Citation
Yurkovetsky, Yevgeny (1998) I. Statistical mechanics of bubbly liquids. II. Behavior of sheared suspensions of nonBrownian particles. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/NMJQ2X32. https://resolver.caltech.edu/CaltechETD:etd06222005110302
Abstract
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. I. Statistical mechanics of bubbly liquids. 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 temperature  a 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, temperature invariant, 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. II. Behavior of sheared suspensions of nonBrownian particles. Suspensions of nonBrownian particles in simple shear flow of a Newtonian solvent in the range of particle phase concentration, [...], from 0.05 to 0.52, are studied numerically by Stokesian Dynamics. The simulations are a function of [...] and the dimensionless shear rate, [...], which measures the relative importance of the shear and shortranged interparticle forces. The pairdistribution functions, shear viscosity, normal stress differences, suspension pressure, longtime selfdiffusion coefficients, and mean square of the particle velocity fluctuations in the velocitygradient and vorticity directions are computed, tabulated and plotted. In concentrated suspensions ([...] > 0.45), two distinct microstructural patterns are shown to exist at the highest and lowest shear rates. At [...] = 0.1 the particles form hexagonally packed strings in the flow direction. As [...] increases, the strings are gradually being replaced by noncompact clusters of particles kept together by strong lubrication forces while the particle pairdistribution displays a broken foreaft symmetry. These changes in the microstructure are accompanied by increases in the shear viscosity, normal stress differences, suspension pressure, longtime selfdiffusion coefficients, and fluctuational motion. Agreement is found between the simulation results and the theoretical predictions of Brady and Morris (1997).
Item Type:  Thesis (Dissertation (Ph.D.)) 

Subject Keywords:  bubbles in ideal fluid; rheology of nonBrownian suspensions 
Degree Grantor:  California Institute of Technology 
Division:  Chemistry and Chemical Engineering 
Major Option:  Chemical Engineering 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  24 July 1996 
NonCaltech Author Email:  yyurkovetsky (AT) ccny.cuny.edu 
Record Number:  CaltechETD:etd06222005110302 
Persistent URL:  https://resolver.caltech.edu/CaltechETD:etd06222005110302 
DOI:  10.7907/NMJQ2X32 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  2684 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  22 Jun 2005 
Last Modified:  21 Dec 2019 04:09 
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