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.

---

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.

---

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 - R₁,R₂ 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 - S₁ surface tension force - t_F impulse time - t time of break-up of jet - U mean velocity acquired by the massM - v droplet velocity - V₀ initial velocity of droplet - W₁ gravitational force