation bubble in a spherical liquid-filled cavity enclosed in an elastic medium

Radial oscillation and translational motion of a gas bubble in a micro-cavity

According to classical nucleation theory, a gas nucleus can grow into a cavitation bubble when the ambient pressure is negative. Here, the growth process of a gas nucleus in a micro-cavity was simplified to two "events", and the full confinement effect of the surrounding medium of the cavity was considered by including the bulk modulus in the equation of state. The Rayleigh-Plesset-like equation of the cavitation bubble in the cavity was derived to model the radial oscillation and translational motion of the cavitation bubble in the local acoustic field. The numerical results show that the nucleation time of the cavitation bubble is sensitive to the initial position of the gas nucleus. The cavity size affects the duration of the radial oscillation of the cavitation bubble, where the duration is shorter for smaller cavities. The equilibrium radius of a cavitation bubble grown from a gas nucleus increases with increasing size of the cavity. There are two possible types of translational motion: reciprocal motion around the center of the cavity and motion toward the cavity wall. The growth process of gas nuclei into cavitation bubbles is also dependent on the compressibility of the surrounding medium and the magnitude of the negative pressure. Therefore, gas nuclei in a liquid cavity can be excited by acoustic waves to form cavitation bubbles, and the translational motion of the cavitation bubbles can be easily observed owing to the confining influence of the medium outside the cavity.

Spherical oscillations of encapsulated microbubbles: Effect of shell compressibility and anisotropy

We introduce a model that describes spherical oscillations of encapsulated microbubbles in an unbounded surrounding fluid. A Rayleigh-Plesset-like equation is derived by coupling the Navier-Stokes equation that describes fluid dynamics with the Navier equation that describes solid dynamics via the internal/external boundary conditions. While previous models were restricted to incompressible isotropic shells, the solid shell is modeled here as a compressible viscoelastic isotropic material and then generalized to an anisotropic material. The exact value of the resonance frequency is calculated analytically, and the damping constant is computed in the approximation of weak damping. A correction of the widely used Church model for incompressible shells is evidenced, and the effects of shell compressibility and anisotropy are discussed.

Accelerated Formation of H2 Nanobubbles from a Surface Nanodroplet Reaction

The compartmentalization of chemical reactions within droplets has advantages in low costs, reduced consumption of reagents, and increased throughput. Reactions in small droplets have also been shown to greatly accelerate the rate of many chemical reactions. The accelerated growth rate of nanobubbles from nanodroplet reactions is demonstrated in this work. The gaseous products from the reaction at the nanodroplet surface promoted nucleation of hydrogen nanobubbles within multiple organic liquid nanodroplets. The nanobubbles were confined within the droplets and selectively grew and collapsed at the droplet perimeter, as visualized by microscopy with high spatial and temporal resolutions. The growth rate of the bubbles was significantly accelerated within small droplets and scaled inversely with droplet radius. The acceleration was attributed to confinement from the droplet volume and effect from the surface area on the interfacial chemical reaction for gas production. The results of this study provide further understanding for applications in droplet enhanced production of nanobubbles and the on-demand liberation of hydrogen.

Acoustic analysis of ultrasonic assisted soldering for enhanced adhesion

Ultrasonic soldering utilizes high-intensity acoustic fields to induce cavitation in the solder melt in order to (i) bond dissimilar materials and (ii) improve solder joint strength. The acoustic energy transfer from the piezoelectric transducer (PZT) into the liquid solder pool is critical in both understanding and optimizing this process. We use finite element analysis of the acoustics and compare with experiment. Our finite-element modeling approach is two-pronged; (i) we develop a one-dimensional model that is used as a design tool to optimize the solder stack geometry to match the transducer frequency for maximal acoustic energy transfer and (ii) we use a three-dimensional model to compute the frequency response in the solder stack assembly (solid acoustics) and the acoustic pressure in the liquid solder pool (solid-fluid interaction). The acoustic pressure is a proxy for cavitation and therefore bond strength. Our simulations show the acoustic pressure rapidly decreases as the height of the solder tip above the substrate surface increases, which correlates with controlled experiments that show the solder bond quality also decreases with increasing tip height.

Jet direction in bubble collapse within rectangular and triangular channels

A vapor bubble collapsing near a solid boundary in a liquid produces a liquid jet that points toward the boundary. The direction of this jet has been studied for boundaries such as flat planes and parallel walls enclosing a channel. Extending these investigations to enclosed polygonal boundaries, we experimentally measure jet direction for collapsing bubbles inside a square and an equilateral triangular channel. Following the method of Tagawa and Peters [Phys. Rev. Fluids 3, 081601 (2018)10.1103/PhysRevFluids.3.081601] for predicting the jet direction in corners, we model the bubble as a sink in a potential flow and demonstrate by experiment that analytical solutions accurately predict jet direction within an equilateral triangle and square. We further use the method to develop predictions for several other polygons, specifically, a rectangle, an isosceles right triangle, and a 30^{∘}-60^{∘}-90^{∘} right triangle.

Nonlinear dynamics of two coupled bubbles oscillating inside a liquid-filled cavity surrounded by an elastic medium

A theory is developed to model the nonlinear dynamics of two coupled bubbles inside a spherical liquid-filled cavity surrounded by an elastic medium. The aim is to study how the conditions of full confinement affect the coupled oscillations of the bubbles. To make the problem amenable to analytical consideration, the bubbles are assumed to be located on a diameter of the cavity, which makes the problem axisymmetric. Equations for the pulsation and translation motion of the bubbles are derived by the Lagrangian formalism. The derived equations are used in numerical simulations. The behavior of two bubbles in a cavity is compared with the behavior of the same bubbles in an unbounded liquid. It is found that both forced and free oscillations of two bubbles in a cavity occur differently than those in an unbounded liquid. In particular, it is shown that the eigenfrequencies of a two-bubble system in a cavity are different from those in an unbounded liquid.

Numerical investigation on the collapse of a bubble cluster near a solid wall

This paper studies numerically the collapse of a cluster of cavitation bubbles (as a primitive model for a bubble cloud) near a solid wall. The homogeneous two-phase mixture model is used, with the liquid-vapor interface resolved by volume of fluid method. The liquid is treated as compressible, allowing the propagation of pressure waves at the speeds determined by a state equation. This cluster consists of 27 identical bubbles, evenly distributed in a cubic region, with various bubble-wall and bubble-bubble distances considered. Our simulations suggest that the bubble-wall distance plays a more significant role. The maximum impulsive pressure of 41MPa is achieved when the cluster is very close to the wall. The inward progress of collapse is observed by examining the evolutions of bubble shapes and flow fields, with two distinctly different sequences of collapse identified between the small and large bubble-wall distances. At a large bubble distance, the centermost bubble is the last to collapse, while at a small bubble distance, it is the central bubble nearest to the wall which collapses lastly. This difference can also explain the more intensive impulsive pressure for the smaller bubble-wall distances. The proposed numerical approach is of special interest because it can resolve the details of bubble-bubble and bubble-wall interactions, which are significant to the study of the collapse of a cavitation cloud, and its potential damage to hydraulic systems.

Cavitation in a liquid-filled cavity surrounded by an elastic medium: Intercoupling of cavitation events in neighboring cavities

The subject of the present theoretical study is the dynamics of a cavitation bubble in a spherical liquid-filled cavity surrounded by an infinite elastic solid. Two objectives are pursued. The first is to derive equations for the velocity and pressure fields throughout the liquid filling the cavity and equations for the stress and strain fields throughout the solid medium surrounding the cavity. This derivation is based on the results of our previous paper [A. A. Doinikov et al., Phys. Rev. E 97, 013108 (2018)10.1103/PhysRevE.97.013108], where equations for the evolution of a bubble inside a cavity were derived. The second objective is to apply the equations obtained at the first step of the study to ascertain if the cavitation process in one cavity can trigger the nucleation in a neighboring cavity. To this end, we consider a neighboring cavity in which a cavitation bubble is absent. We derive equations that describe the disturbance of the liquid pressure inside the second cavity, assuming this disturbance to be caused by the cavitation process in the first cavity. The developed theory is then used to perform numerical simulations. The results of the simulations show that the magnitude of the background negative pressure inside the second cavity increases at the second half period of the pressure disturbance, which in turn enhances the probability of nucleation in the second cavity.