Yurkovetsky, Yevgeny and Brady, John F. (1996) Statistical mechanics of bubbly liquids. Physics of Fluids, 8 (4). pp. 881895. ISSN 10706631. http://resolver.caltech.edu/CaltechAUTHORS:YURpof96

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Abstract
The dynamics of bubbles at high Reynolds numbers is studied from the viewpoint of statistical mechanics. Individual bubbles are treated as dipoles in potential flow. A virtual mass matrix of the system of bubbles is introduced, which depends on the instantaneous positions of the bubbles, and is used to calculate the energy of the bubbly flow as a quadratic form of the bubbles' velocities. The energy is shown to be the system's Hamiltonian and is used to construct a canonical ensemble partition function, which explicitly includes the total impulse of the suspension along with its energy. The Hamiltonian is decomposed into an effective potential due to the bubbles' collective motion and a kinetic term due to the random motion about the mean. An effective bubble temperaturea measure of the relative importance of the bubbles' relative to collective motionis derived with the help of the impulsedependent partition function. Two effective potentials are shown to operate: one due to the mean motion of the bubbles, dominates at low bubble temperatures, where it leads to their grouping in flat clusters normal to the direction of the collective motion, while the other, temperatureinvariant, is due to the bubbles' positiondependent virtual mass and results in their mutual repulsion. Numerical evidence is presented for the existence of the effective potentials, the condensed and dispersed phases, and a phase transition.
Item Type:  Article 

Additional Information:  Copyright © 1996 American Institute of Physics. Received 22 August 1995; accepted 8 December 1995. The authors are grateful to Professor ZhenGang Wang for a number of useful discussions. 
Subject Keywords:  BUBBLES; DIPOLES; HAMILTONIAN FUNCTION; LIQUID FLOW; MULTIPHASE FLOW; PARTITION FUNCTIONS; POTENTIAL FLOW; STATISTICAL MECHANICS; CANONICAL ENSEMBLE; PHASE TRANSFORMATIONS 
Record Number:  CaltechAUTHORS:YURpof96 
Persistent URL:  http://resolver.caltech.edu/CaltechAUTHORS:YURpof96 
Alternative URL:  http://dx.doi.org/10.1063/1.868869 
Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  3376 
Collection:  CaltechAUTHORS 
Deposited By:  Tony Diaz 
Deposited On:  02 Jun 2006 
Last Modified:  26 Dec 2012 08:54 
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