Hydrodynamic analysis of flagellated bacteria swimming in corners of rectangular channels

Squirmer hydrodynamics near a periodic surface topography

The behaviour of microscopic swimmers has previously been explored near large-scale confining geometries and in the presence of very small-scale surface roughness. Here, we consider an intermediate case of how a simple microswimmer, the tangential spherical squirmer, behaves adjacent to singly and doubly periodic sinusoidal surface topographies that spatially oscillate with an amplitude that is an order of magnitude less than the swimmer size and wavelengths that are also within an order of magnitude of this scale. The nearest neighbour regularised Stokeslet method is used for numerical explorations after validating its accuracy for a spherical tangential squirmer that swims stably near a flat surface. The same squirmer is then introduced to different surface topographies. The key governing factor in the resulting swimming behaviour is the size of the squirmer relative to the surface topography wavelength. For instance, directional guidance is not observed when the squirmer is much larger, or much smaller, than the surface topography wavelength. In contrast, once the squirmer size is on the scale of the topography wavelength, limited guidance is possible, often with local capture in the topography troughs. However, complex dynamics can also emerge, especially when the initial configuration is not close to alignment along topography troughs or above topography crests. In contrast to sensitivity in alignment and topography wavelength, reductions in the amplitude of the surface topography or variations in the shape of the periodic surface topography do not have extensive impacts on the squirmer behaviour. Our findings more generally highlight that the numerical framework provides an essential basis to elucidate how swimmers may be guided by surface topography.

Quasi-two-dimensional bacterial swimming around pillars: Enhanced trapping efficiency and curvature dependence

Microswimmers exhibit more diverse behavior in quasi-two dimensions than in three dimensions. Such behavior remains elusive due to the analytical difficulty of dealing with two parallel solid boundaries. The existence of additional obstacles in quasi-two dimensional systems further complicates the analysis. Combining experiments and hydrodynamic simulations, we investigate how the spatial dimension affects the interactions between microswimmers and obstacles. We fabricated microscopic pillars in quasi-two dimensions by etching glass coverslips and observed bacterial swimming among the pillars. Bacteria got trapped around the circular pillars and the trapping efficiency increased as the quasi-two-dimensionality was increased or as the curvature of the pillars was decreased. Numerical simulations of the simplest situation of a confined squirmer showed anomalous increase of hydrodynamic attractions, establishing that the enhanced interaction is a universal property of quasi-two-dimensional microhydrodynamics. We also demonstrated that the local curvature of the obstacle controls the trapping efficiency by experiments with elliptic pillars.

Habitat geometry in artificial microstructure affects bacterial and fungal growth, interactions, and substrate degradation

Microhabitat conditions determine the magnitude and speed of microbial processes but have been challenging to investigate. In this study we used microfluidic devices to determine the effect of the spatial distortion of a pore space on fungal and bacterial growth, interactions, and substrate degradation. The devices contained channels differing in bending angles and order. Sharper angles reduced fungal and bacterial biomass, especially when angles were repeated in the same direction. Substrate degradation was only decreased by sharper angles when fungi and bacteria were grown together. Investigation at the cellular scale suggests that this was caused by fungal habitat modification, since hyphae branched in sharp and repeated turns, blocking the dispersal of bacteria and the substrate. Our results demonstrate how the geometry of microstructures can influence microbial activity. This can be transferable to soil pore spaces, where spatial occlusion and microbial feedback on microstructures is thought to explain organic matter stabilization.

Curvature in the reproductive tract alters sperm-surface interactions

The fallopian tube is lined with a highly complex folded epithelium surrounding a lumen that progressively narrows. To study the influence of this labyrinthine complexity on sperm behavior, we use droplet microfluidics to create soft curved interfaces over a range of curvatures corresponding to the in vivo environment. We reveal a dynamic response mechanism in sperm, switching from a progressive surface-aligned motility mode at low curvatures (larger droplets), to an aggressive surface-attacking mode at high curvatures (smaller droplets of <50 µm-radius). We show that sperm in the attacking mode swim ~33% slower, spend 1.66-fold longer at the interface and have a 66% lower beating amplitude than in the progressive mode. These findings demonstrate that surface curvature within the fallopian tube alters sperm motion from a faster surface aligned locomotion in distal regions to a prolonged physical contact with the epithelium near the site of fertilization, the latter being known to promote capacitation and fertilization competence.

Rebound and scattering of motile Chlamydomonas algae in confined chambers

Motivated by recent experiments demonstrating that motile algae get trapped in draining foams, we study the trajectories of microorganisms confined in model foam channels (section of a Plateau border). We track single Chlamydomonas reinhardtii cells confined in a thin three-circle microfluidic chamber and show that their spatial distribution exhibits strong corner accumulation. Using empirical scattering laws observed in previous experiments (scattering with a constant scattering angle), we next develop a two-dimension geometrical model and compute the phase space of trapped and periodic trajectories of swimmers inside a three-circles billiard. We find that the majority of cell trajectories end up in a corner, providing a geometrical mechanism for corner accumulation. Incorporating the distribution of scattering angles observed in our experiments and including hydrodynamic interactions between the cells and the surfaces into the geometrical model enables us to reproduce the experimental probability density function of micro-swimmers in microfluidic chambers. Both our experiments and models demonstrate therefore that motility leads generically to trapping in complex geometries.

Patterns of bacterial motility in microfluidics-confining environments

Understanding the motility behavior of bacteria in confining microenvironments, in which they search for available physical space and move in response to stimuli, is important for environmental, food industry, and biomedical applications. We studied the motility of five bacterial species with various sizes and flagellar architectures (Vibrio natriegens, Magnetococcus marinus, Pseudomonas putida, Vibrio fischeri, and Escherichia coli) in microfluidic environments presenting various levels of confinement and geometrical complexity, in the absence of external flow and concentration gradients. When the confinement is moderate, such as in quasi-open spaces with only one limiting wall, and in wide channels, the motility behavior of bacteria with complex flagellar architectures approximately follows the hydrodynamics-based predictions developed for simple monotrichous bacteria. Specifically, V. natriegens and V. fischeri moved parallel to the wall and P. putida and E. coli presented a stable movement parallel to the wall but with incidental wall escape events, while M. marinus exhibited frequent flipping between wall accumulator and wall escaper regimes. Conversely, in tighter confining environments, the motility is governed by the steric interactions between bacteria and the surrounding walls. In mesoscale regions, where the impacts of hydrodynamics and steric interactions overlap, these mechanisms can either push bacteria in the same directions in linear channels, leading to smooth bacterial movement, or they could be oppositional (e.g., in mesoscale-sized meandered channels), leading to chaotic movement and subsequent bacterial trapping. The study provides a methodological template for the design of microfluidic devices for single-cell genomic screening, bacterial entrapment for diagnostics, or biocomputation.

Self-organization and multi-line transport of human spermatozoa in rectangular microchannels due to cell-cell interactions

The journey of sperm navigation towards ovum is one of the most important questions in mammalian fertilisation and reproduction. However, we know very little about spermatozoa propagation in a complex fluidic, chemical and topographic environment of a fertility tract. Using microfluidics techniques, we investigate the influence of cell-cell interactions on spermatozoa swimming behavior in constrained environment at different concentrations. Our study shows that at high enough cell concentration the interaction between boundary-following cells leads to formation of areas with preferential direction of cell swimming. In the microchannel of a rectangular cross-section, this leads to formation of a “four-lane” swimming pattern with the asymmetry of the cell distribution of up to 40%. We propose that this is caused by the combination of cell-cell collisions in the corners of the microchannel and the existence of morphologically different spermatozoa: slightly asymmetric cells with trajectories curved left and the symmetric ones, with trajectories curved right. Our findings suggest that cell-cell interactions in highly folded environment of mammalian reproductive tract are important for spermatozoa swimming behavior and play role in selection of highly motile cells.

Optimal actuation of flagellar magnetic microswimmers

We present an automated procedure for the design of optimal actuation for flagellar magnetic microswimmers based on numerical optimization. Using this method, a magnetic actuation method is provided which allows these devices to swim significantly faster compared to the usual sinusoidal actuation. This leads to a novel swimming strategy which makes the swimmer perform a three-dimensional figure-eight trajectory. This shows that a faster propulsion is obtained when the swimmer is allowed to go out of plane. This approach is experimentally validated on a scaled-up flexible swimmer.

Metachronal Swimming with Rigid Arms near Boundaries

Various organisms such as crustaceans use their appendages for locomotion. If they are close to a confining boundary then viscous as opposed to inertial effects can play a central role in governing the dynamics. To study the minimal ingredients needed for swimming without inertia, we built an experimental system featuring a robot equipped with a pair of rigid slender arms with negligible inertia. Our results show that directing the arms to oscillate about the same time-averaged orientation produces no net displacement of the robot each cycle, regardless of any phase delay between the oscillating arms. The robot is able to swim if the arms oscillate asynchronously around distinct orientations. The measured displacement over time matches well with a mathematical model based on slender-body theory for Stokes flow. Near a confining boundary, the robot with no net displacement every cycle showed similar behavior, while the swimming robot increased in speed closer to the boundary.

Oscillatory surface rheotaxis of swimming E. coli bacteria

Bacterial contamination of biological channels, catheters or water resources is a major threat to public health, which can be amplified by the ability of bacteria to swim upstream. The mechanisms of this 'rheotaxis', the reorientation with respect to flow gradients, are still poorly understood. Here, we follow individual E. coli bacteria swimming at surfaces under shear flow using 3D Lagrangian tracking and fluorescent flagellar labelling. Three transitions are identified with increasing shear rate: Above a first critical shear rate, bacteria shift to swimming upstream. After a second threshold, we report the discovery of an oscillatory rheotaxis. Beyond a third transition, we further observe coexistence of rheotaxis along the positive and negative vorticity directions. A theoretical analysis explains these rheotaxis regimes and predicts the corresponding critical shear rates. Our results shed light on bacterial transport and reveal strategies for contamination prevention, rheotactic cell sorting, and microswimmer navigation in complex flow environments.

Thrust and Hydrodynamic Efficiency of the Bundled Flagella

The motility mechanism of prokaryotic organisms has inspired many untethered microswimmers that could potentially perform minimally invasive medical procedures in stagnant fluid regions inside the human body. Some of these microswimmers are inspired by bacteria with single or multiple helical flagella to propel efficiently and fast. For multiple flagella configurations, the direct measurement of thrust and hydrodynamic propulsion efficiency has been challenging due to the ambiguous mechanical coupling between the flow field and mechanical power input. To address this challenge and to compare alternative micropropulsion designs, a methodology based on volumetric velocity field acquisition is developed to acquire the key propulsive performance parameters from scaled-up swimmer prototypes. A digital particle image velocimetry (PIV) analysis protocol was implemented and experiments were conducted with the aid of computational fluid dynamics (CFD). First, this methodology was validated using a rotating single-flagellum similitude model. In addition to the standard PIV error assessment, validation studies included 2D vs. 3D PIV, axial vs. lateral PIV and simultaneously acquired direct thrust force measurement comparisons. Compatible with typical micropropulsion flow regimes, experiments were conducted both for very low and higher Reynolds (Re) number regimes (up to a Re number = 0.01) than that are reported in the literature. Finally, multiple flagella bundling configurations at 0°, 90° and 180° helical phase-shift angles were studied using scaled-up multiple concentric flagella thrust elements. Thrust generation was found to be maximal for the in-phase (0°) bundling configuration but with ~50% lower hydrodynamic efficiency than the single flagellum. The proposed measurement protocol and static thrust test-bench can be used for bio-inspired microscale propulsion methods, where direct thrust and efficiency measurement are required.

Bacterial detachment from a wall with a bump line

The interactions of bacteria with surfaces have important implications in numerous areas of research, such as bioenergy, biofilm, biofouling, and infection. Recently, several experimental studies have reported that the adhesion of bacteria can be reduced considerably by microscale wall features. To clarify the effect of wall configurations, we numerically investigated the behavior of swimming bacteria near a flat wall with a bump line. The results showed that the effects of bump configuration are significant; a detachment time larger than several seconds can be achieved in certain parameter sets. These results illustrate that the number density of bacteria near the wall may be reduced by appropriately controlling the parameter sets. When background shear flow was imposed, the near-wall bacterium mainly moved towards the vorticity axis. The detachment time of cells increased significantly by adjusting the bump line to have 45^{∘} relative to the flow direction. The knowledge obtained in this study is fundamental for understanding the interactions between bacteria and surfaces according to more complex geometries, and is useful for reducing the adhesion of cells to walls.

The swimming of a deforming helix

Many microorganisms and artificial microswimmers use helical appendages in order to generate locomotion. Though often rotated so as to produce thrust, some species of bacteria such Spiroplasma, Rhodobacter sphaeroides and Spirochetes induce movement by deforming a helical-shaped body. Recently, artificial devices have been created which also generate motion by deforming their helical body in a non-reciprocal way (A. Mourran et al. Adv. Mater. 29, 1604825, 2017). Inspired by these systems, we investigate the transport of a deforming helix within a viscous fluid. Specifically, we consider a swimmer that maintains a helical centreline and a single handedness while changing its helix radius, pitch and wavelength uniformly across the body. We first discuss how a deforming helix can create a non-reciprocal translational and rotational swimming stroke and identify its principle direction of motion. We then determine the leading-order physics for helices with small helix radius before considering the general behaviour for different configuration parameters and how these swimmers can be optimised. Finally, we explore how the presence of walls, gravity, and defects in the centreline allow the helical device to break symmetries, increase its speed, and generate transport in directions not available to helices in bulk fluids.

Predominance of sperm motion in corners

Sperm migration through the female tract is crucial to fertilization, but the role of the complex and confined structure of the fallopian tube in sperm guidance remains unknown. Here, by confocal imaging microchannels head-on, we distinguish corner- vs. wall- vs. bulk-swimming bull sperm in confined geometries. Corner-swimming dominates with local areal concentrations as high as 200-fold that of the bulk. The relative degree of corner-swimming is strongest in small channels, decreases with increasing channel size, and plateaus for channels above 200 μm. Corner-swimming remains predominant across the physiologically-relevant range of viscosity and pH. Together, boundary-following sperm account for over 95% of the sperm distribution in small rectangular channels, which is similar to the percentage of wall swimmers in circular channels of similar size. We also demonstrate that wall-swimming sperm travel closer to walls in smaller channels (~100 μm), where the opposite wall is within the hydrodynamic interaction length-scale. The corner accumulation effect is more than the superposition of the influence of two walls, and over 5-fold stronger than that of a single wall. These findings suggest that folds and corners are dominant in sperm migration in the narrow (sub-mm) lumen of the fallopian tube and microchannel-based sperm selection devices.