Study On The Equation Of Motion Of Quasi - Static Cavitation In The Ultrasonic And The Equation Of Motion Of The Isothermal Liquid

In this paper, a new cavitation bubble motion equation is given by studying the method of Rayleigh equation. The definition of the ideal gas polytropic process and the pressure function of the barotropic fluid are considered in the process. This process eliminates the polytropic exponent skillfully. It shifts from the influence of polytropic exponent to the influence of ultrasonic field and the instantaneous bubble size on the result of the movement of cavitation bubble. During this process, the ultrasonic field and the instantaneous bubble size is dynamic.Comparing with a fixed polytropic index value, they can response the thermodynamic state of bubble more timely and accurately. So this new cavitation bubble motion equation can be used to all kinds of quasi static process that ware made up with numerous infinite short polytropic process. The simulation results show that the bigger the amplitude of acoustic pressure or the lower the ultrasonic frequency is, or the smaller the surface tension and the viscosity coefficient of continuous phase liquid are, the greater the movement of cavitation bubble is; The variation of cavitation bubble radius will be bigger when the cavitation bubble initial radius is smaller. But when the surface tension and continuous phase liquid viscous coefficient decrease to a certain extent, their continue reducing has nearly influence on the motion of bubble. Comparing with the cavitation bubble motion equation of adiabatic state whose adiabatic coefficient is 1.67, simulation results show that:With the increase of the sound pressure amplitude, the results from the cavitation bubble motion equation of adiabatic state becomes closer to those of cavitation bubble motion equation of quasi static during the bubble from growth to shrink to the initial radius R=R0. But when the sound pressure amplitude is large enough, no matter how the ultrasonic frequency, surface tension coefficient and the viscous coefficient of continuous phase liquid are, this stage can be nearly as quasi-static adiabatic process; When the initial radius is rather small, the stage that the bubbles from growth to shrink to the initial radius R=R0 can be nearly as quasi-static adiabatic process; When the initial radius is rather larger, this stage can’t be as adiabatic process, but belongs to the other quasi-static process; When the bubble’s radius move to less than the initial radius or will soon collapse, during this short period of time, it cannot be handled as a quasi-static adiabatic process and also should belong to the other quasi-static.Since the similarities and differences of the dispersed phase droplet model and the cavitation bubble model, (The same place:A single cavitation bubble model can be simplified into a tiny bubbles presenting in an infinite region of liquid which is exposured to the ultrasonic field, and a single droplet model can be simplified into a tiny spherical droplets which is immiscible in an infinite region of liquid that exists in ultrasonic field, so droplets and cavitation bubbles have the same shape and the external environment. The different place:In the model of cavitation bubbles, the inside and the outside of the wall of bubble are gas and liquid, and the wall is a gas-liquid surface which is composed by two-phase:gas and liquid; but the inside and the outside of the droplet wall are all liquid, the droplet wall is a liquid-liquid interface which is composed by two-phase:liquid and liquid.) and their movements in the ultrasonic field are all on the basis of the principle of conservation of energy. In this paper, the same places of them are be retained and the differences of them are be considered, then we mainly make the following changes, we have the interfacial tension of liquid-liquid instead of surface tension of gas-liquid, then we have the stress of the wall of liquid droplets, which is deduced by isothermal state equation, instead of the stress of the wall of cavitation bubble, which is deduced from the ideal gas state equation. In view of the above-mentioned facts, we get the isothermal state equations of motion of droplet by using the basic theory of derivation of cavitation bubble equation under the action of ultrasonic. The simulation results showed that the change of the dispersed phase droplets under the effect ultrasonic field, not only depends on the droplet itself and the continuous phase liquid’s parameters, but also depends on ultrasonic irradiation parameters. The different continuous phase liquid have different sound velocity, density and viscosity. Sound velocity had virtually no effect on the change of droplet radius. The smaller the density or viscosity is, the more obvious change the droplet radius will. The change of droplet’s size grows with the reducing of static pressure and droplet initial radius. When the initial radius is large enough, even if under the strong ultrasonic effect, droplet radius is also difficult to change; In the case of the droplets and the continuous phase liquid have be determined, the greater the ultrasonic pressure amplitude or the lower the ultrasonic frequency is, the greater the droplet radius increases. When the frequency is big enough, the droplet radius is almost invariable at the steady state of its initial radius. Comparing with the compression of droplet, the growth of droplet is more obvious under ultrasonic field. Through analyzing the simulation results that the radius’s change of droplets which is in the oil phase and ultrasonic field, we can infer that the part that is in the system of inverse emulsion or similar to the inverse emulsion, and similar to water droplets, may also grow and shrink in ultrasonic filed. Meanwhile, the extent of shrinking and growing not only depends on the various parameters of ultrasonic field, but also depends on some parameters of the system itself that is researched.