I. Statistical mechanics of bubbly liquids. II. Behavior of sheared suspensions of non-Brownian particles

Citation

Yurkovetsky, Yevgeny (1998) I. Statistical mechanics of bubbly liquids. II. Behavior of sheared suspensions of non-Brownian particles. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/NMJQ-2X32. https://resolver.caltech.edu/CaltechETD:etd-06222005-110302

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 motion--is derived with the help of the impulse-dependent 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' position-dependent 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 non-Brownian particles. Suspensions of non-Brownian 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 short-ranged interparticle forces. The pair-distribution functions, shear viscosity, normal stress differences, suspension pressure, long-time self-diffusion coefficients, and mean square of the particle velocity fluctuations in the velocity-gradient 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 non-compact clusters of particles kept together by strong lubrication forces while the particle pair-distribution displays a broken fore-aft symmetry. These changes in the microstructure are accompanied by increases in the shear viscosity, normal stress differences, suspension pressure, longtime self-diffusion coefficients, and fluctuational motion. Agreement is found between the simulation results and the theoretical predictions of Brady and Morris (1997).

Thesis Files