Multibubble Sonoluminescence from a Theoretical Perspective

In the present review, complexity in multibubble sonoluminescence (MBSL) is discussed. At relatively low ultrasonic frequency, a cavitation bubble is filled mostly with water vapor at relatively high acoustic amplitude which results in OH-line emission by chemiluminescence as well as emissions from weakly ionized plasma formed inside a bubble at the end of the violent bubble collapse. At relatively high ultrasonic frequency or at relatively low acoustic amplitude at relatively low ultrasonic frequency, a cavitation bubble is mostly filled with noncondensable gases such as air or argon at the end of the bubble collapse, which results in relatively high bubble temperature and light emissions from plasma formed inside a bubble. Ionization potential lowering for atoms and molecules occurs due to the extremely high density inside a bubble at the end of the violent bubble collapse, which is one of the main reasons for the plasma formation inside a bubble in addition to the high bubble temperature due to quasi-adiabatic compression of a bubble, where “quasi” means that appreciable thermal conduction takes place between the heated interior of a bubble and the surrounding liquid. Due to bubble–bubble interaction, liquid droplets enter bubbles at the bubble collapse, which results in sodium-line emission.     

Dynamics of laser-induced cavitation bubble during expansion over sharp-edge geometry submerged in liquid – an inside view by diffuse illumination

Laser ablation in liquids is growing in popularity for various applications including nanoparticle production, breakdown spectroscopy, and surface functionalization. When laser pulse ablates the solid target submerged in liquid, a cavitation bubble develops. In case of “finite” geometries of ablated solids, liquid dynamical phenomena can occur inside the bubble when the bubble overflows the surface edge. To observe this dynamics, we use diffuse illumination of a flashlamp in combination with a high-speed videography by exposure times down to 250 ns. The developed theoretical modelling and its comparison with the experimental observations clearly prove that this approach widens the observable area inside the bubble. We thereby use it to study the dynamics of laser-induced cavitation bubble during its expansion over a sharp-edge (“cliff-like” 90°) geometry submerged in water, ethanol, and polyethylene glycol 300. The samples are 17 mm wide stainless steel plates with thickness in the range of 0.025–2 mm. Bubbles are induced on the samples by 1064-nm laser pulses with pulse durations of 7–60 ns and pulse energies of 10–55 mJ. We observe formation of a fixed-type secondary cavity behind the edge where low-pressure area develops due to bubble-driven flow of the liquid. This occurs when the velocity of liquid overflow exceeds ~20 m s⁻¹. A re-entrant liquid injection with up to ~40 m s⁻¹ velocity may occur inside the bubble when the bubble overflows the edge of the sample. Formation and characteristics of the jet evidently depend on the relation between the breakdown-edge offset and the bubble energy, as well as the properties of the surrounding liquid. Higher viscosity of the liquid prevents the generation of the jet.     

Space-time finite element methods stabilized using bubble function spaces

ABSTRACT

In this paper, a stabilized space-time finite element method for solving linear parabolic evolution problems is analyzed. The proposed method is developed on a base of a space-time variational setting, that helps on the simultaneous and unified discretization in space and in time by finite element techniques. Stabilization terms are constructed by means of classical bubble spaces. Stability of the discrete problem with respect to an associated mesh dependent norm is proved, and a priori discretization error estimates are presented. Numerical examples confirm the theoretical estimates.     

Shape stability of a gas bubble in a soft solid

Predicting the onset of non-spherical oscillations of bubbles in soft matter is a fundamental cavitation problem with implications to sonoprocessing, polymeric materials synthesis, and biomedical ultrasound applications. The shape stability of a bubble in a Kelvin-Voigt viscoelastic medium with nonlinear elasticity, the simplest constitutive model for soft solids, is analytically investigated and compared to experiments. Using perturbation methods, we develop a model reducing the equations of motion to two sets of evolution equations: a Rayleigh-Plesset-type equation for the mean (volume-equivalent) bubble radius and an equation for the non-spherical mode amplitudes. Parametric instability is predicted by examining the natural frequency and the Mathieu equation for the non-spherical modes, which are obtained from our model. Our theoretical results show good agreement with published experiments of the shape oscillations of a bubble in a gelatin gel. We further examine the impact of viscoelasticity on the time evolution of non-spherical mode amplitudes. In particular, we find that viscosity increases the damping rate, thus suppressing the shape instability, while shear modulus increases the natural frequency, which changes the unstable mode. We also explain the contributions of rotational and irrotational fields to the viscoelastic stresses in the surroundings and at the bubble surface, as these contributions affect the damping rate and the unstable mode. Our analysis on the role of viscoelasticity is potentially useful to measure viscoelastic properties of soft materials by experimentally observing the shape oscillations of a bubble.     

Simulating bubble dynamics in a buoyant system

Multiphase flows are critical components of many physical systems; however, numerical models of multiphase flows with large parameter gradients can be challenging. Here, two different numerical methods, volume of fluid (VOF) and smoothed particle hydrodynamics (SPH), are used to model the buoyant rise of isolated gas bubbles through quiescent fluids for a range of Bond and Reynolds numbers. The VOF is an Eulerian grid–based method, whereas the SPH is Lagrangian and mesh free. Each method has unique strengths and weaknesses, and a comparison of the two approaches as applied to multiphase phenomena has not previously been performed. The VOF and SPH simulations are compared, verified, and validated. Results using two-dimensional VOF and SPH simulations are similar to each other and are able to reproduce numerical benchmarks and experimental results for sufficiently large Morton and Reynolds numbers. It is also shown that at low Reynolds numbers, the two methods, SPH and VOF, diverge in the transient regime of the bubble rise. Regimes that require simulations capable of representing three-dimensional drag are identified as well as regimes in which results from VOF and SPH diverge.     

Effects of bubble size and approach velocity on bubble–particle interaction – a theoretical study

A theoretical analysis of the atomic force microscopy (AFM) approach–retract dynamic interaction between an air bubble and a hydrophilic silica plane was carried out based on the well-established Stokes–Reynolds–Young–Laplace model. An air bubble with different radii attached to the end of a cantilever approached the silica surface with different approach velocities in a 10^?3?M KCl solution. Results showed that with increasing approach velocity (0.1, 1, and 10?µm/s), the repulsive force, flattened area of the film, and hydrodynamic suction force between the 100-µm bubble and the silica plane increased. The film continued thinning at the initial stages of bubble retraction because of the attractive hydrodynamic pressure. When the bubble size decreased, the influence of hydrodynamic pressure was less evident. The final film thickness before bubble retraction was similar to the theoretical equilibrium thickness when the Laplace pressure was equal to the disjoining pressure.     

The Dirac Operator on Nilmanifolds and Collapsing Circle Bundles

We compute the spectrum of the Dirac operator on 3-dimensional Heisenberg manifolds. The behavior under collapse to the 2-torus is studied. Depending on the spin structure either all eigenvalues tend to ± or there are eigenvalues converging to those of the torus. This is shown to be true in general for collapsing circle bundles with totally geodesic fibers. Using the Hopf fibration we use this fact to compute the Dirac eigenvalues on complex projective space including the multiplicities.Finally, we show that there are 1-parameter families of Riemannian nilmanifolds such that the Laplacian on functions and the Dirac operator for certain spin structures have constant spectrum while the Laplacian on 1-forms and the Dirac operator for the other spin structures have nonconstant spectrum. The marked length spectrum is also constant for these families.     

Existence and selection of steady bubbles in a Hele–Shaw cell

This paper concerns the existence of a steadily translating bubble in a Hele–Shaw cell for small but non-zero surface tension ². We rigorously conclude that for bubble velocity U relative to the fluid velocity at infinity in the interval (1,2), analytic symmetric solutions exist in the asymptotic limit of surface tension ²→0 if and only if the Stokes constant for a relatively simple nonlinear differential equation is zero. This Stokes constant S depends on the parameter α(0,1) corresponding to bubble size and . Earlier calculations have shown S to be zero for a discrete set of values of a.     

Gravitational effects in quantum mechanics

To date, both quantum theory and Einstein’s theory of general relativity have passed every experimental test in their respective regimes. Nevertheless, almost since their inception, there has been debate surrounding whether they should be unified, and by now, there exists strong theoretical arguments pointing to the necessity of quantising the gravitational field. In recent years, a number of experiments have been proposed which, if successful, should give insight into features at the Planck scale. Here, we review some of the motivations, from the perspective of semi-classical arguments, to expect new physical effects at the overlap of quantum theory and general relativity. We conclude with a short introduction to some of the proposals being made to facilitate empirical verification.