The mechanism of drop formation from gas or vapour bubbles

This paper presents an interpretation of the mechanism of drop formation due to bubbles of gas or vapour travelling upwards through a liquid and collapsing at the liquid-gas interface. Size-distribution of entrained drops are obtained as a function of height and bubble sizes. Parabolic trajectories have been taken in consideration and an equation is given for the maximum height of drops.

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Zusammenfassung Eine Erklärung für die Bildung von Tropfen an der freien Flüssigkeitsoberfläche beim Zerplatzen von aufsteigenden Gas- oder Dampfblasen wird hier gegeben. Die Größenverteilung der abgeschleuderten Tropfen wird als Funktion der Schleuderhöhe und der Blasengröße erhalten. Parabolische Schleuderbahnen wurden berücksichtigt und eine Gleichung für die maximale Schleuderhöhe der Tropfen angegeben.

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Symbols surface tension - amplitude of the surface disturbance - _w density of liquid - a density of gas - kinematic viscosity - D _d diameter of droplet - D _j diameter of jet - E _d drop energy - E _j total energy absorbed by the jet - E _o energy release by collapsing bubble - E _p potential energy - E _R drag energy - E _s surface tension energy - F vertical force - G _j gravitational force acting on jet - H maximum trajectory height - L length of jet - L _opt length of separated upper portion of jet - l length unseparated lower portion of jet - M mass of water which must be set in motion to fill the crater - m mass of droplet - P _g gas pressure - P _l liquid pressure - P _i inside pressure - P _o outside pressure - R ₁,R ₂ curvatures of bubble - R _j radius of jet - R radius of spherical bubble - R* frictional drag force of jet - R _D frictional drag force of droplet - S ₁ surface tension force - t _F impulse time - t time of break-up of jet - U mean velocity acquired by the massM - v droplet velocity - V ₀ initial velocity of droplet - W ₁ gravitational force