Investigation of a mutual interaction force at different pressure amplitudes in sulfuric acid

This paper investiages the secondary Bjerknes force for two oscillating bubbles in various pressure amplitudes in a concentration of 95% sulfuric acid. The equilibrium radii of the bubbles are assumed to be smaller than 10 μm at a frequency of 37 kHz in various strong driving acoustical fields around 2.0 bars （1 bar=10^5 Pa）. The secondary Bjerknes force is investigated in uncoupled and coupled states between the bubbles, with regard to the quasi-adiabatic model for the bubble interior. It finds that the value of the secondary Bjerknes force depends on the driven pressure of sulfuric acid and its amount would be increased by liquid pressure amplitude enhancement. The results show that the repulsion area of the interaction force would be increased by increasing the driven pressure because of nonlinear oscillation of bubbles.

Interaction of a bubble and a bubble cluster in an ultrasonic field

Using an appropriate approximation, we have formulated the interacting equation of multi-bubble motion for a system of a single bubble and a spherical bubble cluster. The behavior of the bubbles is observed in coupled and uncoupled states. The oscillation of bubbles inside the cluster is in a coupled state. The numerical simulation demonstrates that the secondary Bjerknes force can be influenced by the number density, initial radius, distance, driving frequency, and amplitude of ultrasound. However, if a bubble approaches a bubble cluster of the same initial radii, coupled oscillation would be induced and a repulsive force is evoked, which may be the reason why the bubble cluster can exist steadily. With the increment of the number density of the bubble cluster, a secondary Bjerknes force acting on the bubbles inside the cluster decreases due to the strong suppression of the coupled bubbles. It is shown that there may be an optimal number density for a bubble cluster which can generate an optimal cavitation effect in liquid for a stable driving ultrasound.

Machine learning models for the secondary Bjerknes force between two insonated bubbles

The secondary Bjerknes force plays a significant role in the evolution of bubble clusters.However,due to the complex dependence of the force on multiple parameters,it is highly non-trivial to include its effects in the simulations of bubble clusters.In this paper,machine learning is used to develop a data-driven model for the secondary Bjerknes force between two insonated bubbles as a function of the equilibrium radii of the bubbles,the distance between the bubbles,the amplitude and the center frequency of the ultrasound wave.The sign of the force may change with the phase difference between the oscillating bubbles.Meanwhile,the magnitude of the force varies over several orders of magnitude,which poses a serious challenge for the usual machine learning models.To overcome this difficulty,the magnitudes and the signs of the force are separated and modelled separately.A nonlinear regression is obtained with a feed-forward network model for the logarithm of the magnitude,whereas the sign is modelled by a support-vector machine model.The principle,the practical aspects related to the training and validation of the machine models are introduced.The predictions from the models are checked against the values computed from the Keller-Miksis equations.The results show that the models are extremely efficient while providing accurate estimate of the force.The models make it computationally feasible for the future simulations of the bubble clusters to include the effects of the secondary Bjerknes force.

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 compre- ssibility 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.