Influence of gas motion inside a charged bubble in a liquid on the parameters of bubble oscillations

The influence of a finite rate of leveling of the gas pressure inside a charged bubble in an ideal incompressible liquid on the bubble volume and surface oscillations is studied in a linear approximation with respect to the surface oscillation amplitude. It is shown that the bubble shape is governed by superposition of spherical harmonics with amplitudes strongly depending on their frequencies, as well as on the physical properties of the gas inside the bubble and the ambient liquid.     

Suppressing chaotic oscillations of a spherical cavitation bubble through applying a periodic perturbation

Nonlinear dynamics of a spherical cavitation bubble was studied. A method based on applying a periodic perturbation to suppress chaotic oscillations is introduced. The relation between this method and dual frequency ultrasonic irradiation is correlated to prove its applicability in applications involving cavitation phenomena. Results indicated its strong impact on reducing the chaotic oscillations to regular ones. The governing parameters are the secondary frequency value and the phase difference between the secondary frequency and the fundamental one. In the end, the possible application of this method in high intensity focused ultrasound tumor ablation as an instance, is discussed accounting for both free bubbles and microbubbles.     

Numerical simulation of bubble dynamics in a Phan-Thien–Tanner liquid: Non-linear shape and size oscillatory response under periodic pressure

We study non-linear bubble oscillations driven by an acoustic pressure with the bubble being immersed in a viscoelastic, Phan-Thien–Tanner liquid. Solution is provided numerically through a method which is based on a finite element discretization of the Navier–Stokes flow equations. The proposed computational approach does not rely on the solution of the simplified Rayleigh–Plesset equation, is not limited in studying only spherically symmetric bubbles and provides coupled solutions for the velocity, stress fields and bubble interface. We present solutions for non-spherical bubbles, with asphericity being addressed by means of Legendre polynomials or associated Legendre functions. A parametric investigation of the bubble dynamical oscillatory response as a function of the fluid rheological properties shows that the amplitude of bubble oscillations drastically increases as liquid elasticity (quantified by the Deborah number) increases or as liquid viscosity decreases (quantified by the Reynolds number). Extensive numerical calculations demonstrate that increasing elasticity and/or viscosity of the surrounding liquid tend to stabilize the shape anisotropy of an initially non-spherical bubble. Results are shown for pressure amplitudes 0.2–2 MPa and Deborah, Reynolds numbers in the intervals of 1–8 and 0.094–1.256, respectively.     

Nonlinear gas oscillations in an open tube under anharmonic excitation

Nonlinear gas oscillations excited in a tube with an open end by a piston driven by a crank mechanism are investigated. For the open end of the tube, a nonlinear boundary condition is formulated with allowance for oscillations at the subharmonic resonance frequency. Both first- and second-order approximations to the oscillations at the fundamental frequency and at half this frequency are calculated. The results of theoretical calculations are compared with experimental data.     

Experimental study of detonating gas bubble oscillations using a shock tube

Oscillations of bubbles containing a mixture of a detonating gas with argon in their interior are studied. The bubbles are excited for oscillations by a pressure step generated in a shock tube. A bubble wall motion is observed by a rotating mirror camera and a radiated pressure wave by a needle hydrophone. For weak pressure steps the bubble behaves as an ordinary gas bubble. However, above a certain pressure step threshold ignition of the detonating gas occurs. Due to released heat the bubble oscillation intensity is amplified. The data obtained are used to estimate pressures and temperatures in the compressed bubble.The experimental part of this research was carried out during the author's stay at the Shock Wave Laboratory of the Technical University in Aachen. The author wishes to thank Professor A. E. Beylich for enabling him to do this work, and H. Kleine for taking all the photographs. The author is also grateful to Dr. K. Hel for helpful discussion on the ignition of gas mixtures. During this research the author was the recipient of a grant awarded by the Heinrich Hertz Foundation, which is gratefully acknowledged.     

Nonlinear evolution of periodic gas perturbations

A system of equations describing a 1-D nonsteady gas flow with a power law dependence of pressure on density is considered. General solutions of this system were obtained for several special cases. The problem of a periodic gas flow with respect to a spatial coordinate is solved. An analogy with an initial system of equations that describes the motion of quasi-gaseous media is presented.     

Nonlinear oscillations of a charged jet of a conducting liquid under multimode initial deformation of its surface

The subject of consideration is a uniformly charged jet of an ideal incompressible conducting liquid moving with a constant velocity along the symmetry axis of an undisturbed cylindrical surface. An evolutionary expression for the jet shape is derived accurate to the second order of smallness in oscillation amplitude for the case when the initial deformation of the equilibrium surface is a superposition of a finite number of both axisymmetric and nonaxisymmetric modes. The flow velocity field in the jet and the electric field distribution near it are determined. The positions of internal nonlinear secondary combined three-mode resonances are found, which are typical of nonlinear corrections to the analytical expressions for the jet shape, flow velocity field potentials, and electrostatic field in the vicinity of the jet.     

Nonlinear dynamics of a gas bubble in an incompressible elastic medium

A nonlinear model in the form of the Rayleigh-Plesset equation is developed for a gas bubble in an essentially incompressible elastic medium such as a tissue or rubberlike medium. Two constitutive laws for the elastic medium are considered: the Mooney potential, and Landau's expansion of the strain energy density. These two constitutive laws are compared at quadratic order to obtain a relation between their respective elastic constants. Attention is devoted to the relative importance of shear stress on the bubble dynamics, allowing for the equilibrium gas pressure in the bubble to differ substantially from the pressure at infinity. The model for the bubble motion is approximated to quadratic order to assess the importance of shear stress in the surrounding medium relative to that of the gas pressure in the bubble. Relations are derived for the value of the shear wave speed at which the two contributions are comparable, which provide an assessment of when shear stress in the surrounding medium must be taken into account when modeling bubble dynamics.     

Effect of gas pressure on ionization of ambient gas

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Nonlinear oscillations of gas bubbles in viscoelastic fluids

Nonlinear oscillations of gas bubbles in viscoelastic fluids of a three-constant Oldroyd model are theoretically investigated. The equation of motion for a bubble in a viscoelastic fluid subject to a pulsating pressure, and the pressure equation at the bubble wall are obtained. By numerical calculations on these equations, the effects of relaxation time and retardation time on frequency response curves, and the relation between the maximum pressure at the bubble wall and the initial radius of the bubble are clarified.     

Crumpling under an ambient pressure

A pressure chamber is designed to study the crumpling process under an ambient force. The compression force and its resulting radius for the ball obey a power law with an exponent that is independent of the thickness and initial size of the sheet. However, the exponent is found to be material dependent and less than the universal value, 0.25, claimed by the previous simulations. The power-law behavior disappears at high pressure when the compressibility drops discontinuously, which is suggestive of a locked state.     

Laws governing the combustion of the Ni + Al system under a low ambient gas pressure

The ambient pressure dependences of the combustion rate and combustion-induced elongation for an initial Ni + Al mixture and Ni + Al mixtures subjected to vacuum heat treatment (VHT), mechanical activation, and additional activation in water (dispersion) have been studied. Most of the studies have been conducted for mixtures based on PNK-brand nickel (carbonyl); a separate set of experiments has been conducted for PNE-brand nickel (electrolytic). These powder brands contain different amounts of impurity gases and have different particle sizes. It has been shown that VHT, the ambient gas pressure, and the type of the used nickel have a substantial effect on the combustion rate of these mixtures. For the mixtures based on PNK nickel, the increase in the combustion rate after VHT is more significant than that after mechanical activation despite a more thorough mixing of the precursors and changes in the mixture microstructure. The qualitative change in the behavior of the dependence of the combustion rate of the dispersed mixtures on the external gas pressure has been interpreted in terms of a convective–conductive combustion model. The studies have made it possible to prove the previously made conclusion about the gasless combustion of Ni + Al mixtures (PNK nickel) under high ambient gas pressures.     

Nonlinear capillary vibration of a charged bubble in an ideal dielectric liquid

The problem of nonlinear radial pulsations and surface vibrations of a charged bubble placed in an ideal incompressible dielectric liquid is asymptotically solved up to the second order of smallness by the method of many scales. It is shown that, in the case of nonlinear vibrations, resonance energy exchange may take place not only between surface modes but also between the radial mode and a surface mode. A new type of instability (other than Rayleigh instability against the self-charge), instability against the excess vapor pressure in the bubble, is discovered. The new type of instability shows up as energy transfer from the centrosymmetric pulsation mode to all initially excited surface vibration modes simultaneously.     

Dynamics of laser-induced bubble and free-surface oscillations in an absorbing liquid

A series of laser-driven dynamic photocapillary effects in absorbing liquid are described. We have observed self-oscillations of the free surface of a liquid (iodine solution in ethanol) and laser-induced bubble trapping and oscillations excited by a low power cw argon laser.     

Experimental investigation of the effect of ambient pressure on laser-induced bubble dynamics

The effect of ambient pressure on the dynamics of laser-induced bubbles was investigated by a fiber-optic diagnostic technique based on probe beam deflection (PBD). The experimental criterion for judging the maximum bubble radius is modified to the average value of the detecting distances at which the characteristic waveform signals appear. The ambient pressure affects the maximum radius and collapse of bubble strongly. The experimental results indicate that the maximum bubble radius and the collapse time both decrease nonlinearly while the ambient pressure increases linearly, and the decreasing velocities of them are smaller at a larger ambient pressure. The predicted value of collapse time has a good agreement with experiment at larger ambient pressure.