| Many geological and geophysical processes may be characterized by low Reynolds number multiphase fluid flows. This thesis focuses on the dynamics of deformable drops and bubbles in multiphase fluid systems. Specifically, several model flow problems are considered: the interactions of buoyant drops and bubbles in suspensions, the motion of drops and bubbles through fluid-fluid interfaces, and the deformation of buoyant volumes of fluid in externally-imposed flows. A combination of numerical calculations, laboratory experimental results and analytical methods are used to study the model flow problems.;Geological applications considered in this thesis include the interaction of bubbles in magmas and lavas, the ascent of mantle plume heads in a compositionally layered Earth, the stability of continental roots, the entrainment of the D" layer at the base of the mantle by a convecting mantle, and the formation and evolution of Venusian coronae and highlands.;Bubble deformation leads to a greatly enhanced rate of coalescence in magmas and lavas if the bubbles have radii greater than a few millimeters. An instability is predicted to occur in suspensions of deformable bubbles which will result in spatial variations of bubble concentrations. Plume heads passing from the lower mantle into a less viscous upper mantle become extended vertically and develop a cylindrical geometry. Continental roots must be several orders of magnitude more viscous than the surrounding mantle (in order not to sink, spread or be entrained). If D" is approximately 2-3% more dense than the lower mantle, it is possible that D" is not entrained into the convecting mantle (due to compositional buoyancy) but may still become thermally unstable and form thermal plumes. The surface expression of rising and spreading plume heads or diapirs is consistent with many features associated with coronae on Venus. The surface expression of crustal thickening above downwellings, notably the plateau-shaped topography and pattern of surface stresses, is characteristic of many of the plateau-shaped highlands on Venus. Variations of the thickness of the lithosphere, associated with ocean-continent boundaries, results in large-amplitude and short-wavelength deviatoric stresses and dynamic topography near the ocean-continent boundary.;Free-boundary problems of interface deformation in Stokes flows are solved numerically using the boundary integral method for axisymmetric, two-dimensional and three-dimensional geometries. Boundary integral equations of the second kind involving only the unknown interfacial velocities are presented for problems with multiple fluid-fluid interfaces. Laboratory experiments are presented for two bubbles interactions, and the motion of particles through fluid-fluid interfaces. The experimental results for bubble interactions are used to develop a model for coalescence in suspensions; the model is then used in population dynamics simulations. Analytical results for the far-field interactions of deformable drops are determined using a combination of the method of reflections, domain perturbation methods and the Lorentz reciprocal theorem. |
