טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentYariv Ehud
SubjectDynamics of Particle Suspensions in Ideal Fluid
DepartmentDepartment of Applied Mathematics
Supervisor Professor Itzchak Frankel


Abstract

A kinetic theory is developed with the goal of considering the effect of the local relative motion of particles on the macroscopic description of the bubbly medium. Unlike the central-force molecular interactions underlying classical kinetic theory, the hydrodynamic forces occurring in the present problem explicitly depend upon particle velocities. Starting from Liouville's equation and following Grad, it is established that, in a dilute dispersion of bubbles in a nearly inviscid fluid, the particle density function is governed by a Boltzmann-type integro-differential equation.  In the limit of small Knudsen numbers, the particle density function is calculated via the Chapman-Enskog asymptotic scheme, which enables closure of the system of averaged macroscale equations.  Explicit results are presented for the effective medium transport coefficients obtained through numerical simulations of binary particle encounters.