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Carefully timed tandem microbubbles have been shown to produce directional and targeted membrane poration of individual cells in microfluidic systems, which could be of use in ultrasound-mediated drug and gene delivery. This study aims at contributing to the understanding of the mechanisms at play in such an interaction. The dynamics of single and tandem microbubbles between two parallel plates is studied numerically and analytically. Comparisons are then made between the numerical results and the available experimental results. Numerically, assuming a potential flow, a three-dimensional boundary element method (BEM) is used to describe complex bubble deformations, jet formation, and bubble splitting. Analytically, compressibility and viscous boundary layer effects along the channel walls, neglected in the BEM model, are considered while shape of the bubble is not considered. Comparisons show that energy losses modify the bubble dynamics when the two approaches use identical initial conditions. The initial conditions in the boundary element method can be adjusted to recover the bubble period and maximum bubble volume when in an infinite medium. Using the same conditions enables the method to recover the full dynamics of single and tandem bubbles, including large deformations and fast re-entering jet formation. This method can be used as a design tool for future tandem-bubble sonoporation experiments.

The growth, oscillation and collapse of vortex cavitation bubbles are examined using both two- and three-dimensional numerical models. As the bubble changes volume within the core of the vortex, the vorticity distribution of the surrounding flow is modified, which then changes the pressures at the bubble interface. This interaction can be complex. In the case of cylindrical cavitation bubbles, the bubble radius will oscillate as the bubble grows or collapses. The period of this oscillation is of the order of the vortex time scale, τV= 2πrc/uθ,max, wherercis the vortex core radius anduθ,maxis its maximum tangential velocity. However, the period, oscillation amplitude and final bubble radius are sensitive to variations in the vortex properties and the rate and magnitude of the pressure reduction or increase. The growth and collapse of three-dimensional bubbles are reminiscent of the two-dimensional bubble dynamics. But, the axial and radial growth of the vortex bubbles are often strongly coupled, especially near the axial extents of the bubble. As an initially spherical nucleus grows into an elongated bubble, it may take on complex shapes and have volume oscillations that also scale with τV. Axial flow produced at the ends of the bubble can produce local pinching and fission of the elongated bubble. Again, small changes in flow parameters can result in substantial changes to the detailed volume history of the bubbles.

Tracor Hydronautics Inc., 7210 Pindell School Road, Laurel, Maryland(Received 4 October 1983 and in revised form 5 October 1984)The presence and behaviour of vaporous cavities are of major importance in manymodern industrial applications where heat transfer, boiling or cavitation are involved.n'oilowing a sudden depressurization of a superheated fluid, the bubble growth ratecontrols the generated transients and heat transfer. Most existing computer modellingand prediction codes are based on individual spherical-bubble-growth studies andneglect possible interactions and collective phenomena. This paper addresses thiscollective behaviour using a singular-perturbation approach. The method of matchedasymptotic expansions is used to describe the bubble growth, taking into account itsinteraction with a finite number of surrounding bubbles. A computer program isdeveloped and the influence of the various parameters is studied numerically for theparticular case of a symmetrical equal-size-bubble configuration and a thermal-boundary-layer approximation. A significant influence of these interactions on bubblegrowth and heat transfer is observed: compared to an isolated-bubble case, the growthrate of a bubble is reduced in the presence of other bubbles, and the temperature dropat its wall is smaller. As a result the heat loss due to bubble growth is smaller. Theseeffects increase with the number of interacting bubbles.1. IntroductionThe presence and behaviour of vaporous cavities are of great importance in manymodern industrial applications where heat transfer, boiling, or cavitation areinvolved. For instance, the rate of heat transfer in nucleate boiling dependsessentially on the ability of the heat-transfer surface to nucleate and support thegrowth of vapour bubbles. The conduction of heat in the liquid is greatly affectedby the absorption and release of latent heat during the phase transition at thebubble-liquid interfaces. Wave propagation in the medium is also significantlyaffected by bubble behaviour and volume changes. Consequently, the study of thebubble dynamics and of the two-phase medium constituted by the host liquid andbubbles of its own vapour is fundamental in the design, analysis, and application ofvarious engineering systems.Many modern processes deal with various fluids in conditions where both heat-transfer effects and inertia contribute in controlling the bubble behaviour. Examplesof such fluids are hydrocarbons, liquid metals, cryogenic fluids, and demineralizedhot water at temperatures as high as 300 oC. Heat transfer, boiling or cavitationappears with these liquids in such applications as high-speed flows of sodium-cooledfast-breeder reactors in nuclear-power engineering, circulation of cryogenic liquidin pumps in aerospace engineering, and flow of hot water nrszzles and tubes in