Étude de l'écoulement d'une émulsion : Première partie, étude théorique du mouvement d'une bulle, effet fusée. Pébullon

Study of foam flow Part 1 : Theoretical study of bubble motion. Rocket effect. Pebullon

Maître-Assistant à la chaire d'Electrotechnique. Faculté des Sciences de Paris.

Résumé

A gas or vapour bubble moving at a high velocity of translation within a liquid sometimes enjoys a high degree of independence. By varying its volume, it may propel itself in the same manner as a rocket : this is the rocket effect. An increase in volume accelerates it and a decrease in volume slows it down. This result is obtained from the generalised Bernoulli equation (1) from which identical relationships (9), (10) and (11) are established. With a few simplifying assumptions, we have defined a particle that is equivalent to the bubble in translatory motion : the "pebullon". This "pebullon" conserves constant momentum (14) and is able to propel itself by change of mass. If this particle is assumed to be in a vacuum, a relationship has to be found between the mass variation and the energy involved: m'↔E = m' W2 The rocket effect occurs in a pressure field (centrifugal pump) or a temperature field (boiling). The acceleration to which the "pebullon" is subjected may become quite considerable, up to several thousand m/sec2. An air or vapour bubble inside a centrifugal pump is quasi-covered independent. Its relative velocity is proportional to distance run. Although it is subjected to a considerable buoyancy force it can still escape from the pump, often faster than the liquid. Noteworthy in the study of this problem are considerable kinetic energy variations involved. A subsequent article will show how this directed mechanical energy flux provides an explanation for erosion by mechanical cavitation process. A bubble should be considered not as a physical ball but as a cavity, or a deformation of the medium within which it is moving. This deformation propagates itself in the same manner as an energy wave. The "pebullon" concept is a practical, fertile model for the analysis of complex bubble motion. Whenever a problem involves a foam, it may fruitfully be considered from this angle. This will be done in a subsequent paper referring to an experimental study of the rocket effect.