ICTS

Suspensions of motile living organisms represent a non-equilibrium system of condensed matter of great interest from a fundamental point of view. These are suspensions composed of autonomous units - active particles - capable of converting stored energy into motion. The interactions between the active particles and the liquid in which they swim give rise to mechanical constraints and a large-scale collective movement that have recently attracted a great deal of interest in the physical and mechanical communities. Our recent work on microalgae suspensions will be presented. The micro alga Chlamydomonas Reinhardtii uses its two anterior flagella to propel itself into aqueous media. It then produces a random walk with persistence that can be characterised quantitatively by analysing the trajectories produced. Moreover, in the presence of a light stimulus, it biases its trajectory to direct it towards the light: this phenomenon is called phototaxis. By coupling experiments and modelling, we propose to extract from the hydrodynamic characteristics of this microalga some of the generic properties of microswimmer suspensions.

This talk will focus on the subtle interplay of swimmer shape and shear in determining migration along the gradient, and dispersion along the flow, directions in a pressure-driven channel flow. The migration in the gradient direction reveals a profound asymmetry between disk and rod-shaped swimmers, while the dispersion in the flow direction exhibits anomalous scaling for rod-shaped swimmers. The effect of shear is characterized by the Peclet number (Pe: product of the shear rate and an appropriate orientation relaxation time). The swimmer is modelled as a rigid spheroid with aspect ratio r; r > 1 for rod-shaped swimmers (prolate spheroids), and r < 1 for disk-shaped ones (oblate spheroids). The kinetic equation for the swimmer probability density includes competing effects of both an orientation anisotropy and a spatial inhomogeneity induced by the linearly varying ambient shear, and a relaxation to isotropy on account of run-and-tumble dynamics and rotary diffusion. In the first part of the talk, we examine the effect of swimmer aspect ratio on shear-induced migration along the gradient direction. We employ a multiple scales analysis to separate the orientation relaxation (fast) and spatial diffusion time scales (slow), and obtain a drift-diffusion equation for the evolution of the swimmer concentration. Disk-shaped swimmers migrate towards the centerline for small to moderate Pe, but migrate towards the channel walls for larger Pe. The scalings for the drift (V_z) and diffusivity (D_zz) reveal two asymptotic regimes. In regime I, corresponding to 1 << Pe << r^−3, D_zz ∼ O(Pe^−2/3), V_z ∼ O(Pe^−4/3), the latter being directed towards the centerline. In regime II, corresponding to Pe >> r^−3, both D_zz and V_z scale as O(Pe^−2), the latter being directed away from the centerline. In contrast, rod-shaped swimmers migrate towards the walls for 1 << Pe << r^3 (D_zz, V_z ∼ O(Pe^−4/3)) and towards the centerline for Pe >> r^3 (D_zz, V_z ∼ O(Pe^-2)). Interestingly, while flat-disk (r = 0) swimmers exhibit the maximum inhomogeneity at a finite Pe, infinitely slender rod-swimmers asymptote to the maximum inhomogeneity only in the limit of infinite Pe (Vennamneni et al., J. Fluid Mech., 2020). While a finite-Pe peak in the inhomogeneity, reported in experiments involving rod-shaped swimmers (Rusconi et al., Nat. Phys., 2014)), was likely an artefact of residence time limitations, we show the existence of a true finite-Pe maximum for disk-shaped swimmers. In the second part of the talk, we examine the Taylor dispersion of a population of rod-shaped swimmers. A multiple scales analysis is now employed to separate three different time scales - the shortest orientation relaxation time scale, the longer time scale corresponding to swimmer diffusion in the gradient direction and the longest time scale corresponding to diffusion along the flow direction - and obtain a convection- diffusion equation in the flow coordinate for the transversely averaged swimmer concentration. We examine the axial diffusivity in the aforementioned regimes of near-wall (1 << Pe << r^3) and near- centerline (Pe >> r^3) accumulation. In the former case, the expected O(Pe^10/3) Taylor dispersion scaling arises from an O(Pe^−4/3) gradient-component diffusivity. However, in the regime of near-centerline accumulation, the expected O(Pe^4) scaling for a gradient-component diffusivity of O(Pe^−2) is only obtained for r < 2. Higher aspect ratio swimmers exhibit anomalously reduced dispersion owing to a centerline collapse of swimmers along the gradient direction.

Deviations from Brownian motion leading to anomalous diffusion are found in transport dynamics from quantum physics to life sciences. The characterization of anomalous diffusion from the measurement of an individual trajectory is a challenging task, which traditionally relies on calculating the trajectory mean squared displacement. However, this approach breaks down for cases of practical interest, e.g., short or noisy trajectories, heterogeneous behaviour, or non-ergodic processes. Recently, several new approaches have been proposed, mostly building on the ongoing machine-learning revolution. To perform an objective comparison of methods, we gathered the community and organized an open competition, the Anomalous Diffusion challenge (AnDi). Participating teams applied their algorithms to a commonly-defined dataset including diverse conditions. Although no single method performed best across all scenarios, machine-learning-based approaches achieved superior performance for all tasks. The discussion of the challenge results provides practical advice for users and a benchmark for developers

A new model of microswimmer is introduced to investigate locomotion strategies based on the sinusoidal undulation of a slender body. These active particles are then embedded in a prescribed fluid flow in which their swimming undulations have to compete with the drifts, strains, and deformations inflicted by the outer velocity field. Such an intricate situation, where swimming and navigation are tightly bonded is addressed using reinforcement learning. It is shown that the displacement strategy of the microswimmers can be efficiently optimized using Q-learning. Still, such an approach rapidly becomes rather expensive because of the highly chaotic character of the swimmers dynamics yielding a strong variability in learning efficiencies. A genetic algorithm is employed to circumvent such a pitfall.

The motion of small spheroidal particles in a simple shear was first described by Jeffery in 1922 and remains a cornerstone of modern fluid dynamics. In addition to describing the motion of passive particles, this theory has also been used to understand how flow affects the distribution and transport of micro-swimmers. While fluid shear generally acts to reorient the motility of swimmers away from their intended direction of travel, the dynamics of this interaction crucially depends on the organism’s morphology. I shall present two pieces of work investigating how shape effects the transport of micro-swimmers in shear. Firstly we will consider the 3D transport of elongated active particles under the action of an aligning force (e.g. gyrotactic swimmers) in some simple flow fields; and will see how shape can influence the vertical distribution, for example changing the structure of thin layers [1]; secondly we shall consider elongated bacteria swimming in a bounded channel based upon [2] and recent extensions of this work.

[1] RN Bearon & WM Durham, Elongation enhances migration through hydrodynamic shear (submitted to Phys Rev Fluids),
[2] RN Bearon & AL Hazel, The trapping in high-shear regions of slender bacteria undergoing chemotaxis in a channel (2015) J. Fluid Mech.

The rotations and accelerations of non-spherical particles have proven to be a powerful way to look at the evolutions of turbulent flow structures at the scale of the particle. We use experimental tracking of 3D printed plastic particles in turbulent flow between oscillating grids and in grid turbulence behind an active jet array. For dissipation scale particles, the rotations of particles are strongly affected by preferential alignment by the stain integrated along Lagrangian trajectories. For larger particles, we measure the preferential alignment between particle orientation, rotation rate, acceleration, and rotational acceleration.

Adding even a tiny amount of polymer to a fluid can have dramatic effects on the manner in which it flows. In high-Reynolds-number turbulent flow, polymers dramatically reduce the net drag force, whereas in Stokes flow, polymers induce a series of instabilities resulting in a chaotic state called elastic turbulence. While continuum models can capture qualitative aspects of these phenomena, quantitative predictions demand a detailed understanding of the dynamics of individual polymers and of their interaction with the flow. This comes to the fore when one considers the flow-induced breakup or scission of polymers---an important phenomena which results in the eventual loss of polymeric effects like drag reduction. This is a particularly challenging problem because, being an extreme event at the scale of the polymer molecule, scission defies an obvious coarse-grained continuum description. In this talk, I will present results from multi-scale simulations which combine Brownian dynamics for polymer molecules with Navier-Stokes simulations for the turbulent fluid flow. The results enable us to explain key experimental observations in previous literature, and show that net drag-reduction is maximized by polymers with moderate relaxation times.

Most engineering and geophysical problems in turbulence can be addressed without any need to consider compressibility. Whereas in many astrophysical problems, e.g., dust in galactic scale flows, it is necessary to consider the shocks. As the simplest example of shock dominated turbulence, we consider the randomly forced Burgers equation. In one dimension, we consider a Lagrangian interval of length $\ell$ and calculate the time, $\tau$, it takes for it to collapse into a point. By extensive numerical simulations and analysis we show that the time $\tau$ is a random variable with non-Gaussian statistics. The $p$ moment of $\tau$ scales with $\ell^{z_{\rm p}}$ where the dynamic exponents $z_{\rm p}$ is bifractal. We point out how to generalize our results to higher dimensions.

Heavy particles in turbulent flow, in the process of being centrifuged out of vortices, can form caustics, resulting in singular features in the number-density. Can motile particles without inertia behave in a similar manner, thanks to the persistence of self-propelled motion? We show that they can. We study numerically and analytically the resulting caustics and clustering and comment on the implications for enhanced encounters and interactions of swimming organisms in vortical flows. This work was done with Rahul Chajwa (Stanford) and Rama Govindarajan (ICTS).

I will give an overview of the work that we have carried out in our group on the statistical properties of particles in different types of turbulent flows in superfluids, in binary-fluid mixtures, and in active fluids.  These studies have been carried out with Sanjay Shukla, Akhilesh Kumar Verma, Akshay Bhatnagar, Nadia Bihari Padhan, Kolluru Venkata Kiran, and Anupam Gupta.