Session R39: Biofluids: Swimmer-Surface Interactions

Microscopic suspension feeders near boundaries: Effects of external water flow

Microscopic sessile suspension feeders are an important part of aquatic ecosystems and form a vital link in the transfer of carbon in aquatic food webs. These suspension feeders live attached to boundaries, consume bacteria and small detritus, and are in turn eaten by larger organisms. Many create a feeding current that draws fluid towards them, and from which they filter their food. In still water, the feeding current consists of recirculating eddies which form as a result of fluid forcing near a boundary. These recirculating eddies can be depleted of food and significantly decrease nutrient uptake; a variety of strategies have been proposed for how attached feeders increase their access to undepleted water. We investigate the interaction of the flow produced by a microscopic suspension feeder with external environmental flow, such as the current in a stream or ocean. We show through calculations that even very slow flow (on the order of microns per second) is sufficient to provide a constant supply of undepleted water to suspension feeders when the feeders are modeled with perfect nutrient capture efficiency and in the absence of diffusion. We also discuss which natural flow environments exceed the threshold to supply undepleted water and which do not, and we examine how characteristics of the suspension feeders themselves, such as stalk length and feeding disk size, influence feeding currents and their interactions with external flows.   

Does the stalk contractility of \textit{Vorticella} \textit{convallaria} depend on the stalk length?

\textit{Vorticella convallaria} is a sessile stalked ciliate living in water, and its stalk coils to move the cell body (zooid) towards its residence substrate at a maximum speed of $\sim$ 50 mm/s. Our previous microfluidics study shows that the isometric tension of the \textit{V. convallaria} stalk is linearly proportional to the stalk length. Based on this observation, we hypothesize that the contractility of \textit{V. convallaria} during normal contraction is also dependent on the stalk length. To investigate our hypothesis, we measured the contraction speed of \textit{V. convallaria} using high-speed videography and evaluated the contractile force and energetics of \textit{V. convallaria} using fluid dynamics modeling.   

Traction reveals mechanisms of wall-effects for microswimmers near boundaries

Swimming of microorganism near solid boundaries plays an important role in various biological processes, such as biofilm formation and the early stage of infection. The influence of a plane boundary on low-Reynolds number swimmers has frequently been studied using image systems for flow singularities. However, the effect of a boundary can also be expressed in terms of the flow caused by the force or traction exerted by the boundary on the fluid. Here we show that examining the traction pattern on the boundary caused by a nearby swimmer can yield physical insight into the effect of the boundary on swimming velocities. To illustrate this point, we investigate a three-sphere swimmer initially placed parallel to a solid planar wall. The three spheres are modelled as three stokeslets and the method of images for a stokeslet is employed to solve for the traction on the wall. When the swimmer is close to the boundary, the middle sphere and end spheres produce a quadrupolar and dipolar time-averaged traction, respectively, reflecting the internal structure of the swimmer. Far away from the boundary, the time-averaged traction of the swimmer is similar to that of a pure far-field quadrupole. Thus the traction patterns reveal how close the swimmer must be to the boundary for the internal structure of the swimmer to influence the boundary effects.   

Propulsion of flexible helical flagella near a rigid boundary

We study the locomotion of uni-flagellar bacteria in a viscous fluid at low Reynolds number near a rigid boundary, through a combination of computer simulations and experiments. In our analogue model experiments, we exploit the prominence of geometry of this class of problems to rescale the original micron-scale system onto the desktop-scale. We manufacture elastomeric filaments with fully customizable geometric and material properties, and rotate them in a glycerin bath at a finite distance away from a rigid boundary. The experimental results are compared against numerical simulations that employ the Discrete Elastic Rods method in conjunction with Lighthill Slender Body Theory. The non-slip boundary condition on the wall is implemented by the method of images. We first show that the filament buckles above a critical rotation frequency due to fluid loading, and then quantify the dependence of this critical threshold on the distance from the boundary, both experimentally and numerically. Excellent agreement is found between the two, with no fitting parameters. We then make use of our numerics to systematically investigate the change in the generated propulsion due to presence of a nearby boundary. We find that the propulsion depends strongly on the location of the boundary.   

The biofouling potential of flow on corrugated surfaces

Both natural and man-made surfaces are rarely smooth, and are instead often characterized by geometric heterogeneity or roughness over a broad range of scales. Because of the predicted importance of the local interaction between microorganisms and surfaces, roughness at the microbial scale can be an important element in determining the outcome of microbe-surface interactions, which represent the first step in biofilm formation and biofouling. In microbial habitats this interaction often occurs in flowing fluids, which can be important because regions with high hydrodynamic shear can induce a strong reorientation of bacteria towards surfaces, promoting attachment. Here we study the combination of flow and surface topography using video microscopy of \textit{Escherichia coli}~in corrugated microfluidic channels. We report that flow preferentially promotes attachment to specific regions of a corrugated surface, as result of the hydrodynamics of bacteria swimming in flow. We compute from the data a ``Local Biofouling Potential'' (LBP) and compare this successfully with predictions of a mathematical model, yielding one step towards the ability to mechanistically predict and thus ultimately either prevent or induce biofouling.   

The Effect of Brownian Motion on the Trajectory of Diffusiophoretic Locomotors near a Solid Boundary

Diffusiophoretically self-propelled locomotors are a class of active colloids in which a particle autonomously swims through the liquid as a result of an unbalanced interaction with solute molecules asymmetrically distributed around the colloid. This solute distribution is maintained by a reaction which produces the solute on one catalytically active side of the Janus motor colloid. For the simplest case of diffusiophoretic self-propulsion near a planar infinite wall with zero solute flux, and repulsive solute-colloid interactions, hydrodynamic solutions for deterministic Stokes flow have shown that that for large catalytically active areas pointed away from the wall, and for distances less than the particle radius, the particles can skim at a constant distance along the surface without rotation, or can become stationary. To examine the effect of thermal fluctuations on the stability of these regimes for small motor sizes, Brownian dynamics simulations including the hydrodynamic interaction with the wall are undertaken, and we identify critical Peclet numbers above which the skimming and stationary regimes are stable. Below these values, less predictable behavior is found in which the colloid can be repelled from or intersect with the wall.   

Interactions of micro-organisms near a wall in Stokes flow using a regularized image system

We present an extension of the regularized image system for Stokeslets, where regularization functions and parameters are chosen to satisfy zero flow at the wall for several different fundamental solutions. We study elastic rods near a wall using a Kirchhoff rod formulation. Results are presented for equilibrium states of straight rods and the effect of wall to the time required to reach equilibrium.   

Efficiency of air/liquid interfaces in detaching bacteria from a surface

Gas/liquid interfaces are known to be significantly more effective than shear stress in detaching microscale colloids from substrates by inducing surface tension forces. Providing that a three-phase contact at the interface of a gas bubble, the liquid phase and the particle occurs, the magnitude of the surface tension force can potentially exceed by orders of magnitude the adhesion force, which keeps the micro particles on the surface. We investigate the ability of a moving air/liquid interface to stimulate the detachment of bacteria from a surface. Bacteria are micron-sized living organisms with strong tendency to attach to almost any substrate that they come into contact with. Attachment of bacteria on the surface is a complex process regulated by diverse characteristics of their growth medium, substrate, and cell surface. Moreover, once fixed on the surface, the microorganisms evolve in time to create intricate biofilm structures, which are highly challenging to be removed. The objective of this study to characterise the efficiency of this detachment process as a function of bacterial attachment as well as hydrodynamic parameters such the surface tension and the interface velocity.   

Microfluidic experiments to quantify microbes encountering oil water interfaces

It is known that marine microbes are one of the components of biodegradation of crude oil. Biodegradation of crude oil is initiated by microbes encountering the droplet. To elucidate the key processes involved in bacterial encountering the rising oil droplets we have established microfluidic devices with hydrophilic surfaces to create micro oil droplets with controlled sizes. To quantify effect of motility of bacteria on their encounter rate, using high speed microscopy, we simultaneously tracked motile bacteria and solid particles with equivalent sizes encountering oil droplets. The results show that in the advection dominant regime, where the droplet size and the rising velocity are large, bacterial motility plays no role in the encountering rate; however, in the diffusion dominant regime, where the swimming velocity of the cells are comparable with rising velocity and Peclet number of particles is small, motility of the cells increases their encounter rate. Ongoing analysis focus on developing a mathematical model to predict the encounter rate of the cells based on their size, swimming speed, and dispersion rate and the size of oil droplets.   

Living on the edge: transfer and traffic of \textit{E. coli} in a confined flow

We quantitatively study the transport of \textit{E. coli} near the walls of confined microfluidic channels, and in more detail along the edges formed by the interception of two perpendicular walls. Our experiments establish the connection between bacteria motion at the flat surface and at the edges and demonstrate the robustness of the upstream motion at the edges. Upstream migration of \textit{E. coli} at the edges is possible at much larger flow rates compared to motion at the flat surfaces. Interestingly, the bacteria speed at the edges mainly results from collisions between bacteria moving along this single line. We show that upstream motion not only takes place at the edge but also in an ``edge boundary layer'' whose size varies with the applied flow rate. We quantify the bacteria fluxes along the bottom walls and the edges and show that the result from both the transport velocity of bacteria and the decrease of surface concentration with increasing flow rate due to erosion processes. We rationalize our findings as a function of the local variations of the shear rate in the rectangular channels and hydrodynamic attractive forces between bacteria and walls.   

Position and Trajectrories of helical microswimmers inside circular channels

This work reports the position and orientation of helical mm-sized microswimmers in circular channels obtained by image processing of recorded images. Microswimmers are biologically inspired structures with huge potential for medical practices such as delivery of potent drugs into tissues. In order to understand the hydrodynamic effects of confinement on the velocity and stability of trajectories of swimmers, we developed helical microswimmers with a magnetic head and a rigid helical tail, similar to those of \textit{E. coli} bacteria. The experiments are recorded using a digital camera, which is placed above the experimental setup that consists of three Helmholtz pairs, generating a rotating magnetic field. A channel containing the microswimmer is placed along the axis of the innermost coil. Image processing tools based on contrast-enhancement are used to obtain the centroid of the head of the swimmer and orientation of the whole swimmer in the channel. Swimmers that move in the direction of the head, i.e. pushed kinematically by the tail, has helical trajectories, which are more unstable in the presence of Poiesuille flow inside the channel; and the swimmers that are pulled by the tail, have trajectories that stabilize at the centerline of the channel.   

Coupled Rapid Cell and Lattice Boltzmann Models to Simulate Hydrodynamics of Bacterial Transport in Response to Chemoattractant Gradients in Confined Domains

The Rapid Cell (RC) model was developed to simulate motility and adaptation dynamics of flagellar bacterial chemotaxis in environments with spatiotemporal variations in chemoattractant gradients. RC is best suited to motility studies in unbounded domains within non-fluid environments; this limits its use as a simulation tool. In this study, we eliminate these constraints by dynamically coupling RC with the colloidal lattice-Boltzmann (LB) model, a versatile tool for simulating transport of particles (e.g., surrogate bacteria) of distinct shapes and finite sizes in transient flow fields in geometrically complex microchannels. This was accomplished by tracking positions of chemoreceptor clusters on the particle surface that vary with particle angular and translational velocities, and by including additional forces and torques due to particles tumbling and to running motions in particle force-balance and torque-balance equations. The coupled RC-LB model successfully simulated transport of multiple particles in confined domains with single- or multi-attractant sources in a variety of settings. The coupled RC-LB model represents a first step toward development of a new modeling capability to simulate chemotaxis-driven bacterial transport in a network of geometrically irregular flow channels typically observed in tumor vasculature in the context of targeted drug delivery.