Study of nonlinear oscillations and chaos of a bubble cluster in an oscillatory pressure field

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1. A new laser trapping method is devised to control the position of bubbles out of contact. This method is based on the scanning of a thin laser beam in which the envelope surface of the beam is a corn. This method is adequate to trap a rising bubble because the potential barrier made by the light momentum change due to the refraction at the bubble interface exists only at the upper side of the bubble. A bubble of about 10 mum in diameter in water is trapped and manipulated successfully by this method. It is shown that the optical force acting on the bubble in the lateral direction is about 1pN at 500mW of laser power, and in the axial direction about 6pN at the same power. The stability of trapped bubbles due to the mass diffusion is discussed. The strength of the force and the stability of the trapping state are also evaluated theoretically. The results show that the larger the focal angle is, the stronger the trapping force becomes.2. The governing equations of a cluster of spheric … More al or nonspherical bubbles are derived by taking account of the thermal effects of the internal gas and the mass diffusion of the gas. The equations are applied to the nonlinear oscillations of multiple interacting bubbles. It is shown that the polytropic relation for the internal gas does not hold when the nonlinearity of the radial oscillation becomes strong. Both radial and surface oscillations are affected by the translational motion of each bubble. The subharmonic oscillation of interacting bubbles occurs more easily than that of an isolated bubble due to the bubble-bubble interaction. It is also shown that the threshold value where the bubble oscillation bifurcates and becomes chaotic decreases due to the mass diffusion of the internal gas.3. The boundary element method (BEM) combined with the finite volume method is used in investigating the thermal effects of the internal gas on the dynamics of a gas bubble with large deformation near a plane rigid wall. It is shown that the bubble collapse is accelerated by the heat transfer inside the bubble. The temperature distribution inside the bubble is strongly dependent on the degree of deformation of the bubble. When the jet is produced on the bubble wall, the internal temperature gradient at the side farthest from the rigid wall becomes very steep. This steep gradient increases the liquid temperature to a level higher than that for the single bubble. The dynamics of toroidal bubbles is also investigated using BEM.The results show that the high pressure region is formed in a liquid after a liquid microjet threads a bubble. This high pressure region moves toward the rigid wall and increases the pressure of the wall. Less