Several aspects of the growth and departure of bubbles from a submerged needle are considered. A simple model shows the existence of two different growth regimes according to whether the gas flow rate into the bubble is smaller or greater than a critical value. These conclusions are refined by means of a boundary-integral potentialflow calculation that gives results in remarkable agreement with experiment. It is shown that bubbles growing in a liquid flowing parallel to the needle may detach with a considerably smaller radius than in a quiescent liquid. The study also demonstrates the critical role played by the gas flow resistance in the needle. A considerable control on the rate and size of bubble production can be achieved by a careful consideration of this parameter. The effect is particularly noticeable in the case of small bubbles, which are the most difficult ones to produce in practice.
The impact of a drop on the plane surface of the same liquid is studied numerically. The accuracy of the calculation is substantiated by its good agreement with available experimental data. An attempt is made to explain the recent observation that, in a restricted range of drop radii and impact velocities, small air bubbles remain entrained in the liquid. The implications of this process for the underwater sound due to rain are considered. The numerical approach consists of a new formulation of the boundary-element method which is explained in detail. Techniques to stabilize the calculation in the presence of strong surface-tension effects are also described.
The process by which a liquid jet falling into a liquid pool entrains air is studied
experimentally and theoretically. It is shown that, provided the nozzle from which
the jet issues is properly contoured, an undisturbed jet does not entrap air even at
relatively high Reynolds numbers. When surface disturbances are generated on the
jet by a rapid increase of the liquid flow rate, on the other hand, large air cavities are
formed. Their collapse under the action of gravity causes the entrapment of bubbles
in the liquid. This sequence of events is recorded with a CCD and a high-speed
camera. A boundary-integral method is used to simulate the process numerically with
results in good agreement with the observations. An unexpected finding is that the
role of the jet is not simply that of conveying the disturbance to the pool surface.
Rather, both the observed energy budget and the simulations imply the presence of a
mechanism by which part of the jet energy is used in creating the cavity. A hypothesis
on the nature of this mechanism is presented.
The process by which two surfaces of the same liquid establish contact, as when two drops collide or raindrops fall on water, is studied. The mathematical formulation is based on the assumption of an incompressible, inviscid fluid with surface tension. A model problem with a simplified geometry is solved numerically by means of a boundary-integral method. The results imply that a number of toroidal bubbles form and remain entrapped between the contacting surfaces. Experimental evidence for this process, which is important for boiling nucleation and the formation of condensation nuclei for rain drops, is found in the literature.
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