Gwynn Elfring

Both biological swimming microorganisms and artificial active particles capable of propulsion have recently been active areas of research in fluid dynamics. The influence of nearby boundaries or other active particles or swimmers is critical in many important cases for understanding various phenomena. Bacteria, for example, accumulate near surfaces and interact closely to form biofilms. Accordingly, this dissertation addresses a few gaps in the literature of microorganism hydrodynamics. First, we focus on the suspension of active particles near solid boundaries. We start with the study of the hydrodynamics of two unequal swimmers at close proximity by considering the squirming model. In comparison to passive particles, microorganisms have surface activity that provides the impetus for swimmers to move. In order to satisfy both the boundary conditions on the swimmers' skin and the Stokes equations, a regular perturbation in the velocity and pressure field of the inner creeping flow between the swimmers is employed. A relatively large size ratio leads to the hydrodynamics of a squirmer near a flat surface. Afterwards, we calculate the far-field hydrodynamics of a suspension of squirmers near a solid boundary. In the course of calculations, an extension of Stokesian Dynamics (SD) method, developed for passive particles, is utilized for active particles. This technique, called active SD, offers a good starting point for further research questions in the field. The transition between near-field and far-field solutions is also discussed. Thereafter, we propose a rigid and a flexible toy model to examine the effect of elasticity on the dynamics of a swimmer. Eventually, the developed method can help to establish a relation between hydrodynamics and biological behaviours, e.g., biofilm formation.Ultimately, we focus on axisymmetric particles in non-Newtonian fluids as a first step toward extending the SD method for poly disperse nonspherical active particles in complex fluids. We investigate the dynamics of a prolate spheroid in a shear flow of a shear-thinning Carreau fluid. The motion of a prolate particle is developed analytically for asymptotically weak shear thinning and then integrated numerically.

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In this thesis, we present an experimental investigation of turbulent flows of elasto-viscoplastic fluids. The motivation comes from the oil and gas industry, where turbulent flows of non-Newtonian fluids are frequently encountered. We characterize the turbulent flow of viscoplastic fluids, both under a fully turbulent flow and also when it is displaced by another fluid under turbulence in an eccentric annular geometry. Further, we investigate the fully turbulent flow of a drag reducing, elasto-viscoplastic wormlike micellar (or surfactant) solution, and compare those results to better known polymer solutions under turbulent flows.Our experiments in fully turbulent flows of viscoplastic Carbopol solutions show an enhancement of streamwise velocity fluctuations and a decrease in wall normal velocity fluctuations in comparison to water. As we increase the Reynolds numbers, the turbulence statistics approach Newtonian values. With regards to turbulent displacements of 0.15% Carbopol solutions in an eccentric annulus, we observe that the displacement is successful without the obstruction regardless of the displacing fluid. The obstruction at eccentricity e ≈ 0.5 is mostly detrimental to removal of the yield stress fluid stuck downstream of it. At high eccentricity values of e ≈ 0.7, the effect of the obstruction on the displacement of Carbopol is seen to be negligible.When wormlike micellar gels are submitted to a turbulent flow, the micellar structure near the wall appears to be mostly broken down during turbulent flow. Turbulent flows at low concentrations of surfactant show a Newtonian-like flow field throughout most of the duct, where the energy spectra shows a -5/3 power law scale with wavenumber. Conversely, energy spectra of the micellar solutions at large percentages of drag reduction show approximately a -3 power law decay. Moreover, a direct comparison of turbulent flows with flexible and rigid polymer solutions also shows similar turbulence statistics at approximately the same percentages of drag reduction. A -3 power law decay in the energy spectra is also observed with both flexible and rigid polymer solutions, and we hypothesize it may be a consequence of elasto-inertial turbulence.

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The focus of this thesis is on small non-Brownian particles in fluids that show deviations from standard Newtonian fluids. We study the motion of swimmers and sedimenting particles in Newtonian fluids with viscosity gradients, in shear-thinning fluids, and in fluids with viscoelasticity. The work is theoretical; its aim is to study the first effects of non-Newtonian rheology on particle motion and towards this end uses the reciprocal theorem of low Reynolds number hydrodynamics and methods of perturbation expansion. We find that the dynamics of the particles is often qualitatively changed due to the rheological properties of the fluid, and such changes are difficult to predict a priori.

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In this dissertation, the effects of elasticity on hydrodynamic interactions at small scales are investigated.In the microscale realm of microorganisms, inertia is irrelevant and viscous dissipation dominates the fluid motion and particles within it. As a result of this inertialess environment, microorganisms use non-reciprocal body distortions to facilitate locomotion and exhibit nontrivial behaviors in interacting with their surroundings; behaviors that have been shown to be intimately correlated to the elasticity of the cell body, or its small appendages called flagella (or cilia). Motivated by experimental observations, the effects of elasticity on hydrodynamic interactions of motile cells are investigated, using theoretical approaches. First, to model the flow field induced by microswimmers, a framework is given to account for the effects of the higher-order force moments. Specifically, the contribution of the second-order force moments of the flow field is evaluated, and explicit formulas are reported for the stresslet dipole, rotlet dipole, and potential dipole for an arbitrarily shaped active particle. For an elastic swimmer near a boundary, it is shown that the rotlet dipole bends the swimmer and results in qualitatively different swimming behaviors in comparison to the case of a rigid swimmer. Furthermore, it is demonstrated that elasticity can be exploited to evade the kinematic reversibility of the field equations in Stokes flow. A model elastic swimmer is proposed that despite the reversible actuation, can propel forward due to its nonreciprocal body deformations. The effect of elasticity in the formation of metachronal waves in ciliated microorganisms such as Paramecium and Volvox is also studied. Using a minimal model, it is shown that elastohydrodynamic interactions of cilia attached to a curved body lead to synchronization, with zero phase difference, thereby preventing the formation of wave-like behaviors unless an asymmetry is introduced to the system. Finally, the dynamics of capillary rise between two porous and elastic sheets are investigated. The liquid, as it rises, diffuses through the sheets and changes their properties. The significant drop in sheet bending rigidity due to wetting, causes the system to coalesce faster, compared to the case of impermeable sheets, and also remarkably reduces the absorbance capacity.

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