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Graduate Student Supervision
Doctoral Student Supervision (Jan 2008 - April 2022)
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.
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.
Master's Student Supervision (2010 - 2021)
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.
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.