Session R8: Biofluids: Microswimmers IV - Complex Fluids

Swimming of bacteria in polymer solutions

The ``standard model'' of bacteria swimming in polymer solutions consists of experimental observations that the swimming speed first increases and then decreases as the function of the polymer concentration. This non-monotonic behaviour is usually explained by either swimming in pores in the polymer solutions or by its viscoelasticity. Using new, high-throughput methods for characterising motility, we have measured the swimming speed and the angular frequency of cell-body rotation of motile Escherichia coli as a function of polymer concentration in polyvinylpyrrolidone (PVP) and Ficoll solutions of different molecular weights. We find that non-monotonic speed-concentration curves are typically due to low-molecular weight impurities and, when cleaned, most molecular weight solutions exhibit Newtonian behaviour. For the highest molecular weight of PVP we observe non-newtonian effects. We present a simple theory that consists of the fast-rotating flagella ``seeing'' a lower viscosity than the cell body but otherwise Newtonian in nature. We show that our theory successfully describes the experimental observations and suggest that flagella can be seen as nano-rheometers for probing the non-newtonian behaviour of high polymer solutions on a molecular scale.   

Swimming of Taylor wavy sheets in viscoelastic fluids

We consider a model swimmer, the Taylor wavy sheet, moving in a viscoelastic fluid. Based on the solution obtained by E. Lauga (Phys. Fluids '97), we propose a mechanism for sheet's propulsion in elastic fluids. We present a full numerical calculation of swimming at arbitrary amplitudes, and compute the most efficient and fastest waveforms for undulatory swimming in bulk and next to a boundary.   

Flexible polymers suppress wobbling and tumbling of \textit{E. coli} cells

The run-and-tumble dynamics of swimming \textit{E. coli} has been extensively studied. In this talk, we experimentally investigate the role of polymer concentration on the swimming dynamics of \textit{E. coli} using tracking methods. We find that the addition of small amount of polymer to water drastically changes the run-and-tumble behavior of \textit{E. coli} cells, enhancing translation while hindering rotational diffusion. Here, the cells are suspended in dilute solutions of carboxy-methyl cellulose (CMC) and imaged in a liquid film away from surfaces. The addition of polymer molecules to the fluid (water) leads to cell trajectories that are highly correlated in time; cells move in nearly straight lines and rotational diffusion is greatly reduced. By varying the polymer molecular weight, we show that trajectories are a result of two mechanisms: (1) suppression of cell wobbling due to elasticity and (2) enhancement of run times due to viscosity. Our experiments show that this combination of increased speed and suppressed reorientation dramatically changes overall cell dynamics in the presence of polymers.   

Enhanced helical swimming in Boger fluids

We conduct experiments with force-free magnetically-driven helical swimmers in Newtonian and viscoelastic (Boger) fluids. In order assess the effect of viscoelasticity on the swimming performance, we conduct experiments for swimmers with different helical tail geometries. We use helices with the same wave length and total length but vary the angle of the helix. As previously reported by the computational study of Spagniole and collaborators, we found that the swimming performance can either increase, decrease or remain unchanged, depending on the geometry of the tail. With the right geometry, the enhancement can be up to a factor of two.   

Mechanisms of elastic enhancement and hindrance for finite length undulatory swimmers in viscoelastic fluids

A computational model of finite-length undulatory swimmers is used to examine the physical origin of the effect of elasticity on swimming speed. We explore two distinct target swimming strokes, one derived from the motion of \textit{C. elegans}, with large head undulations, and a contrasting stroke with large tail undulations. We show that both favorable stroke asymmetry and swimmer elasticity contribute to a speed-up, but a substantial boost results only when these two effects work together. We reproduce conflicting results from the literature simply by changing relevant physical parameters.   

Theory of locomotion in complex fluids

Microorganisms often swim in environments that cannot be classified as Newtonian. Biological fluids can contain polymers or other heterogeneities which may yield complex rheology. For a given set of boundary conditions flows can be substantially different in complex fluids, while non-Newtonian stresses can alter the gait of the microorganisms themselves. Heterogeneities in the fluid may also occur on length scales on the order of the swimmer leading to additional complexity. In this talk we will discuss a theoretical description of the effects on locomotion of a non-Newtonian constitutive relation and discuss our current understanding of the interplay between swimming kinematics and the nonlinear response of the fluid.   

Ciliary kinematics of Chlamydomonas reinhardtii in Complex Fluids: Role of viscosity

The motility behavior of microorganisms can be significantly affected by the rheology of their fluidic environment. Guided by our experiments on the swimming gait of Chlamydomonas reinhardtii in viscoelastic fluids, we focus on ciliary waveforms in Newtonian fluids and systematically study the effect of increasing viscosity. We find that the beat frequency as well as the wave speed are both strongly influenced by fluid viscosity. Interestingly, ciliary waveforms at low viscosity show a larger influence of the cell body than waveforms at higher viscosity. We use slender body theory and principal component analysis to elucidate the role of fluid viscosity in regulating the kinematics of the swimming process.   

Swimming and pumping of helical structures in viscous fluids

Many flagellated microorganisms including E. coli swim by rotating slender helical flagella, while ciliated organisms like Paramecia swim by passing helical waves along their surfaces. We will discuss a framework for studying such problems where the Stokes equations describing viscous flow are written in helical coordinates. Analytical predictions match well with full numerical simulations, and suggest optimal geometries. This work may also aid designs in microfluidic manipulation, microswimmer engineering, and the mixing of viscous fluids.   

Fluid transport by an unsteady microswimmer

We study the drift caused by the microscopic algae \emph{Chlamydomonas reinhardtii}. This microorganism swims by rapidly beating two frontal flagella. Previous studies of transport by microswimmers have neglected the ubiquitous time-dependence of their swimming. We model the organism by a time-dependent dumbbell consisting of two regularized Stokeslets. We study individual particle paths and their displacements in a region around the swimmer. Of particular interest are particle trajectories that remain trapped near the swimmer, forming the so-called ``atmosphere" of the moving body. Atmospheres are common in the steady case, and they persist for unsteady motion though their size is reduced due to broken barriers. We vary the parameters in our model to determine their effect on the size and shape of the atmosphere. Finally we determine the importance of this atmosphere on overall fluid transport and mixing.