Gwynn Elfring
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Graduate Student Supervision
Doctoral Student Supervision
Dissertations completed in 2010 or later are listed below. Please note that there is a 6-12 month delay to add the latest dissertations.
Long-chained zwitterionic surfactants form wormlike micellar (WLM) gels in solutionat room temperature and revert back to a Maxwell viscoelasticity at highertemperatures. We study the rheology and flow dynamics of such WLM gels usinga combination of rheometry and flow experiments. First, we rheologically characterizethe material and reveal details of its microstructure along with signatures ofshear-induced fracture and banding. Then we pump these WLM gels in a capillarypipe and measure the development of velocity profiles in time. Our experimentscapture flow features like strong slip, plug and shear layers along with flow-inducedheterogeneity. In the third part of the thesis we study droplet detachment and filamentthinning of our WLM gels. We show the existence of elastocapillary thinningregimes, power-law failure and discuss dependencies of said dynamics on surfactantconcentration. Our experiments reveal hitherto unknown complex dynamicseven in simple flows of WLM gels and is likely to inform research on flows whererheology and transient fluid dynamics of similar soft matter systems play a crucialrole.
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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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Master's Student Supervision
Theses completed in 2010 or later are listed below. Please note that there is a 6-12 month delay to add the latest theses.
Particle-based numerical methods are becoming increasingly popular for the solution of continuum mechanics problems involving large topological changes. These methods do not depend on the sensitive and time-intensive step of mesh generation, unlike more conventional, grid-based numerical techniques. However, particle methods do face several unique challenges which prevent widespread industry adoption, one of which is simulation refinement. Localized refinement of a simulation is required to make many simulations computationally feasible, but such techniques have yet to be adopted in practice. This study focuses on developing an adaptive spatial resolution algorithm for the optimal transportation meshfree method. The study first attempts to automatically determine where simulations most need refinement. Inspiration is drawn from the field of design of experiments, and a stand-alone, gradient-based adaptive sampling method is proposed for design of experiments applications. The new method balances space filling, local refinement, and error minimization objectives while reducing reliance on delicate tuning parameters. Higher-order local maximum entropy approximants are used for metamodelling to confer the approach with intrinsic resistance to data noise and make it more suitable to situations with unreplicated data points. Tests find it performs favourably compared to conventional design of experiments approaches, and investigate the effects of a time-varying dataset on its performance in anticipation of application to particle-based methods. The remainder of the adaptive spatial resolution algorithm is then developed. The novel adaptive design of experiments approach is used to automatically determine the locations in greatest need of refinement and additional nodes are added in the vicinity. Refining the optimal transportation meshfree method requires a novel approach to material point splitting and mass redistribution, which is accomplished through a combination of kernel density estimation and kernel functions. The negative effect of disorder on the optimal transportation meshfree method is also investigated, and motivates the inclusion of particle shifting into the new algorithm. Finally, simple canonical PDEs are investigated using the complete adaptive spatial resolution method, and the solution accuracy is found to increase by up to an order of magnitude for the same number of nodes when the adaptive spatial resolution algorithm is applied.
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Viscoelastic fluids are non-Newtonian fluids exhibiting both viscous and elastic properties. Many fluids of practical importance (polymers, surfactants, mucus, shampoos etc.) display viscoelastic effects to different degrees under a wide range of flow conditions and thus, these fluids present a variety of problems. In this work, we study two problems at very different flow conditions in viscoelastic fluids: a) the effect of swimming gait on bio-locomotion and b) characterizing the drag reducing fluids used for gravel-packing operations in the petroleum industry. For the first problem, we give formulas for the swimming of simplified two-dimensional bodies at low Reynolds numbers in complex fluids using the reciprocal theorem. By way of these formulas, we calculate the swimming velocity due to small-amplitude deformations on the simplest of these bodies, a two-dimensional sheet, to explore general conditions on the swimming gait under which the sheet may move faster, or slower, in a viscoelastic fluid compared to a Newtonian fluid. We show that in general, for small amplitude deformations, a speed increase can only be realized by multiple deformation modes in contrast to slip flows. Additionally, we show that a change in swimming speed is directly due to a change in thrust generated by the swimmer. Later, we work with viscoelastic additives (xanthan and a zwitterionic viscoelastic surfactant, VES), widely used as drag reducers for gravel-packing applications. While the behavior of xanthan is well characterized in the literature, much less is known about the VES characteristics, despite widespread use. We performed a number of rheological tests and flow-loop experiments on VES solutions to understand the structural characteristics to make better process predictions. Unlike xanthan, which displays typical viscoelastic liquid characteristics, VES displays elastic gel-like behaviour. The gel-like behaviour suggests long and relatively unbreakable chain lengths of the wormlike micelles in the VES at room temperature leading to gelation by entanglement. Also, a shear-thickening behaviour of VES samples at higher shear rates is observed, possibly as a result of shear-induced structures. Finally, we present a novel representation scheme to depict the flow-loop results relating the rheological characterization while observing drag reduction.
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In this thesis, two problems relevant to the biological locomotion in inertialess environments are studied, one is the characteristics of undulatory locomotion in granular media, the other is the optimal flexibility of a driven microfilament in a viscous fluid. Undulatory locomotion is ubiquitous in nature and observed in different media, from the swimming of flagellated microorganisms in biological fluids, to the slithering of snakes on land, or the locomotion of sandfish lizards in sand. Despite the similarity in the undulating pattern, the swimming characteristics depend on the rheological properties of different media. Analysis of locomotion in granular materials is relatively less developed compared with fluids partially due to a lack of validated force models but recently a resistive force theory in granular media has been proposed and shown useful in studying the locomotion of a sand-swimming lizard. In this work, we employ the proposed model to investigate the swimming characteristics of a slender filament, of both finite and infinite length, undulating in a granular medium and compare the results with swimming in viscous fluids. In particular, we characterize the effects of drifting and pitching in terms of propulsion speed and efficiency for a finite sinusoidal swimmer. We also find that, similar to Lighthill's results using resistive force theory in viscous fluids, the sawtooth swimmer is the optimal waveform for propulsion speed at a given power consumption in granular media. Though it is understood that flexibility can improve the propulsive performance of a filament in a viscous fluid, the flexibility distribution that generates optimal propulsion remains largely unexplored. In this work, we employ the resistive force theory combined with the Euler-Bernoulli beam model to examine the optimal flexibility of a boundary driven filament in the small oscillation amplitude limit. We show that the optimality qualitatively depends on the boundary actuation. For large amplitude actuation, our numerics show that complex asymmetry in the waveforms emerge. The results complement our understanding of inertialess locomotion and provide insights into the effective design of locomotive systems in various environments.
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