Session R09: Biofluids: Locomotion, Non-Newtonian Fluids

Fluid­–body interactions in passive and active liquid crystals

Fluid anisotropy, or direction-dependent response to deformation, can be observed in biofluids like mucus or, at a larger scale, self-aligning swarms of active bacteria. A model fluid used to investigate such environments is a nematic liquid crystal. Large colloidal particles undergo shape-dependent interactions when immersed in such fluids, whilst many microorganisms must propel themselves through these complex environments. Furthermore, the interaction between these active swimmers and passive particles gives rise to active stresses. In this talk, we will bring the power of complex variables to bear on this problem, in order to analytically solve for the interactions inside a liquid crystalline environment. This approach allows for the solution of a wide range of problems, opening the door to studying the role of body shape and orientation, liquid crystal anchoring conditions, and body deformability. Shape-dependent forces between bodies, local tractions, and active stresses will all be discussed.   

Force- and Torque-Free Swimming in Shear-Thinning Fluids

Artificial bacteria are strong candidates to achieve biomedical applications such as drug delivery and minimally invasive surgery. Swimming characteristics of the force- and torque-free swimming of a bacterium with a helical tail in a Newtonian fluid has been studied extensively, however, many biological fluids are shear-thinning. In this talk, we will present the effects of shear-thinning rheology on the force- and torque-free swimming. Results of our computational study could help optimize the bioinspired artificial bacterium design and its actuation for use in biomedical applications.   

Effect of fluid elasticity on the emergence of oscillations in an active elastic filament

Many microorganisms propel themselves through complex media by deformations of their flagella. The  beat is thought to emerge from  interactions between forces of the surrounding fluid, passive elastic response from deformations of the flagellum, and active forces from internal molecular motors. The beat varies in response to changes in the fluid rheology, including elasticity, but there is limited data on how systematic changes in elasticity alters the beat. This work analyzes a related problem with fixed-strength driving force: the emergence of beating of an elastic planar filament driven by a follower force at the tip in a viscoelastic fluid. This analysis examines how the onset of oscillations depends on the strength of the force and viscoelastic parameters. The linear analysis predicts that the frequency increases with the fluid relaxation time. Using numerical simulations, the model predictions are compared with experimental data on frequency changes in bi-flagellated alga C. reinhardtii. The model shows the same trends in response to changes in both fluid viscosity and Deborah number, and thus provides a mechanistic understanding of the experimental observations.    

Helical Swimming Through a Viscoplastic Fluid

The motility of microorganisms exerts profound effects on various life processes, encompassing reproduction, infection, and marine ecosystem dynamics. This talk presents experiments on a 3D-printed helical swimmer in yield stress fluids using Carbopol. In our previous study, three distinct stages controlling helical swimmer locomotion in viscoplastic fluids were identified [Nazari et al., 2023]. This talk focuses on the impact of drag and propulsion on swimming stages in viscoplastic fluids through variation of helix filament thickness (T_t), swimmer head length (H_L), and cylindrical head cross-section (D). The study reveals that some of these geometric factors significantly influence the third locomotion stage by modulating drag and thrust forces experienced by the swimmer. Our results indicate that the swimmer shape does not affect the critical yield strain (ε_y) to initiate rotational motion. Forward motion occurs only when rotational motion induces material yielding far from the swimmer, specifically occurring below a critical Bingham number (Bi_c). Intriguingly,  remains independent of geometric factors, T_t, H_L, and D.  Subsequently at the third stage of swimming, (Bi〈Bi_c), at low pitch angles (12° ≤ ψ ≤ 37°) and below the critical Bi_c, the yield stress to Newtonian swimming speed ratio remains below unity. However, at larger pitch angles, this ratio can exceed one (up to 10). Notably, an optimal T_t is associated with the highest swimming speed. Moreover, an increase in D results in a hindrance to the swimming speed, while surprisingly, in this stage, swimming speed exhibits no significant dependency on H_L. Flow visualizations depict highly localized fluid deformation, with swimming speed governed by a balance between tail propulsion and bulk deformation around the head. These findings offer valuable insights into helical swimmers' locomotion in yield stress fluids, with implications in complex biological environments.   

Bacteria Navigate Anisotropic Media Using A Flagellar Tug-of-Oars

Bacterial navigation of anisotropic fluids plays a vital role in biofilm formation, bacterial colonization of the mucosal linings of lungs and reproductive tract, and the organization of the gut microbiome. In these settings, hydrodynamic interactions force bacteria to swim along a preferred direction, rather than the classical run-and-tumble walk in three dimensions. Using nematic phase DSCG liquid crystal as a model system, we have observed a novel swimming mechanism employed by peritrichous bacteria to explore anisotropic fluids. Bacteria adopt a polar flagella configuration along the direction of nematic alignment that resembles a 'Tug-of-Oars' between opposing bundles. Further, they can exchange flagella between bundles and reverse directions by buckling flagella during motor reversals (tumbles). The critical compression for the Euler buckling of a flagellum is determined by the Frank energies for liquid crystal deformation. At high DSCG concentrations, this forbids buckling and rearrangement of flagella. Despite this limitation, bacteria can still alternate swimming directions by activating/deactivating bundles on opposite sides of the cell body. Our results shed light on bacterial strategies to navigate anisotropic media, and raise questions on signal transduction in flagella motors located on the cell membrane.   

Enhanced upstream swimming of bacteria in complex fluids: part II, viscoelasticity

Surface-thriving bacteria are commonly found in environments that involve both shear flow and the presence of biological macromolecules. Airway mucus, for instance, contains high concentrations of polymeric mucins and exhibits non-Newtonian rheology. Having previously studied the effect of shear thinning, we started to focus on investigating the rheotaxis of E. Coli in a variety of viscoelastic fluids. Our experimental findings demonstrated efficient upstream propulsion and enhanced upstream swimming in these viscoelastic fluids under shear flow. To shed light on the underlying mechanisms, we developed a theoretical model showing how fluid elasticity enhances bacteria's ability to swim upstream. We propose that, in DNA suspensions, both the shear-thinning effect and fluid elasticity work synergistically to enhance the weathervane effect, thereby facilitating bacteria to swim upstream. This study of bacterial motion in polymeric flow uncovers fundamental aspects of bacterial transport and infection dynamics in viscoelastic environments such as the respiratory flows.   

Enhanced upstream swimming of bacteria in complex fluids: part I, shear-thinning.

Many swimming microorganisms exhibit positive rheotaxis, i.e. the ability to swim upstream, which allows them to explore environments and enhance contamination. Our work investigates how this ability is affected by complex fluid rheology.

In this talk, we present experimental evidence that shear-thinning (ST) viscosity can significantly enhance rheotaxis of the bacteria E. coli swimming near surfaces relative to Newtonian fluids. A simple model that accounts for the modified interaction of E. coli with surface due to ST effects captures the main experimental observations, namely a transition to rheotaxis occurring at lower flow rates and an increased alignment of upstream swimmers. Importantly, this analysis singles out traits that could predict the spreading ability of a population or of individual swimming E. coli. Our results for shear-thinning fluids provide an essential step towards understanding the spreading of swimming bacteria in more complex biological fluids.   

A novel numerical method for a swimming bacterium in a two-fluid model of a polymer solution

We develop a novel numerical method for studying the motion of a swimming bacterium in a concentrated, entangled polymer solution modeled as a two-fluid medium composed of a solvent and a polymer phase. The two-fluid model captures the non-continuum effects at the scale of the flagellar bundle, arising due to the underlying microstructure of an entangled polymer solution. The motivation for the problem is to gain a mechanistic understanding of the motion of bacteria in complex biological liquids (e.g. mucus) and is therefore useful in understanding the spread of bacterial diseases. The numerical scheme combines slender body theory, boundary element method, and a finite-difference solver for the flow of an inertialess, viscoelastic polymer medium. Additionally, the method exploits a novel decomposition of the problem into Newtonian and non-Newtonian parts, where the Newtonian part is linear with non-linearities arising in the non-Newtonian part through the time-dependent polymer constitutive equation. We show that this decomposition results in a linear system of equations for the unknown swimming parameters of the bacterium, which are easily solved. The method is validated by comparing the results of a bacterium swimming in a Newtonian liquid, with previous numerical studies. We then analyse the motion of our model bacterium, with a helical flagellar bundle and a spheroidal head, in a polymer solution using this method and comment on the effect of elasticity and microstructure on its motility.