This thesis is composed of three separate projects in the field of Non-Newtonian fluid mechanics.;The first project consists of an experimental investigation of the motion of a sphere accelerating from rest along the centerline of a cylindrical tube filled with a polyisobutylene Boger fluid. Deborah numbers in the range ;In the second project, a reciprocal theorem is used to predict the steady three-dimensional creeping motion of a sphere sedimenting near a single vertical plane wall. Weak Non-Newtonian effects up to second order in Deborah number are calculated as are inertial effects up to first order in Reynolds number. At low Deborah numbers, the theoretical calculations indicate that fluid elasticity results in a migration of the sphere away from the wall and a drag decrease greater than that predicted in the unbounded case. Shear thinning in the fluid viscosity tends to cause the sphere to rotate more slowly, which may lead to "anomalous" rotation at higher Deborah numbers. Inertial effects, on the other hand, cause no modification to the rotation speed, but do produce a drift velocity away from the wall. In addition, illustrative experiments are performed with spheres sedimenting through a polyacrylamide solution in a sufficiently large tank to focus on the interaction with a single vertical boundary.;The third and final project provides an investigation of the linear stability of creeping plane Couette and Poiseuille flow with viscous heating for a non-isothermal formulation of the FENE-P constitutive model. Viscous heating is observed to have a destabilizing tendency at long to moderate disturbance wavelengths, and a stabilizing effect at short wavelengths, but no instabilities are found in the inertialess flow limit.
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