Session D11: Active Suspensions & Microswimmers

Entrainment and scattering in microswimmer--colloid interactions

We use boundary element simulations to study the interaction of model microswimmers with a neutrally buoyant spherical particle. Three swimmer models are used: a spherical squirmer and two bacteria with different flagellum lengths. The particle size is varied from much smaller than to much larger than the size of the swimmer. These two extremes respectively approximate swimmers encountering a tracer and a fixed, flat surface. We find that the centre of mass motion of the particle due to hydrodynamic interactions is insensitive to the particle radius when the swimmer passes distantly. In head-on collisions, particles become entrained by the swimmer and can experience large displacements. Simultaneously, swimmers can be deflected through large angles by interactions with a particle if the particle is large enough. This deflection, in turn, alters the path of the particle. Based on numerical results, we estimate the effective diffusivity of a particle in a dilute bath of swimmers and show that there is a non-monotonic dependence on particle radius. Similarly, we show that the effective diffusivity of a swimmer scattering in a suspension of particles varies non-monotonically with particle radius.   

Unstable intrusion of active matter into a fluid

We investigate numerically and analytically the intrusion of motile and non-motile stress-generating particles into a surrounding fluid environment. Gaussian patches of initially isotropic particle orientation and initially polar particle alignment are found to extend into the fluid with geometries dependent on the mechanism of particle propulsion. In the isotropic case the particles never generate a fluid flow as the patch evolves. Patches of aligned ``pusher'' particles elongate in the direction of particle orientation, then undergo a transverse concentration instability, and finally converge to the classical fluctuating state with long spatial correlations. Aligned ``puller'' particles elongate in the direction opposite the particle orientation direction and exhibit dramatic splay as the group moves into the bulk. The dynamics are rationalized using the particle distribution moment equations and perturbation stability analysis.   

Vertical migration of motile phytoplankton chains through turbulence

Daily, phytoplankton needs to migrate vertically from and towards the ocean surface to find nutrients such as dissolved oxygen. To travel through the water column they need to fight against gravity (by swimming) and fluid turbulence (1) which can make their journey longer. It is often observed that cells migrate across the water column as chains. The first benefit to form chains is that micro-organisms sum up their thrust while reducing their drag. Therefore, upwards swimming is faster for chains in a quiescent fluid with steady vertical orientation. However, as chain length increases their tendency to periodically tumble in turbulent structures increases which reduces orientation stability and limits their capacity to swim upwards. The purpose of our study is to elaborate on this apparent contradiction. We carried out direct numerical simulations and physical analysis of the coupled system of homogeneous isotropic turbulence and chain trajectories through Lagrangian tracking. Formation of chains is indeed favorable for vertical migration through the upper layer of the ocean. (1) - Turbulence drives microscale patches of motile phytoplankton. W. M. Durham, E. Climent, M. Barry, F. De Lillo G. Boffetta, M. Cencini and R. Stocker. Nature Communications (2013) – 4:2148   

Quincke random walkers

The spontaneous rotation of a sphere in an applied uniform DC electric field (Quincke effect) has been utilized to engineer self-propelled particles (Bricard et al, Nature (2013)): if the sphere is initially resting on a surface, it rolls. The Quincke rollers have been widely used as a model system to study collective behavior in “active” suspensions. If the applied field is DC, an isolated Quincke roller follows a straight line trajectory. In this talk, we discuss the design of a Quincke roller that executes a random-walk-like behavior. We utilize AC field – upon reversal of the field direction a fluctuation in the axis of rotation (which is degenerate in the plane perpendicular to the field and parallel to the surface) introduces randomness in the direction of motion. The MSD of an isolated Quincke walker depends on frequency, amplitude, and waveform of the electric field. Experiment and theory are compared. We also investigate the collective behavior of Quincke walkers,the transport of inert particles in a bath of Quincke walkers, and the spontaneous motion of a drop containing Quincke active particle.   

Sedimentation dynamics and diffusion of suspensions of swimming E. coli

Sedimentation in active fluids has come into focus due to the ubiquity of swimming micro-organisms in natural and man-made environments. Here, we experimentally investigate sedimentation of passive particles in water containing various concentrations of the bacterium {\it E. coli}. Results show that the presence of live bacteria reduces the velocity of the sedimentation front even in the dilute regime, where constant sedimentation velocity is expected to be independent of particle concentration. The presence of live bacteria increases the effective diffusion coefficient, which determines the width of the sedimentation front. For higher bacteria concentration, we find the development of two sedimentation fronts due to bacterial death. A model in which the advection-diffusion equation describing the settling of particles under gravity is coupled to the population dynamics of the bacteria captures the experimental trends relatively well.   

Three-dimensional flow structure in a kinesin-driven active gel

An active gel of kinesin-driven microtubule bundles gives rise to a turbulent-like flow which, for a specific set of toroidal geometries, spontaneously gives rise to a coherent azimuthal flow (Wu \textit{et al.} \textit{Science} (2017)). Here we present results from a two-color velocimetry that simultaneously measures (i) the planar components of velocity of the active microtubule bundles in several $r-\theta$ planes at multiple $z$ stacks and (ii) the three-dimensional motion of passive tracer particles throughout the entire system. This technique is used to reconstruct the structure of the active flow for both coherent and non-coherent (``turbulent'') systems. We present data on the activity of the gel as a function of confinement as well as the mean velocity and fluctuating profiles for the cases in which a coherent flow develops. In addition to the azimuthal flow around the torus, we observe large-scale vortex-like secondary flow structures that form and break up in the $r-z$ plane.   

Autonomous propulsion of nanorods trapped in an acoustic field

Recent measurements demonstrate that nanorods trapped in acoustic fields generate autonomous propulsion, with their direction and speed controlled by both the particle's shape and density distribution. In this talk, we investigate the physical mechanisms underlying this combined density/shape induced phenomenon by developing a simple yet rigorous mathematical framework for arbitrary axisymmetric particles. This only requires solution of the (linear) unsteady Stokes equations. Geometric and density asymmetries in the particle generate axial jets that can produce motion in either direction. Strikingly, the propulsion direction is found to reverse with increasing frequency, an effect that is yet to be reported experimentally. The general theory and mechanism described here enable the \textit{a priori} design and fabrication of nano-motors in fluid for transport of small-scale payloads and robotic applications.   

Undulatory swimming in viscoelastic fluids under geometric confinement: experiments with C. elegans

Many natural biological processes, such as bacteria moving through vesicles in the circulatory system and spermatozoa swimming through millimeter-scale fallopian tubes, require low Reynolds number swimmers to move between two fluid-solid interfaces. Furthermore, these biological systems typically involve non-Newtonian fluids (e.g. blood and mucus), which can be shear-thinning, viscoelastic, or both. Using the model biological organism C. elegans, we introduce two far-field no-slip boundary conditions in the beating plane by observing swimming through thin channels in viscosified Newtonian and viscoelastic fluids. Using image processing and particle tracking velocimetry techniques, we measure both the swimming kinematics and the resulting flow fields as a function of decreasing channel width. As this width approaches the characteristic transverse length scale of the nematode's swimming gate, we observe (i) swimming speed decreases with increasing De, (ii) this decrease in speed can be non-monotonic with decreasing channel width at a given De, and (iii) the change in nematode kinematics appears to be associated with a structural change in the flow field around the swimmer quantified using the flow type parameter.   

Chemotaxis of C. elegans in 3D media: a model for navigation of undulatory microswimmers

While the natural environment of \textit{C.\ elegans} consists of complex 3D media (e.g., decomposing organic matter and water), most studies of chemotactic behavior of this nematode are limited to 2D. We present a 3D chemotaxis model that combines a realistic geometrical representation of body movements associated with 3D maneuvers, an analysis of mechanical interactions of the nematode body with the surrounding medium to determine nematode trajectories, and a simple memory-function description of chemosensory apparatus that controls the frequency, magnitude, and timing of turning maneuvers. We show that two main chemotaxis strategies of \textit{C.\ elegans} moving in 2D, i.e., the biased random walk and gradual turn, are effective also in 3D, provided that 2D turns are supplemented by the roll maneuvers that enable 3D reorientation. Optimal choices of chemosensing and gait-control parameters are discussed; we show that the nematode can maintain efficient chemotaxis in burrowing and swimming by adjusting the undulation frequency alone, without changing the chemotactic component of the body control. Understanding how \textit{C. elegans} efficiently navigates in 3D media may help in developing self-navigating artificial microswimmers.   

Rheological aspects of C. elegans suspensions under oscillatory shear

The rheological nature of an active suspension of nematodes is discussed. The nematode chosen for the study is Caenorhabditis elegans and its motion is subjected to the time reversibility of creeping flows. We investigate how the movement of the nematodes under different volumetric fractions alter the fluid rheological characteristics, considering collective behavior. We provide a deep discussion based on the experimental data obtained through a rotating disk rheometer. Oscillatory shear and step strain tests were conducted in order to present a discussion regarding zero shear viscosity and relaxation time for different nematodes concentrations. Moreover, theassociated time scales coupling provide a good physical comprehension of active suspensions.