arXiv subjects

Tanniemola B. Liverpool

Publications and source records attributed to Tanniemola B. Liverpool.

At least 37 records · Page 2Linked to original sources

arXiv2020

Non-equilibrium systems have steady-state distributions and non-steady dynamics

We search for steady states in a class of fluctuating and driven physical systems that exhibit sustained currents. We find that the physical concept of a steady state, well known for systems at equilibrium, must be generalised to describe such systems. In these, the generalisation of a steady state is associated with a stationary probability density of micro-states and a deterministic dynamical system whose trajectories the system follows on average. These trajectories are a manifestation of non-stationary macroscopic currents observed in these systems. We determine precise conditions for the steady state to exist as well as the requirements for it to be stable. We illustrate this with some examples.

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arXiv2019

Tractionless Self-Propulsion of Active Drops

We report on a new mode of self-propulsion exhibited by compact drops of active liquids on a substrate which, remarkably, is tractionless, i.e., which imparts no mechanical stress locally on the surface. We show, both analytically and by numerical simulation, that the equations of motion for an active nematic drop possess a simple self-propelling solution, with no traction on the solid surface and in which the direction of motion is controlled by the winding of the nematic director field across the drop height. The physics underlying this mode of motion has the same origins as that giving rise to the zero viscosity observed in bacterial suspensions. This topologically protected tractionless self-propusion provides a robust physical mechanism for efficient cell migration in crowded environments like tissues.

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arXiv2019

Active suspensions have non-monotonic flow curves and multiple mechanical equilibria

We point out unconventional mechanical properties of confined active fluids, such as bacterial suspensions, under shear. Using a minimal model of an active liquid crystal with no free parameters, we predict the existence of a window of bacteria concentration for which a suspension of \textit{E.~Coli} effectively behaves, at steady-state, as a negative viscosity fluid and reach quantitative agreement with experimental measurements. Our theoretical analysis further shows that a negative apparent viscosity is due to a non-monotonic local velocity profile, and is associated with a non-monotonic stress vs. strain rate flow curve. This implies that fixed stress and fixed strain rate ensembles are not equivalent for active fluids.

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arXiv2019

Competing Active and Passive Interactions Drive Amoeba-like Living Crystallites and Ordered Bands

Swimmers and self-propelled particles are physical models for the collective behaviour and motility of a wide variety of living systems, such as bacteria colonies, bird flocks and fish schools. Such artificial active materials are amenable to physical models which reveal the microscopic mechanisms underlying the collective behaviour. Here we study colloids in a DC electric field. Our quasi-two-dimensional system of electrically-driven particles exhibits a rich and exotic phase behaviour. At low field strengths, electrohydrodynamic flows lead to self-organisation into crystallites with hexagonal order. Upon self-propulsion of the particles due to Quincke rotation, we find an ordered phase of active matter in which the motile crystallites constantly change shape and collide with one another. At higher field strengths, this "dissolves" to an active gas. We parameterise a particulate simulation model which reproduces the experimentally observed phases and, at higher field strengths predicts an activity-driven demixing to band-like structures.

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arXiv2018

From hydrodynamic lubrication to many-body interactions in dense suspensions of active swimmers

We study how hydrodynamic interactions affect the collective behaviour of active particles suspended in a fluid at high concentrations, with particular attention to lubrication forces which appear when the particles are very close to one another. We compute exactly the limiting behaviour of the hydrodynamic interactions between two spherical (circular) active swimmers in very close proximity to one another in the general setting in both three and (two) dimensions. Combining this with far-field interactions, we develop a novel numerical scheme which allows us to study the collective behaviour of large numbers of active particles with accurate hydrodynamic interactions when close to one another. We study active swimmers whose intrinsic flow fields are characterised by force dipoles and quadrupoles. Using this scheme, we are able to show that lubrication forces when the particles are very close to each other can play as important a role as long-range hydrodynamic interactions in determining their many-body behaviour. We find that when the swimmer force dipole is large, finite clusters and open gel-like clusters appear rather than complete phase separation. This suppression is due to near-field lubrication interactions. For swimmers with small force dipoles, we find surprisingly that a globally polar ordered phase appears because near-field lubrication rather than long-range hydrodnamics dominate the alignment mechanism. Polar order is present for very large system sizes and is stable to fluctuations with a finite noise amplitude. We explain the emergence of polar order using a minimal model in which only the leading rotational effect of the near-field interaction is included. These phenomena are also reproduced in two dimensions.

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arXiv2018

Yielding of a Model Glassformer: an Interpretation with an Effective System of Icosahedra

We consider the yielding under simple shear of a binary Lennard-Jones glassformer whose super-Arrhenius dynamics are correlated with the formation of icosahedral structures. We recast this glassformer as an effective system of icosahedra [Pinney et al. J. Chem. Phys. 143 244507 (2015)]. Looking at the small-strain region of sheared simulations, we observe that shear rates affect the shear localisation behavior particularly at temperatures below the glass transition as defined with a fit to the Vogel-Fulcher-Tamman equation. At higher temperature, shear localisation starts immediately upon shearing for all shear rates. At lower temperatures, faster shear rates can result in a delayed start in shear localisation; which begins close to the yield stress. Building from a previous work which considered steady-state shear [Pinney et al. J. Chem. Phys. 143 244507 (2016)], we interpret the response to shear and the shear localisation in terms of a \emph{local} effective temperature with our system of icosahedra. We find that the effective temperatures of the regions undergoing shear localisation increase significantly with increasing strain (before reaching a steady state plateau).

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arXiv2017

Shape dependent phoretic propulsion of slender active particles

We theoretically study the self-propulsion of a thin (slender) colloid driven by asymmetric chemical reactions on its surface at vanishing Reynolds number. Using the method of matched asymptotic expansions, we obtain the colloid self-propulsion velocity as a function of its shape and surface physico-chemical properties. The mechanics of self-phoresis for rod-like swimmers has a richer spectrum of behaviours than spherical swimmers due to the presence of two small length scales, the slenderness of the rod and the width of the slip layer. This leads to subtleties in taking the limit of vanishing slenderness. As a result, even for very thin rods, the distribution of curvature along the surface of the swimmer, namely its shape, plays a surprising role in determining the efficiency of propulsion. We find that thin cylindrical self-phoretic swimmers with blunt ends move faster than thin prolate spheroid shaped swimmers with the same aspect ratio.

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arXiv2017

Pair creation, motion, and annihilation of topological defects in 2D nematics

We present a novel framework for the study of disclinations in two-dimensional active nematic liquid crystals, and topological defects in general. The order tensor formalism is used to calculate exact multi-particle solutions of the linearized static equations inside a uniformly aligned state. Topological charge conservation requires a fixed difference between the number of half charges. Starting from a set of hydrodynamic equations, we derive a low-dimensional dynamical system for the parameters of the static solutions, which describes the motion of a half-disclination pair, or of several pairs. Within this formalism, we model defect production and annihilation, as observed in experiments. Our dynamics also provide an estimate for the critical density at which production and annihilation rates are balanced.

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arXiv2017

Beyond icosahedral symmetry in packings of proteins in spherical shells

The formation of quasi-spherical cages from protein building blocks is a remarkable self-assembly process in many natural systems, where a small number of elementary building blocks are assembled to build a highly symmetric icosahedral cage. In turn, this has inspired synthetic biologists to design de novo protein cages. We use simple models, on multiple scales, to investigate the self-assembly of a spherical cage, focusing on the regularity of the packing of protein-like objects on the surface. Using building blocks, which are able to pack with icosahedral symmetry, we examine how stable these highly symmetric structures are to perturbations that may arise from the interplay between flexibility of the interacting blocks and entropic effects. We find that, in the presence of those perturbations, icosahedral packing is not the most stable arrangement for a wide range of parameters; rather disordered structures are found to be the most stable. Our results suggest that (i) many designed, or even natural, protein cages may not be regular in the presence of those perturbations, and (ii) that optimizing those flexibilities can be a possible design strategy to obtain regular synthetic cages with full control over their surface properties.

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arXiv2017

Hydrodynamic interactions in dense active suspensions: from polar order to dynamical clusters

We study the role of hydrodynamic interactions in the collective behaviour of collections of microscopic active particles suspended in a fluid. We introduce a novel calculational framework that allows us to separate the different contributions to their collective dynamics from hydrodynamic interactions on different length scales. Hence we are able to systematically show that lubrication forces when the particles are very close to each other play as important a role as long-range hydrodynamic interactions in determining their many-body behaviour. We find that motility-induced phase separation is suppressed by near-field interactions, leading to open gel-like clusters rather than dense clusters. Interestingly, we find a globally polar ordered phase appears for neutral swimmers with no force dipole that is enhanced by near field lubrication forces in which the collision process rather than long-range interaction dominates the alignment mechanism.

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arXiv2017

Multiple phoretic mechanisms in the self-propulsion of a Pt-insulator Janus swimmer

We present a detailed theoretical study which demonstrates that electrokinetic effects can also play a role in the motion of metallic-insulator spherical Janus particles. Essential to our analysis is the identification of the fact that the reaction rates depend on Pt- coating thickness and that the thickness of coating varies from pole to equator of the coated hemisphere. We find that their motion is due to a combination of neutral and ionic diffusiophoretic as well as electrophoretic effects whose interplay can be changed by varying the ionic properties of the fluid. This has great potential significance for optimising performance of designed synthetic swimmers.

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arXiv2016

Structure in Sheared Supercooled Liquids: Dynamical Rearrangements of an Effective System of Icosahedra

We consider a binary Lennard-Jones glassformer whose super-Arrhenius dynamics are correlated with the formation of particles organized into icosahedra under simple steady state shear. We recast this glassformer as an effective system of icosahedra [Pinney et al. J. Chem. Phys. 143 244507 (2015)]. From the observed population of icosahedra in each steady state, we obtain an effective temperature which is linearly dependent on the shear rate in the range considered. Upon shear banding, the system separates into a region of high shear rate and a region of low shear rate. The effective temperatures obtained in each case show that the low shear regions correspond to a significantly lower temperature than the high shear regions. Taking a weighted average of the effective temperature of these regions (weight determined by region size) yields an estimate of the effective temperature which compares well with an effective temperature based on the global mesocluster population of the whole system.

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arXiv2016

How walls affect the dynamics of self-phoretic microswimmers

We study the effect of a nearby planar wall on the propulsion of a spherical phoretic micro-swimmer driven by reactions on its surface. An asymmetric coverage of catalysts on its surface which absorb reactants and generate products gives rise to an anisotropic interfacial flow that propels the swimmer. We analyse the near-wall dynamics of such a self-phoretic swimmer as a function of the asymmetric catalytic coverage of the surface. By an analysis of the fundamental singularities of the flow and concentration or electrostatic potential gradients generated we are able to obtain and rationalise a phase diagram of behaviours as a function of the characteristics of the swimmer surface. We find a variety of possible behaviours, from "bound states" where the swimmer remains near the wall to "scattering" or repulsive trajectories in which the swimmer ends far from the wall. The formation of some of the bound states is a purely wall-phoretic effect and cannot be obtained by simply mapping a phoretic swimmer to a hydrodynamic one.

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arXiv2016

Recasting a model atomistic glassformer as a system of icosahedra

We consider a binary Lennard-Jones glassformer whose super-Arrhenius dynamics are correlated with the formation of icosahedral structures. Upon cooling these icosahedra organize into mesoclusters. We recast this glassformer as an effective system of icosahedra which we describe with a population dynamics model. This model we parameterize with data from the temperature regime accessible to molecular dynamics simulations. We then use the model to determine the population of icosahedra in mesoclusters at arbitrary temperature. Using simulation data to incorporate dynamics into the model we predict relaxation behavior at temperatures inaccessible to conventional approaches. Our model predicts super-Arrhenius dynamics whose relaxation time remains finite for non-zero temperature.

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arXiv2015

The dynamics of a self-phoretic Janus swimmer near a wall

We study the effect of a nearby planar wall on the propulsion of a phoretic Janus micro-swimmer driven by asymmetric reactions on its surface which absorb reactants and generate products. We show that the behaviour of these swimmers near a wall can be classified ${\bf based \ on \ whether}$ the swimmers are ${\bf mainly}$ absorbing or producing reaction solutes ${\bf and \ whether}$ their swimming directions are such that the inert or active face is at the front. We find that the wall-induced solute gradients always promote swimmer propulsion along the wall while the effect of hydrodynamics leads to re-orientation of the swimming direction away from the wall.

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arXiv2014

Hydrodynamic suppression of phase separation in active suspensions

We simulate with hydrodynamics a suspension of active disks squirming through a Newtonian fluid. We explore numerically the full range of squirmer area fractions from dilute to close packed and show that "motility induced phase separation" (MIPS), which was recently proposed to arise generically in active matter, and which has been seen in simulations of active Brownian disks, is strongly suppressed by hydrodynamic interactions. We give an argument for why this should be the case and support it with counterpart simulations of active Brownian disks in a parameter regime that provides a closer counterpart to hydrodynamic suspensions than in previous studies.

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arXiv2014

Stress reorganisation and response in active solids

We present a microscopic model of a disordered viscoelastic active solid, i.e. an active material whose long time behaviour is elastic as opposed to viscous. It is composed of filaments, passive crosslinks and molecular motors powered by stored chemical energy, e.g. actomyosin powered by ATP. Our model allows us to study the collective behaviour of contractile active elements and how their interaction with each other and the passive elastic elements determines the macroscopic mechanical properties of the active material. As a result of the (un)binding dynamics of the active elements, we find that this system provides a highly responsive material with a dynamic mechanical response strongly dependent on the amount of deformation.

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arXiv2011

Generic phases of cross-linked active gels: Relaxation, Oscillation and Contractility

We study analytically and numerically a generic continuum model of an isotropic active solid with internal stresses generated by non-equilibrium `active' mechano-chemical reactions. Our analysis shows that the gel can be tuned through three classes of dynamical states by increasing motor activity: a constant unstrained state of homogeneous density, a state where the local density exhibits sustained oscillations, and a steady-state which is spontaneously contracted, with a uniform mean density.

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