The motion of two equal spherical bubbles moving along their line of centres in a viscous liquid is studied numerically in bispherical coordinates. The unsteady Navier-Stokes equations are solved using a mixed spectral/finite-difference scheme for Reynolds numbers up to 200. Free-slip conditions at the bubble surfaces are imposed, while the normal stress condition is replaced by the sphericity constraint under the assumption of small Weber number. The vorticity shed by the upstream bubble affects the drag on the trailing bubble in a very complex fashion that appears to be quite beyond the power of existing asymptotic analyses. The separation between two equal bubbles rising in line under the action of buoyancy is predicted to reach an equilibrium value dependent on the Reynolds number. This result is at variance with experiment. The explanation offered of this difference casts further doubt on the feasibility of a simplified simulation of bubbly liquid dynamics.

The uid mechanical aspects of the axisymmetric growth and collapse of a bubble in a narrow tube lled with a viscous liquid are studied numerically. The tube is open at both ends and connects two liquid reservoirs at constant pressure. The bubble is initially a small sphere and growth is triggered by a large internal pressure applied for a short time. After this initial phase, the motion proceeds by inertia. This model simulates the e ect of an intense, localized, brief heating of the liquid which leads to the nucleation and growth of a bubble. The dimensionless parameters governing the problem are discussed and their e ects illustrated with several examples. It is also shown that, when

The flow induced by the suitably timed growth and collapse of one or several bubbles in a finite tube joining two liquid reservoirs is simulated by a simple quasi-one-dimensional model. Viscous and surface tension effects are accounted for in an approximate manner. It is shown that, in certain parameter ranges, the system is capable of a net pumping action that moves the liquid from one reservoir to the other even in the presence of an adverse pressure difference. The fact that this net pumping effect is also encountered in the case of a single bubble, provided it is not located at the midpoint of the tube, is particularly remarkable. The mechanism responsible for this result is discussed. In practice the effect can be exploited to build a micropump by embedding electrical heaters in the wall of a small channel.

This paper describes a novel pumping device without mechanical moving parts based on the periodic generation and collapse of a single vapour bubble in a channel. The channel shape is such that it creates an asymmetry in the surface tension forces, which results in a pumping effect. The principle can be implemented over a broad range of channel sizes and repetition frequencies. For illustration purposes, a particular implementation is described here where the working fluid is a salt solution in water, the channel diameters are of the order of 1 mm and the repetition frequency is between 1-10 Hz. In these conditions, the device develops a head of a few centimetres of water with typical flow rates in the range of 100 µl per minute. It appears possible to increase both head and flow rate by adjusting geometrical parameters and operating conditions. A simple modification of the design would render the same principle also applicable to the pumping of non-conducting liquids.

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