Effects Of Liquid Compressibility Research Articles

Numerical study of the effect of liquid compressibility on acoustic droplet vaporization

In acoustic droplet vaporization (ADV), a cavitated bubble grows and collapses depending on the pressure amplitude of the acoustic pulse. During the bubble collapse, the surrounding liquid is compressed to high pressure, and liquid compressibility can have a significant impact on bubble behavior and ADV threshold. In this work, a one-dimensional numerical model considering liquid compressibility is presented for ADV of a volatile microdroplet, extending our previous Rayleigh-Plesset based model [Ultrason. Chem. 71 (2021) 105361]. The numerical results for bubble motion and liquid energy change in ADV show that the liquid compressibility highly inhibits bubble growth during bubble collapse and rebound, especially under high acoustic frequency conditions. The liquid compressibility effect on the ADV threshold is quantified with varying acoustic frequencies and amplitudes.

Numerical and experimental study on fluid compressibility in a two-stage reciprocating pump-compressor

• Liquid piston velocity decreases with increasing pressure due to liquid compressibility. • Liquid piston brings the compression process closer to thermodynamically efficient. • Liquid expansion leads to a decrease of the pump volumetric efficiency. • Pressure ratio has the greatest impact on a decrease of liquid layer height and velocity. Currently, multistage (two and three-stage) reciprocating compressors are used to compress the gas to medium and high pressures. One of the promising operating principles of such machines is a preliminary compression in a single-stage piston compressor and a final gas compression in a working cavity with a liquid piston. The main advantages of a compressor using a liquid piston are intensive cooling of the compressed gas and the absence of leaks and leakages in the cylinder-piston group. This makes it possible to increase the indicated isothermal efficiency and actual volumetric efficiency. The article considered the effect of liquid compressibility in the two-stage piston hybrid positive-displacement machine with a liquid piston. We developed a calculus methodology for the liquid compressibility during gas compression in the second stage of the compression section based on the volume conservation equation and Hooke's law. Numerical simulation showed that the degree of pressure ratio had the greatest impact on the relative decrease in the height and velocity of the liquid layer. We found that the relative decrease in the liquid layer height was within 1%. The relative decrease in the liquid piston velocity was within 5%. We carried out the experiment and validation of the results with a numerical simulation, which reflected the mathematical model validity. The model worked correctly based on an estimated experimental error. The parametric analysis of the test model showed the influence of the main working cavity parameters. The discrepancy in determining the dynamic pressure in the machine cavities conducting theoretical and experimental studies is within 10–15%. The paper analysed the liquid piston compressibility influence on the thermodynamic efficiency of the compression process and compressor performance.

Analysis of Liquid Piston Compressibility in the Two-Stage Hybrid Positive-Displacement Machine

The effect of liquid compressibility in the two-stage piston hybrid positive-displacement machine with a liquid piston was considered. Based on the volume conservation equation, we developed a calculus methodology for the liquid compressibility during gas compression in the second stage of the compressor section. A numerical experiment made it possible to establish that some parameters have the greatest effect on the relative decrease in the height and velocity of the liquid layer. These parameters are the degree of pressure ratio; pipeline length; the polytropic index of the compression; the number of crankshaft revolutions. We found that the relative decrease in the liquid layer height is within 1 %, and the relative decrease in the liquid piston velocity is within 5 %. The paper analyses the liquid piston compressibility influence on the thermodynamic efficiency of the compression process and compressor performance.

Effects of liquid compressibility on the dynamics of ultrasound contrast agent microbubbles

Ultrasound contrast agents (UCA) have been widely used in ultrasonic medical applications. The dynamics of UCA should be simulated accurately to maximize the application effects. The acoustic radiation of UCA oscillations is affected by the liquid compressibility which has to be considered. This paper deduces a simple equation based on Keller-Miksis equation to describe the dynamics of UCA with a polymer shell, taking consideration of compressibility of the liquid. The volume of UCA shell is constant. The shell is described by the Kelvin-Voigt viscoelasticity model.The extended compressible model is verified by comparing with experimental data and Hoff model in predicting the variations of bubble radius with time, resonance frequency, damping constants and acoustical scattering cross section of the UCA microbubbles. The physical explanations of the differences between the extended compressible model and Hoff model in predicting resonance frequency and acoustical scattering cross section are listed. The liquid compressibility correction in UCA model can be better used to predict the bubble dynamics at large radius with high excitation frequency, and it will give us some valuable references in ultrasonic medical applications.

Liquid compressibility effect on the acoustic generation of free radicals

Even through the liquid compressibility effect on acoustic cavitation has already been investigated by several authors, their results, however, are still limited to the radial dynamics and the thermodynamic behavior of the gas inside the bubble. In this computational study, the effect of liquid compressibility was investigated on both the bubble dynamics and the resulted chemical reactions inside the bubble at the collapse. Two cavitation models, based on Rayleigh-Plesset (RP) equation for incompressible medium and that of Keller-Miksis (KM) for compressible one, were adopted. A reaction scheme consisting on 25 reversible reactions was used for simulating the chemistry occurring inside the bubble at the strong collapse. The inclusion of liquid compressibility induced lower bubble temperature (T max), pressure (p max) and chemical yield of the oxidants inside the bubble at the strong collapse. Furthermore, frequency and acoustic strongly affected the effect of liquid compressibility.

Effect of Liquid Compressibility at a Jet Impact on a Wall

The liquid compressibility effect during impact of a liquid jet at a speed of 250 m/s on the surface of a solid wall is investigated, depending on the jet shape. The study is conducted by the comparison of the numerical solutions obtained with and without taking into account the liquid compressibility (by the CIP-CUP and BEM methods, respectively). It is shown that the manifestation of the liquid compressibility during impact substantially depends on the jet shape. For example, the neglect of the compressibility in the case of impact of a cylindrical jet with a plane end strongly distorts the impact pattern over a long time. In the case of a cylindrical jet with a hemispherical end, a distorted picture appears only at the short-term initial stage of impact. For a pointed cone-shaped jet with an angle between the cone surface and the wall equal to π/4, the flow patterns obtained with and without allowing for the liquid compressibility are almost identical.

The elastic fields of a compressible liquid inclusion

Elastic composites containing liquid inclusions exist widely in rocks, food, tissues and hydrogels. We investigate a single ellipsoidal compressible liquid inclusion embedded in an infinite elastic matrix, such as an isolated cell embedded in an extracellular matrix or an oil or gas pocket embedded within shale. We first derive the displacement and stress fields in the matrix under far field loading. For the special case of a spherical inclusion, we arrive at simple, explicit expressions for these fields. We next focus on the shape evolution of the liquid inclusion and the stress concentration in the matrix, from which we identify when the effect of liquid compressibility is most significant. Finally, we classify common examples of liquid inclusions in nature and engineering. According to our theoretical results, we estimate the importance of liquid compressibility in these examples and provide guidelines for further application of the theory of liquid inclusions in practical situations.

Influence of liquid compressibility on the dynamics of single bubble sonoluminescence

The main effects of liquid compressibility on the dynamics of single bubble sonoluminescence are investigated via three different radial dynamics models. In order to precise description of the interior gas thermodynamics, a hydrochemical model is used. In the case of an argon gas bubble in water, the results obtained with the Gilmore model and the Lezzi and Prosperetti model are compared with those resulting from the Keller and Miksis model. It is shown that the variation of liquid density at bubble surface in a very short time interval around the end of the bubble collapse, which has been incorporated into the first two models, strongly influences the bubble cavitation dynamics at higher acoustic amplitudes. The simulation results denote an increase in the bubble temperature and pressure and a reduction in the bubble minimum radius, compared with those ones obtained with Keller and Miksis model. As the acoustic amplitude increases, the difference between the models becomes larger. Moreover, it is shown that increasing the bubble ambient radius leads to an improved match between the results of the models.

Long-range stress correlations in viscoelastic and glass-forming fluids.

A simple and rigorous approach to obtain stress correlations in viscoelastic liquids (including supercooled liquid and equilibrium amorphous systems) is proposed. The long-range dynamical correlations of local shear stress are calculated and analyzed in 2-dimensional space. It is established how the long-range character of the stress correlations gradually emerges as the relevant dynamical correlation length l grows in time. The correlation range l is defined by momentum propagation due to acoustic waves and vorticity diffusion which are the basic mechanisms for transmission of shear stress perturbations. We obtain the general expression defining the time- and distance-dependent stress correlation tensor in terms of material functions (generalized relaxation moduli). The effect of liquid compressibility is quantitatively analyzed; it is shown to be important at large distances and/or short times. The revealed long-range stress correlation effect is shown to be dynamical in nature and unconnected with static structural correlations in liquids (correlation length ξs). Our approach is based on the assumption that ξs is small enough as reflected in weak wave-number dependencies of the generalized relaxation moduli. We provide a simple physical picture connecting the elucidated long-range fluctuation effect with anisotropic correlations of the (transient) inherent stress field, and discuss its implications.

Effects of liquid compressibility on bubble-bubble interactions between oscillating bubbles

The mutual interaction between cavitation bubbles plays an important role in the physical processes of cavitation. In this paper, a complete model is developed for modelling the mutual interaction between cavitation bubbles with the effects of liquid compressibility fully included. It is found that the liquid compressibility is an important parameter in the determination of the direction of the force (the attraction or repulsion force), as well as the magnitude of the force. The influences of the liquid compressibility on the mutual interaction force can be categorized into three terms: the first is a new term added on the mutual interaction force in incompressible liquids and this term will vanish if the sizes of two bubbles are equal, the second is the radiation damping term, the third one can be considered as a correction of the mutual interaction force in incompressible liquids with a coefficient and this correction will be prominent for small bubbles and a high ambient pressure.

Cross validation of analytical and finite element models for Hydrodynamic Ram loads prediction in thin walled liquid filled containers

To reduce the vulnerability of both civilian and military aircraft, it is important to take the Hydrodynamic Ram pressure into account when designing their fuel tanks. Hydrodynamic Ram is especially dangerous for thin walled lightweight structures that cannot be armoured due to weight penalty reasons. Similarities in bubble behaviour between Hydrodynamic Ram and underwater explosion situations were observed in recent high-speed tank penetration/water entry experiments. A confined version of the Rayleigh–Plesset equation – which is classically used for incompressible bubble dynamics analysis (including underwater explosion) – was developed to simulate a bubble created by a Hydrodynamic Ram event induced by projectile penetration at ballistic speed in a confined geometry filled with a liquid. In the present work, the authors validate the proposed confined Rayleigh–Plesset equation for application on a spherical container thanks to quasi-incompressible ALE finite element simulation results. Then to determine the effect of liquid compressibility on confined bubble dynamics, the authors compare predictions of bubble radii obtained with the confined Rayleigh–Plesset equation with the prediction obtained using compressible finite element simulations. Eventually, the authors discuss differences in the bubble dynamics and hydrodynamic loads predictions obtained with the two approaches.

Constitutive models for linear compressible viscoelastic flows of simple liquids at nanometer length scales

Simple bulk liquids such as water are commonly assumed to be Newtonian. While this assumption holds widely, the fluid-structure interaction of mechanical devices at nanometer scales can probe the intrinsic molecular relaxation processes in a surrounding liquid. This was recently demonstrated through measurement of the high frequency (20 GHz) linear mechanical vibrations of bipyramidal nanoparticles in simple liquids [Pelton et al., “Viscoelastic flows in simple liquids generated by vibrating nanostructures,” Phys. Rev. Lett. 111, 244502 (2013)]. In this article, we review and critically assess the available constitutive equations for compressible viscoelastic flows in their linear limits—such models are required for analysis of the above-mentioned measurements. We show that previous models, with the exception of a very recent proposal, do not reproduce the required response at high frequency. We explain the physical origin of this recent model and show that it recovers all required features of a linear viscoelastic flow. This constitutive equation thus provides a rigorous foundation for the analysis of vibrating nanostructures in simple liquids. The utility of this model is demonstrated by solving the fluid-structure interaction of two common problems: (1) a sphere executing radial oscillations in liquid, which depends strongly on the liquid compressibility and (2) the extensional mode vibration of bipyramidal nanoparticles in liquid, where the effects of liquid compressibility are negligible. This highlights the importance of shear and compressional relaxation processes, as a function of flow geometry, and the impact of the shear and bulk viscosities on nanometer scale flows.

Pressure controlled bubble growth in microchannels

As microfluidic devices are used with high-pressure fluids, the effects of liquid compressibility become important for understanding system behavior. Bubble growth in a microfluidic channel, for instance, is qualitatively different in a rigid fixed-volume high pressure microfluidic device than it is in a flexible or open microfluidic device. With a fixed volume, bubble growth must be accompanied by compression of the surrounding liquid, increasing the system pressure. Increased pressure decreases the diffusion drive, slowing bubble growth. A nonlinear equation for system pressure is derived relating these coupled effects. This equation is linearized in the limit of small supersaturation, yielding a closed form solution. For larger supersaturations, the governing equations are solved numerically. Experiments on bubble growth in gas saturated liquid agree well with this one-dimensional model.

Delay differential equations for single-bubble dynamics in a compressible liquid

Most common methods to include the effects of liquid compressibility in models for single-bubble dynamics rely on series expansions to some order in the inverse of the sound speed in the liquid. It has been shown that the Keller-Miksis model for single-bubble dynamics can be obtained from a series expansion of a delay differential equation related to the Rayleigh-Plesset equation for a single bubble. The iterative approach used to obtain the series expansion of the delay-based model becomes unworkable for more complicated models of bubble dynamics. Therefore, to provide an alternative, simpler method to model the effects of liquid compressibility, the delay differential equation model proposed by Ilinskii and Zabolotskaya [J. Acoust. Soc. Am. 92, 2837 (1992)] is analyzed directly. The results of the delay-based formulations are compared to those produced by models based on common series expansions. Alternative formulations of the delay differential equation are also considered and compared.

Effects of liquid compressibility on radial oscillations of gas bubbles in liquids

For forced radial oscillations of gas bubbles in liquids, a more rigorous expression of the acoustic damping constant based on Keller's equation is developed. Comparison with those in published papers is also made. The expression offered in this paper will improve the predictions of total damping constant in particular for high frequencies and large bubbles, i.e., large ωR0/c1 (ω is the frequency of driving sound field, R0 is the equilibrium bubble radius, c1 is the sound speed in the liquid). Examples in ultrasound imaging and acoustical oceanography are demonstrated.

Liquid compressibility effects in the dynamics of acoustically coupled bubbles

Accurate models for clusters of interacting bubbles are sought for both biomedical and underwater applications. Multiple bubble models have been developed by treating the bubbles as a system of interacting oscillators. The models are obtained initially for bubbles in an incompressible, irrotational, and inviscid liquid; additional effects are included in an ad hoc fashion. The existing oscillator models for the dynamics of interacting bubbles are improved by including the effect of liquid compressibility. In particular, while existing models have been improved by including propagation delays in the bubble interactions, the effect of bubble interaction on radiation damping has not been considered. The current work develops corrections for the radiation damping of coupled bubbles in both linear and nonlinear models of bubble dynamics. These corrections eliminate certain instabilities that have been observed in delay differential equation models of coupled-bubble dynamics. Additionally, an increase in the coupling strength between bubbles undergoing high-amplitude radial motion is predicted when coupled radiation damping is included; this increase in coupling strength strongly affects the predicted motion of the system and the resultant pressure in the surrounding medium. [Work supported by the ARL:UT McKinney Fellowship in Acoustics and NIH DK070618.]

Growth of small deformations of the sphericity of a vapor bubble

Evolution of small deformations of the sphericity of a cavitation bubble under its strong compression in water is studied. The liquid pressure oscillation amplitude is 15 bar. A mathematical model is used, in which the motion of vapor and liquid is split into the spherical component and its small non-spherical perturbation. The spherical component is governed by the gas dynamics equations realistic wide-range equations of state by Nigmatulin and Bolotnova. Non-stationary thermal conductivity in vapor and liquid, non-equilibrium evaporation/condensation processes at the interphase boundary are taken into account. The non-spherical component is described without taking into account the effect of liquid compressibility and the inhomogeneity of the vapor. This allows one to govern the evolution of the non-spherical component by ordinary differential equations of the second order. It has been found that the amplitude of small initial distortions of the bubble sphericity can increase during its compression by no more than 320 times.

Propagation of Pressure Waves in Two-Component Bubbly Flow in Horizontal Pipes

The propagation of pressure waves in two-component bubbly flow was analytically and experimentally investigated. An analysis is presented that accounts for the effects attributable to liquid compressibility, pipe elasticity, and temperature rise across pressure waves. Analytical results indicate that the effects of liquid compressibility and pipe wall elasticity are important at low gas content, although the effect of temperature change is generally negligible. Pressure waves were generated in the laboratory by rapid closure of a valve at the downstream end of a horizontal pipe. The experimental results indicate that there were two major pressure surges generated by valve closure; the first was attributable to stoppage of the two-phase mixture at the valve, and the second attributable to the arrest of the liquid column at the upstream end of the mixing device. The transient flow model provides a satisfactory prediction of the initial pressure rise at the valve and the average velocity of the initial pressure waves.

The effect of liquid compressibility, heat loss, and the induction period of the chemical reaction on the structure of a bubble-detonation wave

Calculations were performed of the structure of a bubble detonation wave in a chemically reactive gas-liquid medium with bubbles arranged in layers. With the liquid compressibility taken into account, the amplitude of pressure pulsations decreases, and they move to the leading edge. It is shown that the wave profile depends weakly on the method of calculating the induction period of the reactive mixture and method of taking into account heat losses. A comparison is made of the calculated and experimental pressure profiles of the bubble-detonation wave.

The effects of fluid compressibility on multibubble cavitation for high-intensity focused ultrasound.

In this talk the effects of liquid compressibility and viscosity on cavitation occurring during high-intensity focused ultrasound treatments are discussed. Using techniques from dynamical systems analysis, the criterion for inertial cavitation is formally generalized for multi-bubble models. It is shown that the threshold for inertial cavitation remains independent of the number of bubbles present. It is conjectured that this is because the re-radiated pressure field from any one bubble only has a significant influence on the oscillations of the surrounding bubbles if it collapses inertially. For interacting bubbles the effects of compressibility are analyzed through the inclusion of the appropriate time delays in the bubble interactions. This may result in instability, but it is shown that for values of viscosity relevant to tissue, the system is stable. Instabilities may develop in the full system limiting the ability of a bubble to undergo repetitive bounded oscillations. There are four main mechanisms by which a bubble can become unstable: radial, translational, diffusive, and non-spherical instabilities. In each case it is shown that on including delayed interactions the bubbles are more likely to undergo stable oscillations. The physical implications of these findings are discussed.