Nail S. Khabeev

Bio: Nail S. Khabeev is an academic researcher from University of Bahrain. The author has contributed to research in topics: Bubble & Heat transfer. The author has an hindex of 9, co-authored 46 publications receiving 423 citations. Previous affiliations of Nail S. Khabeev include Moscow State University.

Heat exchange between a gas bubble and a liquid

Abstract: The nonlinear problem of thermal and dynamic interaction between a single gas bubble and surrounding liquid is considered. This problem is met in studies of gas-liquid mixture flows, in particular, in Shockwave propagation in such media. A numerical solution is presented for various modes of bubble surface radial motion. The modes correspond to bubble behavior directly beyond a shock-wave front, where the latter enters the bubble screen, and to the behavior of a bubble located in the depths of the bubble curtain, where the wave becomes diffuse. Analytic solutions of the linearized problem of thermal conductivity for free and constrained small harmonic oscillations of a gas bubble in a liquid were obtained in [1, 2]. Cooling of a hot gas bubble was considered in [3], that study, however, contains inaccuracies. In particular, it was assumed in the solution that the gas density in the bubble was homogeneous. The equation for heat flux in dimensionless variables was written inaccurately. However, in the examples considered in [3] these inaccuracies do not lead to significant errors in the numerical results.

Waves in liquids with vapour bubbles

Abstract: An investigation of wave processes in liquids with vapour bubbles with interphase heat and mass transfer is presented. A single-velocity two-pressure model is used which takes into account both the liquid radial inertia due to medium volume changes, and the temperature distribution around the bubbles. An analysis of the microscopic fields of physical parameters is aimed at closing the system of equations for averaged characteristics. The original system of differential equations of the model is modified to a form suitable for numerical integration. An elliptic equation is obtained to determine the field of the mixture average pressure at an arbitrary time through the known fields of the remaining quantities. The existence of the steady structure of shock waves, either monotonic or oscillatory, is proved. The effect of the initial conditions, shock strength, volume fraction, and dispersity of the vapour phase and of the thermophysical properties of the phases on shock-wave structure and relaxation time is studied. The influence of nonlinear, dispersion and dissipative effects on the wave evolution is also investigated. The shock adiabat for reflected waves is analysed. The results obtained have proved that the interphase heat and mass transfer determined by the thermal diffusivity of the liquid greatly influences the wave structure. The possible enhancement of disturbances in the region of their initiation is shown. The model has been tested for suitability and the results of calculations have been compared with experimental data.

Dynamics of vapor bubbles

Abstract: The nonlinear problem of the thermal, mass, and dynamic interaction of a single vapor bubble with the surrounding liquid is discussed. This problem has ramifications in research on flows of vapor-liquid mixtures with a bubble-matrix structure, in particular, the propagation of shock waves in such media. Results are given from a numerical solution of the problem of the radial motion imparted to a bubble by a sudden change of pressure in the liquid; this problem corresponds, in particular, to the behavior of bubbles behind a shock front when the latter enters a bubble curtain.

Dynamics of vapor-gas bubbles

Abstract: The nonlinear problem of thermal, mass, and dynamic interaction between a vapor-gas bubble and a liquid is considered. The results of numerical solution of the problem of radial motion of the bubble caused by a sudden pressure change in the liquid, illustrating the behavior of vapor-gas bubbles in compression and rarefaction waves, are presented. The corresponding problem for single-component gas and vapor bubbles was considered in [1, 2].

The temperature of cavitation.

Abstract: Ultrasonic irradiation of liquids causes acoustic cavitation: the formation, growth, and implosive collapse of bubbles. Bubble collapse during cavitation generates transient hot spots responsible for high-energy chemistry and emission of light. Determination of the temperatures reached in a cavitating bubble has remained a difficult experimental problem. As a spectroscopic probe of the cavitation event, sonoluminescence provides a solution. Sonoluminescence spectra from silicone oil were reported and analyzed. The observed emission came from excited state C2 (Swan band transitions, d3IIg—a3IIµ), which has been modeled with synthetic spectra as a function of rotational and vibrational temperatures. From comparison of synthetic to observed spectra, the effective cavitation temperature was found to be 5075 ± 156 K.

The growth of vapor bubbles in superheated liquids. report no. 26-6

Abstract: The growth of a vapor bubble in a superheated liquid is controlled by three factors: the inertia of the liquid, the surface tension, and the vapor pressure. As the bubble grows, evaporation takes place at the bubble boundary, and the temperature and vapor pressure in the bubble are thereby decreased. The heat inflow requirement of evaporation, however, depends on the rate of bubble growth, so that the dynamic problem is linked with a heat diffusion problem. Since the heat diffusion problem has been solved, a quantitative formulation of the dynamic problem can be given. A solution for the radius of the vapor bubble as a function of time is obtained which is valid for sufficiently large radius. This asymptotic solution covers the range of physical interest since the radius at which it becomes valid is near the lower limit of experimental observation. It shows the strong effect of heat diffusion on the rate of bubble growth. Comparison of the predicted radius‐time behavior is made with experimental observations in superheated water, and very good agreement is found.

Physics of bubble oscillations

Abstract: Bubbles in liquids, soft and squeezy objects made of gas and vapour, yet so strong as to destroy any material and so mysterious as at times turning into tiny light bulbs, are the topic of the present report. Bubbles respond to pressure forces and reveal their full potential when periodically driven by sound waves. The basic equations for nonlinear bubble oscillation in sound fields are given, together with a survey of typical solutions. A bubble in a liquid can be considered as a representative example from nonlinear dynamical systems theory with its resonances, multiple attractors with their basins, bifurcations to chaos and not yet fully describable behaviour due to infinite complexity. Three stability conditions are treated for stable trapping of bubbles in standing sound fields: positional, spherical and diffusional stability. Chemical reactions may become important in that respect, when reacting gases fill the bubble, but the chemistry of bubbles is just touched upon and is beyond the scope of the present report. Bubble collapse, the runaway shrinking of a bubble, is presented in its current state of knowledge. Pressures and temperatures that are reached at this occasion are discussed, as well as the light emission in the form of short flashes. Aspherical bubble collapse, as for instance enforced by boundaries nearby, mitigates most of the phenomena encountered in spherical collapse, but introduces a new effect: jet formation, the self-piercing of a bubble with a high velocity liquid jet. Examples of this phenomenon are given from light induced bubbles. Two oscillating bubbles attract or repel each other, depending on their oscillations and their distance. Upon approaching, attraction may change to repulsion and vice versa. When being close, they also shoot self-piercing jets at each other. Systems of bubbles are treated as they appear after shock wave passage through a liquid and with their branched filaments that they attain in standing sound fields. The N-bubble problem is formulated in the spirit of the n-body problem of astrophysics, but with more complicated interaction forces. Simulations are compared with three-dimensional bubble dynamics obtained by stereoscopic high speed digital videography.

Collapse and rebound of a laser-induced cavitation bubble

Abstract: A strong laser pulse that is focused into a liquid produces a vapor cavity, which first expands and then collapses with subsequent rebounds. In this paper a mathematical model of the spherically symmetric motion of a laser-induced bubble is proposed. It describes gas and liquid dynamics including compressibility, heat, and mass transfer effects and nonequilibrium processes of evaporation and condensation on the bubble wall. It accounts also for the occurrence of supercritical conditions at collapse. Numerical investigations of the collapse and first rebound have been carried out for different bubble sizes. The results show a fairly good agreement with experimental measurements of the bubble radius evolution and the intensity of the outgoing shock wave emitted at collapse. Calculations with a small amount of noncondensable gas inside the bubble show its strong influence on the dynamics.

The thermal behaviour of oscillating gas bubbles

Abstract: Several aspects of the oscillations of a gas bubble in a slightly compressible liquid are discussed by means of a simplified model based on the assumption of a spatially uniform internal pressure. The first topic considered is the linear initial-value problem for which memory effects and the approach to steady state are analysed. Large-amplitude oscillations are studied next in the limit of large and small thermal diffusion lengths obtaining, in the first case, an explicit expression for the internal pressure, and, in the second one, an integral equation of the Volterra type. The validity of the assumption of uniform pressure is then studied analytically and numerically. Finally, the single-bubble model is combined with a simple averaged-equation model of a bubbly liquid and the propagation of linear and weakly nonlinear pressure waves in such a medium is considered.