Collective behaviour of active systems

Active systems are collections of particles that continuously take energy from their surrounding and use it to do work. Examples include bacterial colonies and living cells. Hydrodynamic instabilities are inherent to active fluids, and active suspensions spontaneously generate complex flow patterns at length scales much larger than the microscopic constituents. These are characterised by strong variations in vorticity and topological defects that are self-propelling. Such turbulent-like patterns have been observed in experiments on mixtures of actin or microtubules and motor proteins designed to isolate the important ingredients leading to cellular motility and in dense suspensions of swimming E-coli. We have recently shown that layers of cells show many of the features of dense active matter. In particular it is possible to identify motile topological defects. These are correlated with cells which die and are ejected from the layer, a process vital in promoting healthy tissue and avoiding the formation of tumours. We are also interested in active material in confined spaces where the interplay of the active and the confining length scales, together with the possible creation of motile topological defects, can lead to surprisingly complex behaviour. For example in narrow channels a one-dimensional line of flow vortices forms a racetrack for defects which move right or left on sinusoidal trajectories. More details can be found in our review: Active nematics, Nature Communications 9 3246 (2018) and in our recent papers

Flow in an active nematic: the shading represents the vorticity field and the lines are streamlines of the flow

Emergence of active puffs from a vortex-lattice controls the transition to turbulence in living fluids. (a) A highly ordered flow vortex-lattice is formed at lower activities when an active fluid is confined and (b) active turbulence is fully established at higher activities. Lower panels in (a), (b) show the height-averaged enstrophy signal along the channel. (c) Coexistence of the vortex-lattice and meso-scale turbulence close to the transition point. The zoomed-in panel in (d) illustrates the formation of active puffs from the vortex-lattice. Colormaps show vorticity contours with blue and red colors corresponding to clockwise and anti-clockwise vortices, respectively. The average radius of vortices is 0:32h, where h denotes the channel height.

Mechanobiology

The ways in which cells move, both individually but more particularly collectively, has implications for a vast range of cellular processes, from embryogenesis and morphogenesis to cancer metastasis and the viability of medical implants. The mechanisms behind cell motility, particularly collective cell motion, are not well understood, although recent experiments and theories have made considerable progress in the context of the simplified model system of two-dimensional, confluent cell layers. We have developed a numerical model of cell motility, based on a phase field description of each cell, to investigate unresolved questions about collective cell motility. Hence we aim to provide a framework on which to interpret future experiments studying the ways cells move. For example this paper discusses active inter-cellular interactions.

Active turbulence in a phase field mobel of epithelial cells

Swimming at low Reynolds number

Microorganisms have evolved to swim in complex environments. Often they move in confined spaces, and in fluids crowded by inert particles such as colloids and biopolymers. Our aim is to understand how their motion and swimming strategies are affected by details of their surroundings, and how the environment is, in turn, perturbed by the motion of the swimmers.

Prominent examples of biological fluids which contain high-molecular weight polymeric material include the extracellular matrix, mucosal barriers and polymer-aggregated marine snow. Surprisingly there is some evidence that bacteria swim faster in these crowded surroundings. Experiments do not, however, yet have the resolution to distinguish between the different theories predicting this. Therefore there is a vital role for detailed numerical models that explicitly measure the fluid properties around the bacterium and explore the consequences for locomotion. The figure below shows mesoscale simulations of a model bacterium moving through a dense biopolymer suspension. The model reproduced the increase in swimming speed and allowed us to explain this in terms of the distribution of polymers near the bacterium. For more details see A. Zoettl andJ.M. Yeomans, Nature Physics 15 554 (2019)

Wetting on micropatterned surfaces

We have, some time ago now, worked extensively on fluid-structure interactions. If a hydrophobic surface is patterned with micron scale posts it can become superhydrophobic. The surface is strongly water repellent, and drops slide off very easily. There are many examples where nature has exploited superhydrophobic designs, for example, on the surfaces of leave to aid the run-off of rainwater. We used analytic and numerical approaches to understand the pinning and dynamics of drops on micro-patterned surfaces.

Simulations (above) and experiments (left) showing a fluid spreading through a lattice of triangular microposts.

Anisotropic imbibition through slanted microposts

Click here to read about pancake bouncing on a superhydrophobic surface.