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This study analyzes the growth of a vapour bubble in a superheated nanofluid with variable surface tension at the bubble interface. The governing equations describing the problem are formulated, converted to a single integrodifferential equation, and solved analytically. The results are implemented in one of the favorable nanofluids, namely, Al2O3/water, since it is widely used in nanofluid applications, which include self-cooling devices and as a coolant in newly designed photovoltaic/thermal systems, because it has higher thermal and electrical physical properties than the base fluid and a lower economical preparation cost. The results showed that the growth process is proportional to the thermal diffusivity and the Jakob number, while it is inversely proportional to surface tension, dynamic viscosity, initial bubble radius, coefficient of the initial pressure difference, initial void fraction, and nanoparticle volume fraction. Moreover, we conducted a comparison to the experimental data obtained by Hamda and Hamed (2016), and our results achieved a better agreement with these data than some famous studies for both experiments for superheated Al2O3/water nanofluid and pure water (base fluid), because our model considered the effects of several parameters that were ignored in the previous theories, which have been derived as special cases of our result. Furthermore, the effects of nanoparticle characteristics and slip mechanisms; base fluid type and temperature; and the addition of surfactants on bubble growth rates are investigated. Implications drawn from this study may have consequences for the optimum design of thermal systems/devices based on nanofluid technology.

To facilitate practical medical applications such as cancer treatment utilizing focused ultrasound and bubbles, a mathematical model that can describe the soft viscoelasticity of human body, the nonlinear propagation of focused ultrasound, and the nonlinear oscillations of multiple bubbles is theoretically derived and numerically solved. The Zener viscoelastic model and Keller–Miksis bubble equation, which have been used for analyses of single or few bubbles in viscoelastic liquid, are used to model the liquid containing multiple bubbles. From the theoretical analysis based on the perturbation expansion with the multiple-scales method, the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation, which has been used as a mathematical model of weakly nonlinear propagation in single phase liquid, is extended to viscoelastic liquid containing multiple bubbles. The results show that liquid elasticity decreases the magnitudes of the nonlinearity, dissipation, and dispersion of ultrasound and increases the phase velocity of the ultrasound and linear natural frequency of the bubble oscillation. From the numerical calculation of resultant KZK equation, the spatial distribution of the liquid pressure fluctuation for the focused ultrasound is obtained for cases in which the liquid is water or liver tissue. In addition, frequency analysis is carried out using the fast Fourier transform, and the generation of higher harmonic components is compared for water and liver tissue. The elasticity suppresses the generation of higher harmonic components and promotes the remnant of the fundamental frequency components. This indicates that the elasticity of liquid suppresses shock wave formation in practical applications.

A physico-mathematical model composed of a single equation that consistently describes nonlinear focused ultrasound, bubble oscillations, and temperature fluctuations is theoretically proposed for microbubble-enhanced medical applications. The Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation that has been widely used as a simplified model for nonlinear propagation of focused ultrasound in pure liquid is extended to that in liquid containing many spherical microbubbles, by applying the method of multiple scales to the volumetric averaged basic equations for bubbly liquids. As a result, for two-dimensional and three-dimensional cases, KZK equations composed of the linear combination of nonlinear, dissipation, dispersion, and focusing terms are derived. Especially, the dissipation term depends on three factors, i.e., interfacial liquid viscosity, liquid compressibility, and thermal conductivity of gas inside bubbles; the thermal conduction is evaluated by using four types of temperature gradient models. Finally, we numerically solve the derived KZK equation and show a moderate temperature rise appropriate to medical applications.

This study aims to characterize the interaction of doublet bubbles growing near a solid wall in ferroparticle nanofluids. Accordingly, we analyzed the behavior of spherical bubbles near a rigid wall considering liquid compressibility of suspended ferro-nanoparticles. In addition to the interaction effect between two bubbles, we considered the rigid wall forces and thermophysical configurations of the particles in nanofluids to understand the bubble growth. The equation of motion of the doublet bubbles was formulated based on the continuity equation, Euler equation, wave equation, and thermophysical configurations of the particles in nanofluids. Subsequently, the developed model was analytically solved by modifying the Plesset–Zwick technique. Throughout the bubble growth, we examined the thermal effects on the cavitation bubble dynamics, such as the distance between the interacting bubbles, vertical distance between the bubble center and rigid wall, and ferro-nanoparticle volume concentration. The analysis results revealed that the bubble growth was directly proportional to the Jacob number and thermal diffusivity, and inversely proportional to the distance between the boundary rigid wall and bubble center. Furthermore, it can be deduced from the results that the presence of the wall significantly influenced the bubble growth and made a significant deviation between the moving velocities of the interfaces both near and far from the wall. Ultimately, the phenomenon was physically interpreted based on the theory of bubble dynamics, and the water pressure induced by the bubble growth was estimated. The results were well aligned with the theoretical and experimental results from previous studies.

Based on the unified theory by the present authors (Kanagawa et al., J. Fluid Sci. Tech., 5, 2010), the Korteweg-de Vries-Burgers (KdVB) equation and the nonlinear Schrödinger (NLS) equation with an attenuation term for weakly nonlinear waves in bubbly liquids are re-derived from a system of bubble-liquid mixture model equations composed of the conservation equations of mass and momentum, the Keller equation for bubble dynamics, and supplementary equations. We show that the re-derived KdVB equation and NLS equation are essentially the same as those derived from a system of two-fluid model equations except for the coefficients of nonlinear, dissipation, and dispersion terms. The differences in these coefficients are studied in detail, and we find that for the case of KdVB equation, the mixture model is valid only for sufficiently small initial void fractions. On the other hand, for the case of NLS equation, the range of validity of the mixture model depends on not only the initial void fraction but also the wavenumber concerned.

In our previous paper (Kanagawa et al., J. Fluid Sci. Tech., 5, 2010), we have proposed a systematic method for derivation of various types of nonlinear wave equations for plane waves in bubbly liquids. The method makes use of an asymptotic expansion with multiple scales in terms of a small wave amplitude as an expansion parameter and a set of scaling relations of physical parameters, based on basic equations of two-fluid model of bubbly flows. In this paper, we extend the method so as to handle a weakly diffracted ultrasound beam in a quiescent liquid containing a number of spherical gas bubbles distributed with a weak nonuniformity. Because of the high expandability of the original method, the extension can be accomplished by adding a scaling relation of the diameter of the beam to the original set of scaling relations. As a result, we derive a generalized Khokhlov—Zabolotskaya—Kuznetsov (KZK) equation [or a generalized Kadomtsev—Petviashvili (KP) equation] for a long wave and low frequency case.

We propose a systematic derivation method of the Korteweg-de Vries-Burgers (KdVB) equation and nonlinear Schrödinger (NLS) equation for nonlinear waves in bubbly liquids on the basis of appropriate choices of scaling relations of physical parameters. The basic equations are composed of a set of conservation equations for mass and momentum and the equation of bubble dynamics in a two-fluid model. The scaling of parameters is related to the wavelength, frequency, propagation speed, and amplitude of waves concerned. With the help of the method of multiple scales, appropriate choices of the parameter scaling allow us to derive various nonlinear wave equations systematically from a set of basic equations. The result shows that the one-dimensional nonlinear propagation of a long wave with a low frequency is described by the KdVB equation, and that of an envelope of a carrier wave with a high frequency by the NLS equation. Thus, we establish a unified theory of derivation of nonlinear wave equations in bubbly liquids.

This paper experimentally studies the influence of two-phase flow behavior on the operating limits of steam injector (SI). SI is the passive jet pump with a converging-diverging structure. SI operates without the electrical power and discharges water at high pressure. However, in regard to the operating limits of SI, it is unclear which takes into account the discharged flow structure. In this paper, the pressure distributions along the flow direction and the discharge pressure were measured by changing the inlet steam pressure and the load on the exit of the test section. Furthermore, the discharged flow at the diffuser was observed with a high-speed camera. As a result, a boundary was observed in the discharged flow at which the flow structure changed. The area from the throat to this boundary is considered as a two-phase region which steam did not condense completely in the mixing nozzle remained. This boundary moved upstream as the load on the exit increased, and a significant pressure rise occurred at the position where the boundary was reached. In addition, white propagations towards the downstream direction were observed. This propagation is considered as pressure wave propagation. The propagating speed was estimated using image processing. Assuming that the pressure wave propagates at sonic speed, the void fraction at the discharged flow was estimated by the existing model. Based on the above, the influence of the two-phase flow (in the discharged flow structure) on the operating characteristics of SI is discussed.

The acoustic levitation is one of the levitation techniques to control a sample in sound pressure. The acoustic levitation induces the internal and external flow of the levitated droplet. It is considered that these flows affect heat and mass transfer of the levitated droplet. The purpose of this study is to investigate the relationship between convective heat transfer and flow behavior of the levitated droplet. The convective heat transfer between ambient air and the droplet is calculated by an evolution of the surface area and temperature. The convective heat transfer increases as the temperature of water droplet increases. The external flow structure is measured by PIV. The non-heated water droplet has a toroidal vortex below a levitated droplet. As the temperature of water droplet increases, the external flow structure changes from that of non-heated droplet. The larger the diameter and temperature of droplet become, the larger external flow velocity near the surface of the levitated droplet becomes. It is suggested that the increase of external flow velocity enhances the convective heat transfer and the convective heat transfer is more enhanced by the increase of temperature. [ABSTRACT FROM AUTHOR]

Jet breakup is an important behavior at a core disruptive accident for a sodium-cooled fast reactor. The lattice Boltzmann (LB) method is adopted to simulate the jet breakup behavior. The Multiple-Relaxation Time (MRT) scheme is introduced into the existing three-dimensional 19-velocity (D3Q19) LB model for immiscible two-phase flow to enhance the numerical stability for low kinematic viscosity. The simulation results show that the present LB model using MRT enables to simulate the jet breakup behavior, where the kinematic viscosity is of the order of 10-3. The velocity field and interfacial shape are compared with the experimental result using PIV and Laser-Induced Fluorescence (LIF). The interfacial instability and fragmentation behavior of the jet can be also simulated. Comparison of the LB simulation with experimental data shows that the time series of jet leading edge can be simulated within an error of around 10%. [ABSTRACT FROM AUTHOR]

This paper theoretically treats the weakly nonlinear propagation of diffracted sound beams in nonuniform bubbly liquids. The spatial distribution of the number density of the bubbles, initially in a quiescent state, is assumed to be a slowly varying function of the spatial coordinates; the amplitude of variation is assumed to be small compared to the mean number density. A previous derivation method of nonlinear wave equations for plane progressive waves in uniform bubbly liquids [Kanagawa, Yano, Watanabe, and Fujikawa (2010). J. Fluid Sci. Technol. 5(3), 351-369] is extended to handle quasi-plane beams in weakly nonuniform bubbly liquids. The diffraction effect is incorporated by adding a relation that scales the circular sound source diameter to the wavelength into the original set of scaling relations composed of nondimensional physical parameters. A set of basic equations for bubbly flows is composed of the averaged equations of mass and momentum, the Keller equation for bubble wall, and supplementary equations. As a result, two types of evolution equations, a nonlinear Schrödinger equation including dissipation, diffraction, and nonuniform effects for high-frequency short-wavelength case, and a Khokhlov-Zabolotskaya-Kuznetsov equation including dispersion and nonuniform effects for low-frequency long-wavelength case, are derived from the basic set. [ABSTRACT FROM AUTHOR]

A droplet of millimeter-to-centimeter scale can exhibit electrostatic levitation, and such levitated droplets can be used for the measurement of the surface tension of the liquids by observing the characteristic frequency of oscillatory deformation. In the present study, a simple mechanical model is proposed by considering a single mode of oscillation in the ellipsoidal deformation of a levitated rotating droplet. By measuring the oscillation frequency with respect to the rotational speed and oscillation amplitude, it is expected that the accuracy of the surface tension measurement could be improved. Using the proposed model, the dependences of the characteristic frequency of oscillatory deformation and the averaged aspect ratio are calculated with respect to the rotational angular velocity of a rotating droplet. These dependences are found to be consistent with the experimental observations. [ABSTRACT FROM AUTHOR]