Bubble pulsations between parallel plates

Numerical study of cavitation shock wave emission in the thin liquid layer by power ultrasonic vibratory machining

In the field of power ultrasonic vibration processing, the thin liquid layer nestled between the tool head and the material serves as a hotbed for cavitation shock wave emissions that significantly affect the material's surface. The precise manipulation of these emissions presents a formidable challenge, stemming from a historical deficit in the quantitative analysis of both the ultrasonic enhancement effect and the shock wave intensity within this niche environment. Our study addresses this gap by innovatively modifying the Gilmore-Akulichev equation, laying the groundwork for a sophisticated bubble dynamics model and a pioneering shock wave propagation model tailored to the thin liquid layer domain. Firstly, our study investigated the ultrasound enhancement effect under various parameters of thin liquid layers, revealing an amplification of ultrasound pressure in the thin liquid layer area by up to 7.47 times. The mathematical model was solved using the sixth-order Runge-Kutta method to examine shock wave velocity and pressure under different conditions. our study identified that geometric parameters of the tool head, thin liquid layer thickness, ultrasonic frequency, and initial bubble radius all significantly influenced shock wave emission. At an ultrasonic frequency of 60 kHz, the shock wave pressure at the measurement point exhibited a brief decrease from 182.6 to 179.5 MPa during an increase. Furthermore, rapid attenuation of the shock wave was found within the range of R0-3R0 from the bubble wall. This research model aims to enhance power ultrasonic vibration processing technology, and provide theoretical support for applications in related fields.

Cavitation in thin liquid layer: A review

This review tries to cover as many research fields and literatures associated with cavitation in thin liquid layer as possible. The intent was to summarize (i) list all the research fields related to cavitation in thin liquid layer that can be collected, (ii) advances in the investigation of cavitation in thin liquid layer, and (iii) draw attention to the relatively macroscopic cavitation behavior in thin liquid layer.

Ultrasound triggered drug delivery with liposomal nested microbubbles

When ultrasound contrast agent microbubbles are nested within a liposome, damage to the liposome membrane caused by both stable and inertial cavitation of the microbubble allows for release of the aqueous core of the liposome. Triggered release was not accomplished unless microbubbles were present within the liposome. Leakage was tested using fluorescence assays developed specifically for this drug delivery vehicle and qualitative measurements using an optical microscope. These studies were done using a 1 MHz focused ultrasound transducer while varying parameters including peak negative ultrasound pressure, average liposome diameter, and microbubble concentration. Two regimes exist for membrane disruption caused by cavitating microbubbles. A faster release rate, as well as permanent membrane damage are seen for samples exposed to high pressure (2.1-3.7 MPa). A slower release rate and dilation/temporary poration are characteristic of stable cavitation for low pressure studies (0.54-1.7 MPa).

Inertial cavitation threshold of nested microbubbles

Cavitation of ultrasound contrast agents (UCAs) promotes both beneficial and detrimental bioeffects in vivo (Radhakrishnan et al., 2013) [1]. The ability to determine the inertial cavitation threshold of UCA microbubbles has potential application in contrast imaging, development of therapeutic agents, and evaluation of localized effects on the body (Ammi et al., 2006) [2]. This study evaluates a novel UCA and its inertial cavitation behavior as determined by a home built cavitation detection system. Two 2.25 MHz transducers are placed at a 90° angle to one another where one transducer is driven by a high voltage pulser and the other transducer receives the signal from the oscillating microbubble. The sample chamber is placed in the overlap of the focal region of the two transducers where the microbubbles are exposed to a pulser signal consisting of 600 pulse trains per experiment at a pulse repetition frequency of 5 Hz where each train has four pulses of four cycles. The formulation being analyzed is comprised of an SF6 microbubble coated by a DSPC PEG-3000 monolayer nested within a poly-lactic acid (PLA) spherical shell. The effect of varying shell diameters and microbubble concentration on cavitation threshold profile for peak negative pressures ranging from 50 kPa to 2 MPa are presented and discussed in this paper. The nesting shell decreases inertial cavitation events from 97.96% for an un-nested microbubble to 19.09% for the same microbubbles nested within a 2.53 μm shell. As shell diameter decreases, the percentage of inertially cavitating microbubbles also decreases. For nesting formulations with average outer capsule diameters of 20.52, 14.95, 9.95, 5.55, 2.53, and 1.95 μm, the percentage of sample destroyed at 1 MPa was 51.02, 38.94, 33.25, 25.27, 19.09, and 5.37% respectively.

Sounds of marine seeps: a study of bubble activity near a rigid boundary

A passive acoustic method for detecting environmentally dangerous gas leaks from pipelines and methane naturally leaking from the seabed has been investigated. Gas escape involves the formation and release of bubbles of different sizes. Each bubble emits a sound at a specific frequency. Determination of the bubble radius from the frequency of its signature passive acoustic emission by use of so-called Minnaert formula has a restricted area of applicability near the seabed. The point is that the inertial mass and the damping constant of the birthing bubble are markedly different from those of a free bubble. The theoretical model for the bubble volume oscillations near the seabed has been proposed and an analytical solution has been derived. It was shown that the bispherical coordinates provide separation of variables and are more suitable for analysis of the volume oscillations of these constrained bubbles. Explicit formulas have been derived, which describe the dependence of the bubble emission near a rigid wall on its size and the separation distance between the bubble and the boundary.

Investigation of a method for real time quantification of gas bubbles in pipelines

The need to measure the dynamic void fraction (the proportion of flowing bubbly liquid that is gas) is common across many power, processing and manufacturing industries. Many such pipelines and liquids are optically opaque, and work on margins that require a low cost solution that is not commensurate with the size of the challenge. Such a solution will therefore be a compromise, and in this paper costs are reduced by using a narrowband acoustic solution that cannot, on its own, contain enough information to characterize the void fraction in real time unambiguously. The ambiguity is reduced using likely estimates of the general shape of the bubble size distribution so that, with a single source-receiver pair attached to the outside of the pipe, the absolute gas content can be estimated. While the data that are required a priori (the general shape of the bubble size distribution) are not identical to the output of the inversion (the absolute void fraction of gas entrained as bubbles in the flow), the requirement for such a priori information could limit the usefulness of the technique in industry.

Modelling single- and tandem-bubble dynamics between two parallel plates for biomedical applications

Carefully timed tandem microbubbles have been shown to produce directional and targeted membrane poration of individual cells in microfluidic systems, which could be of use in ultrasound-mediated drug and gene delivery. This study aims at contributing to the understanding of the mechanisms at play in such an interaction. The dynamics of single and tandem microbubbles between two parallel plates is studied numerically and analytically. Comparisons are then made between the numerical results and the available experimental results. Numerically, assuming a potential flow, a three-dimensional boundary element method (BEM) is used to describe complex bubble deformations, jet formation, and bubble splitting. Analytically, compressibility and viscous boundary layer effects along the channel walls, neglected in the BEM model, are considered while shape of the bubble is not considered. Comparisons show that energy losses modify the bubble dynamics when the two approaches use identical initial conditions. The initial conditions in the boundary element method can be adjusted to recover the bubble period and maximum bubble volume when in an infinite medium. Using the same conditions enables the method to recover the full dynamics of single and tandem bubbles, including large deformations and fast re-entering jet formation. This method can be used as a design tool for future tandem-bubble sonoporation experiments.

Microbubble oscillations in capillary tubes

In diagnostic medicine, microbubbles are used as contrast agents to image blood flow and perfusion in large and small vessels. The small vessels (the capillaries) have diameters from a few hundred micrometers down to less than 10 μ m. The effect of such microvessels surrounding the oscillating microbubbles is currently unknown, and is important for increased sensitivity in contrast diagnostics and manipulation of microbubbles for localized drug release. Here, oscillations of microbubbles in tubes with inner diameters of 25 μm and 160 ¿m are investigated using an ultra-high-speed camera at frame rates of ~12 million frames/s. A reduction of up to 50% in the amplitude of oscillation was observed for microbubbles in the smaller 25-μm tube, compared with those in a 160-μm tube. In the 25-μm tube, at 50 kPa, a 48% increase of microbubbles that did not oscillate above the noise level of the system was observed, indicating increased oscillation damping. No difference was observed between the resonance frequency curves calculated for microbubbles in 25-μm and 160-μm tubes. Although previous investigators have shown the effect of microvessels on microbubble oscillation at high ultrasound pressures, the present study provides the first optical images of low-amplitude microbubble oscillations in small tubes.

Models of cylindrical bubble pulsation

Three models are considered for describing the dynamics of a pulsating cylindrical bubble. A linear solution is derived for a cylindrical bubble in an infinite compressible liquid. The solution accounts for losses due to viscosity, heat conduction, and acoustic radiation. It reveals that radiation is the dominant loss mechanism, and that it is 22 times greater than for a spherical bubble of the same radius. The predicted resonance frequency provides a basis of comparison for limiting forms of other models. The second model considered is a commonly used equation in Rayleigh-Plesset form that requires an incompressible liquid to be finite in extent in order for bubble pulsation to occur. The radial extent of the liquid becomes a fitting parameter, and it is found that considerably different values of the parameter are required for modeling inertial motion versus acoustical oscillations. The third model was developed by V. K. Kedrinskii [Hydrodynamics of Explosion (Springer, New York, 2005), pp. 23-26] in the form of the Gilmore equation for compressible liquids of infinite extent. While the correct resonance frequency and loss factor are not recovered from this model in the linear approximation, it provides reasonable agreement with observations of inertial motion.

Model for bubble pulsation in liquid between parallel viscoelastic layers

A model is presented for a pulsating spherical bubble positioned at a fixed location in a viscous, compressible liquid between parallel viscoelastic layers of finite thickness. The Green's function for particle displacement is found and utilized to derive an expression for the radiation load imposed on the bubble by the layers. Although the radiation load is derived for linear harmonic motion it may be incorporated into an equation for the nonlinear radial dynamics of the bubble. This expression is valid if the strain magnitudes in the viscoelastic layer remain small. Dependence of bubble pulsation on the viscoelastic and geometric parameters of the layers is demonstrated through numerical simulations.

The inertial terms in equations of motion for bubbles in tubular vessels or between plates

Equations resembling the Rayleigh-Plesset and Keller-Miksis equations are frequently used to model bubble dynamics in confined spaces, using the standard inertial term RR+3R([middle dot]) (2)/2, where R is the bubble radius. This practice has been widely assumed to be defensible if the bubble is much smaller than the radius of the confining vessel. This paper questions this assumption, and provides a simple rigid wall model for worst-case quantification of the effect on the inertial term of the specific confinement geometry. The relevance to a range of scenarios (including bubbles confined in microfluidic devices; or contained in test chambers for insonification or imaging; or in blood vessels) is discussed.

Regimes of bubble volume oscillations in a pipe

The effect of an acoustically driven bubble on the acoustics of a liquid-filled pipe is theoretically analyzed and the dimensionless groups of the problem are identified. The different regimes of bubble volume oscillations are predicted theoretically with these dimensionless groups. Three main regimes can be identified: (1) For small bubbles and weak driving, the effect of the bubble oscillations on the acoustic field can be neglected. (2) For larger bubbles and still small driving, the bubble affects the acoustic field, but due to the small driving, a linear theory is sufficient. (3) For large bubbles and large driving, the two-way coupling between the bubble and the flow dynamics requires the solution of the full nonlinear problem. The developed theory is then applied to an air bubble in a channel of an inkjet printhead. A numerical model is developed to test the predictions of the theoretical analysis. The Rayleigh-Plesset equation is extended to include the influence of the bubble volume oscillations on the acoustic field and vice versa. This modified Rayleigh-Plesset equation is coupled to a channel acoustics calculation and a Navier-Stokes solver for the flow in the nozzle. The numerical simulations indeed confirm the predictions of the theoretical analysis.

Nonspherical shape oscillations of coated microbubbles in contact with a wall

In this experimental study, the nonspherical and translational behavior of individual coated microbubbles of different sizes, in contact with a 20-μm thickness cellulose wall, are observed and categorized systematically. Images from two orthogonally positioned microscopes are merged and then recorded with an ultra-fast framing camera. Large nonspherical deformations were found with 2.25 MHz frequency ultrasound pulses having driving pressures from 80 to 325 kPa. A parametric model combining potential flow theory with a viscous boundary layer at the wall is developed and used to calculate stresses from the optically recorded microbubble oscillations. Peak shear stress of up to 300 kPa and normal stresses of up to 1 MPa are estimated when microbubbles are insonifed with a 2.25 MHz pulse at 325 kPa. The clinical relevance of these results is discussed.

Acoustic measurement of bubble size in an inkjet printhead

The volume of a bubble in a piezoinkjet printhead is measured acoustically. The method is based on a numerical model of the investigated system. The piezo not only drives the system but it is also used as a sensor by measuring the current it generates. The numerical model is used to predict this current for a given bubble volume. The inverse problem is to infer the bubble volume from an experimentally obtained piezocurrent. By solving this inverse problem, the size and position of the bubble can thus be measured acoustically. The method is experimentally validated with an inkjet printhead that is augmented with a glass connection channel, through which the bubble was observed optically, while at the same time the piezocurrent was measured. The results from the acoustical measurement method correspond closely to the results from the optical measurement.

Ultrasound contrast microbubbles in imaging and therapy: physical principles and engineering

Microbubble contrast agents and the associated imaging systems have developed over the past 25 years, originating with manually-agitated fluids introduced for intra-coronary injection. Over this period, stabilizing shells and low diffusivity gas materials have been incorporated in microbubbles, extending stability in vitro and in vivo. Simultaneously, the interaction of these small gas bubbles with ultrasonic waves has been extensively studied, resulting in models for oscillation and increasingly sophisticated imaging strategies. Early studies recognized that echoes from microbubbles contained frequencies that are multiples of the microbubble resonance frequency. Although individual microbubble contrast agents cannot be resolved-given that their diameter is on the order of microns-nonlinear echoes from these agents are used to map regions of perfused tissue and to estimate the local microvascular flow rate. Such strategies overcome a fundamental limitation of previous ultrasound blood flow strategies; the previous Doppler-based strategies are insensitive to capillary flow. Further, the insonation of resonant bubbles results in interesting physical phenomena that have been widely studied for use in drug and gene delivery. Ultrasound pressure can enhance gas diffusion, rapidly fragment the agent into a set of smaller bubbles or displace the microbubble to a blood vessel wall. Insonation of a microbubble can also produce liquid jets and local shear stress that alter biological membranes and facilitate transport. In this review, we focus on the physical aspects of these agents, exploring microbubble imaging modes, models for microbubble oscillation and the interaction of the microbubble with the endothelium.

Progress and problems in the application of focused ultrasound for blood-brain barrier disruption

Advances in neuroscience have resulted in the development of new diagnostic and therapeutic agents for potential use in the central nervous system (CNS). However, the ability to deliver the majority of these agents to the brain is limited by the blood-brain barrier (BBB), a specialized structure of the blood vessel wall that hampers transport and diffusion from the blood to the brain. Many CNS disorders could be treated with drugs, enzymes, genes, or large-molecule biotechnological products such as recombinant proteins, if they could cross the BBB. This article reviews the problems of the BBB presence in treating the vast majority of CNS diseases and the efforts to circumvent the BBB through the design of new drugs and the development of more sophisticated delivery methods. Recent advances in the development of noninvasive, targeted drug delivery by MRI-guided ultrasound-induced BBB disruption are also summarized.

Measurement of the resonance frequency of single bubbles using a laser Doppler vibrometer

The behavior of bubbles confined in tubes and channels is important in medical and industrial applications. In these small spaces, traditional means of experimentally observing bubble dynamics are often impossible or significantly perturb the system. A laser Doppler vibrometer (LDV) requires a narrow (<1 mm diameter) line-of-sight access for the beam and illumination of the bubble does not perturb its dynamics. LDV measurements of the resonance frequency of a bubble suspended in a small tank are presented to illustrate the utility of this measurement technique. The precision of the technique is similar to the precision of traditional acoustic techniques.

Suppression of shocked-bubble expansion due to tissue confinement with application to shock-wave lithotripsy

Estimates are made of the effect of tissue confinement on the response of small bubbles subjected to lithotriptor shock pressures. To do this the Rayleigh-Plesset equation, which governs the dynamics of spherical bubbles, is generalized to treat a bubble in a liquid region (blood), which is in turn encased within an elastic membrane (like a vessel's basement membrane), beyond which a Voigt viscoelastic material models the exterior tissue. Material properties are estimated from a range of measurements available for kidneys and similar soft tissues. Special attention is given to the constitutive modeling of the basement membranes because of their expected importance due to their proximity to the bubble and their toughness. It is found that the highest expected values for the elasticity of the membrane and surrounding tissue are insufficient to suppress bubble growth. The reduced confinement of a cylindrical vessel should not alter this conclusion. Tissue viscosities taken from ultrasound measurements suppress bubble growth somewhat, though not to a degree expected to resist injury. However, the higher reported viscosities measured by other means, which are arguably more relevant to the deformations caused by growing bubbles, do indeed significantly suppress bubble expansion.

Effect of an entrained air bubble on the acoustics of an ink channel

Piezo-driven inkjet systems are very sensitive to air entrapment. The entrapped air bubbles grow by rectified diffusion in the ink channel and finally result in nozzle failure. Experimental results on the dynamics of fully grown air bubbles are presented. It is found that the bubble counteracts the pressure buildup necessary for the droplet formation. The channel acoustics and the air bubble dynamics are modeled. For good agreement with the experimental data it is crucial to include the confined geometry into the model: The air bubble acts back on the acoustic field in the channel and thus on its own dynamics. This two-way coupling limits further bubble growth and thus determines the saturation size of the bubble.

Ultrasound microbubble contrast agents: fundamentals and application to gene and drug delivery

This review offers a critical analysis of the state of the art of medical microbubbles and their application in therapeutic delivery and monitoring. When driven by an ultrasonic pulse, these small gas bubbles oscillate with a wall velocity on the order of tens to hundreds of meters per second and can be deflected to a vessel wall or fragmented into particles on the order of nanometers. While single-session molecular imaging of multiple targets is difficult with affinity-based strategies employed in some other imaging modalities, microbubble fragmentation facilitates such studies. Similarly, a focused ultrasound beam can be used to disrupt delivery vehicles and blood vessel walls, offering the opportunity to locally deliver a drug or gene. Clinical translation of these vehicles will require that current challenges be overcome, where these challenges include rapid clearance and low payload. The technology, early successes with drug and gene delivery, and potential clinical applications are reviewed.

Cavitation threshold of microbubbles in gel tunnels by focused ultrasound

The investigation of inertial cavitation in micro-tunnels has significant implications for the development of therapeutic applications of ultrasound such as ultrasound-mediated drug and gene delivery. The threshold for inertial cavitation was investigated using a passive cavitation detector with a center frequency of 1 MHz. Micro-tunnels of various diameters (90 to 800 microm) embedded in gel were fabricated and injected with a solution of Optison(trade mark) contrast agent of concentrations 1.2% and 0.2% diluted in water. An ultrasound pulse of duration 500 ms and center frequency 1.736 MHz was used to insonate the microbubbles. The acoustic pressure was increased at 1-s intervals until broadband noise emission was detected. The pressure threshold at which broadband noise emission was observed was found to be dependent on the diameter of the micro-tunnels, with an average increase of 1.2 to 1.5 between the smallest and the largest tunnels, depending on the microbubble concentration. The evaluation of inertial cavitation in gel tunnels rather than tubes provides a novel opportunity to investigate microbubble collapse in a situation that simulates in vivo blood vessels better than tubes with solid walls do.