arXiv subjects

T. B. Liverpool

Publications and source records attributed to T. B. Liverpool.

At least 19 recordsLinked to original sources

arXiv2023

Necking and failure of a colloidal gel arm: signatures of yielding on different length scales

Colloidal gels consist of percolating networks of interconnected arms. Their mechanical properties depend on the individual arms, and on their collective behaviour. We use numerical simulations to pull on a single arm, built from a model colloidal gel-former with short-ranged attractive interactions. Under elongation, the arm breaks by a necking instability. We analyse this behaviour at three different length scales: a rheological continuum model of the whole arm; a microscopic analysis of the particle structure and dynamics; and the local stress tensor. Combining these different measurements gives a coherent picture of the necking and failure: the neck is characterised by plastic flow that occurs for stresses close to the arm's yield stress. The arm has an amorphous local structure and has large residual stresses from its initialisation. We find that neck formation is associated with increased plastic flow, a reduction in the stability of the local structure, and a reduction in the residual stresses; this indicates that {the} system loses its solid character and starts to behave more like a viscous fluid. We discuss the implications of these results for the modelling of gel dynamics.

cond-mat.soft↗

arXiv2013

Electrokinetic Effects in Catalytic Pt-Insulator Janus Swimmers

The effect of added salt on the propulsion of Janus platinum-polystyrene colloids in hydrogen peroxide solution is studied experimentally. It is found that micromolar quantities of potassium and silver nitrate salts reduce the swimming velocity by similar amounts, while leading to significantly different effects on the overall rate of catalytic breakdown of hydrogen peroxide. It is argued that the seemingly paradoxical experimental observations could be theoretically explained by using a generalised reaction scheme that involves charged intermediates and has the topology of two nested loops.

cond-mat.soft↗

arXiv2013

Synchronisation and liquid crystalline order in soft active fluids

We introduce a phenomenological theory for a new class of soft active fluids, with the ability to synchronise. Our theoretical framework describes the macroscopic behaviour of a collection of interacting anisotropic elements with cyclic internal dynamics and a periodic phase variable. This system (i) can spontaneously undergo a transition to a state with macroscopic orientational order, with the elements aligned: a liquid crystal, (ii) attain another broken symmetry state characterised by synchronisation of their phase variables or (iii) a combination of both types of order. We derive the equations describing a spatially homogeneous system and also study the hydrodynamic fluctuations of the soft modes in some of the ordered states. We find that synchronisation can promote the transition to a state with orientational order; and vice-versa. Finally, we provide an explicit microscopic realisation: a suspension of micro-swimmers driven by cyclic strokes.

cond-mat.soft↗

arXiv2012

Soft Active Matter

In this review we summarize theoretical progress in the field of active matter, placing it in the context of recent experiments. Our approach offers a unified framework for the mechanical and statistical properties of living matter: biofilaments and molecular motors in vitro or in vivo, collections of motile microorganisms, animal flocks, and chemical or mechanical imitations. A major goal of the review is to integrate the several approaches proposed in the literature, from semi-microscopic to phenomenological. In particular, we first consider "dry" systems, defined as those where momentum is not conserved due to friction with a substrate or an embedding porous medium, and clarify the differences and similarities between two types of orientationally ordered states, the nematic and the polar. We then consider the active hydrodynamics of a suspension, and relate as well as contrast it with the dry case. We further highlight various large-scale instabilities of these nonequilibrium states of matter. We discuss and connect various semi-microscopic derivations of the continuum theory, highlighting the unifying and generic nature of the continuum model. Throughout the review, we discuss the experimental relevance of these theories for describing bacterial swarms and suspensions, the cytoskeleton of living cells, and vibrated granular materials. We suggest promising extensions towards greater realism in specific contexts from cell biology to ethology, and remark on some exotic active-matter analogues. Lastly, we summarize the outlook for a quantitative understanding of active matter, through the interplay of detailed theory with controlled experiments on simplified systems, with living or artificial constituents.

cond-mat.soft↗

arXiv2012

Hydrodynamic synchronisation of non-linear oscillators at low Reynolds number

We introduce a generic model of weakly non-linear self-sustained oscillator as a simplified tool to study synchronisation in a fluid at low Reynolds number. By averaging over the fast degrees of freedom, we examine the effect of hydrodynamic interactions on the slow dynamics of two oscillators and show that they can lead to synchronisation. Furthermore, we find that synchronisation is strongly enhanced when the oscillators are non-isochronous, which on the limit cycle means the oscillations have an amplitude-dependent frequency. Non-isochronity is determined by a nonlinear coupling $α$ being non-zero. We find that its ($α$) sign determines if they synchronise in- or anti-phase. We then study an infinite array of oscillators in the long wavelength limit, in presence of noise. For $α> 0$, hydrodynamic interactions can lead to a homogeneous synchronised state. Numerical simulations for a finite number of oscillators confirm this and, when $α<0$, show the propagation of waves, reminiscent of metachronal coordination.

cond-mat.soft↗

arXiv2010

Swimmers in thin films: from swarming to hydrodynamic instabilities

We investigate theoretically the collective dynamics of a suspension of low Reynolds number swimmers that are confined to two dimensions by a thin fluid film. Our model swimmer is characterized by internal degrees of freedom which locally exert active stresses (force dipoles or quadrupoles) on the fluid. We find that hydrodynamic interactions mediated by the film can give rise to spontaneous continuous symmetry breaking (swarming), to states with either polar or nematic homogeneous order. For dipolar swimmers, the stroke averaged dynamics are enough to determine the leading contributions to the collective behaviour. In contrast, for quadrupolar swimmers, our analysis shows that detailed features of the internal dynamics play an important role in determining the bulk behaviour. In the broken symmetry phases, we investigate fluctuations of hydrodynamic variables of the system and find that these destabilize order. Interestingly, this instability is not generic and depends on length-scale.

physics.bio-ph↗

arXiv2010

Dynamics and interactions of active rotors

We consider a simple model of an internally driven self-rotating object; a rotor, confined to two dimensions by a thin film of low Reynolds number fluid. We undertake a detailed study of the hydrodynamic interactions between a pair of rotors and find that their effect on the resulting dynamics is a combination of fast and slow motions. We analyse the slow dynamics using an averaging procedure to take account of the fast degrees of freedom. Analytical results are compared with numerical simulations. Hydrodynamic interactions mean that while isolated rotors do not translate, bringing together a pair of rotors leads to motion of their centres. Two rotors spinning in the same sense rotate with an approximately constant angular velocity around each other, while two rotors of opposite sense, both translate with the same constant velocity, which depends on the separation of the pair. As a result a pair of counter-rotating rotors are a promising model for controlled self-propulsion.

cond-mat.soft↗

arXiv2008

Mechanical response of active gels

We study a model of an active gel of cross-linked semiflexible filaments with additional active linkers such as myosin II clusters. We show that the coupling of the elasticity of the semiflexible filaments to the mechanical properties of the motors leads to contractile behavior of the gel, in qualitative agreement with experimental observations. The motors, however, soften the zero frequency elastic constant of the gel. When the collective motor dynamics is incorporated in the model, a stiffening of the network at high frequencies is obtained. The frequency controlling the crossover between low and high frequency network elasticity is estimated in terms of microscopic properties of motors and filaments, and can be as low as 10^(-3)Hz.

cond-mat.soft↗

arXiv2008

Short-time inertial response of viscoelastic fluids measured with Brownian motion and with active probes

We have directly observed short-time stress propagation in viscoelastic fluids using two optically trapped particles and a fast interferometric particle-tracking technique. We have done this both by recording correlations in the thermal motion of the particles and by measuring the response of one particle to the actively oscillated second particle. Both methods detect the vortex-like flow patterns associated with stress propagation in fluids. This inertial vortex flow propagates diffusively for simple liquids, while for viscoelastic solutions the pattern spreads super-diffusively, dependent on the shear modulus of the medium.

cond-mat.soft↗

arXiv2007

Designing phoretic micro- and nano-swimmers

Small objects can swim by generating around them fields or gradients which in turn induce fluid motion past their surface by phoretic surface effects. We quantify for arbitrary swimmer shapes and surface patterns, how efficient swimming requires both surface ``activity'' to generate the fields, and surface ``phoretic mobility.'' We show in particular that (i) swimming requires symmetry breaking in either or both of the patterns of "activity" and ``mobility,'' and (ii) for a given geometrical shape and surface pattern, the swimming velocity is size-independent. In addition, for given available surface properties, our calculation framework provides a guide for optimizing the design of swimmers.

cond-mat.soft↗

arXiv2006

Hydrodynamics of isotropic and liquid crystalline active polymer solutions

We describe the large-scale collective behavior of solutions of polar biofilaments and both stationary and mobile crosslinkers. Both mobile and stationary crosslinkers induce filament alignment promoting either polar or nematic order. In addition, mobile crosslinkers, such as clusters of motor proteins, exchange forces and torques among the filaments and render the homogeneous states unstable via filament bundling. We start from a Smoluchowski equation for rigid filaments in solutions, where pairwise crosslink-mediated interactions among the filaments yield translational and rotational currents. The large-scale properties of the system are described in terms of continuum equations for filament and motor densities, polarization and alignment tensor obtained by coarse-graining the Smoluchovski equation. The possible homogeneous and inhomogeneous states of the systems are obtained as stable solutions of the dynamical equations and are characterized in terms of experimentally accessible parameters. We make contact with work by other authors and show that our model allows for an estimate of the various parameters in the hydrodynamic equations in terms of physical properties of the crosslinkers.

cond-mat.soft↗

arXiv2006

Rheology of Active Filament Solutions

We study the viscoelasticity of an active solution of polar biofilaments and motor proteins. Using a molecular model, we derive the constitutive equations for the stress tensor in the isotropic phase and in phases with liquid crystalline order. The stress relaxation in the various phases is discussed. Contractile activity is responsible for a spectacular difference in the viscoelastic properties on opposite sides of the order-disorder transition.

cond-mat.soft↗

arXiv2005

Nematic and Polar order in Active Filament Solutions

Using a microscopic model of interacting polar biofilaments and motor proteins, we characterize the phase diagram of both homogeneous and inhomogeneous states in terms of experimental parameters. The polarity of motor clusters is key in determining the organization of the filaments in homogeneous isotropic, polarized and nematic states, while motor-induced bundling yields spatially inhomogeneous structures.

cond-mat.soft↗

arXiv2004

Bridging the microscopic and the hydrodynamic in active filament solutions

Hydrodynamic equations for an isotropic solution of active polar filaments are derived from a microscopic mean-field model of the forces exchanged between motors and filaments. We find that a spatial dependence of the motor stepping rate along the filament is essential to drive bundle formation. A number of differences arise as compared to hydrodynamics derived (earlier) from a mesoscopic model where relative filament velocities were obtained on the basis of symmetry considerations. Due to the anisotropy of filament diffusion, motors are capable of generating net filament motion relative to the solvent. The effect of this new term on the stability of the homogeneous state is investigated.

cond-mat.soft↗

arXiv2003

Dynamics of rigid and flexible extended bodies in viscous films and membranes

We study the dynamics of extended rod-like bodies in (or associated with) membranes and films. We demonstrate a striking difference between the mobilities in films and bulk fluids, even when the dissipation is dominated by the fluid stress: for large inclusions we find that rotation and motion perpendicular to the rod axis exhibits purely local drag, in which the drag coefficient is algebraic in the rod dimensions. We also study the dynamics of the {\em internal} modes of a semiflexible inclusion and find two dynamical regimes in the relaxation spectrum.

cond-mat.soft↗

arXiv2003

On the mobility of extended bodies in viscous films and membranes

We develop general methods to calculate the mobilities of extended bodies in (or associated with) membranes and films. We demonstrate a striking difference between in-plane motion of rod-like inclusions and the corresponding case of bulk (three-dimensional) fluids: for rotations and motion perpendicular to the rod axis, we find purely local drag, in which the drag coefficient is purely algebraic in the rod dimensions. These results, as well as the calculational methods are applicable to such problems as the diffusion of objects in or associated with Langmuir films and lipid membranes. The methods can also be simply extended to treat viscoelastic systems.

cond-mat.soft↗

arXiv1998

Statistical mechanics of double-stranded semi-flexible polymers

We study the statistical mechanics of double-stranded semi-flexible polymers using both analytical techniques and simulation. We find a transition at some finite temperature, from a type of short range order to a fundamentally different sort of short range order. In the high temperature regime, the 2-point correlation functions of the object are identical to worm-like chains, while in the low temperature regime they are different due to a twist structure. In the low temperature phase, the polymers develop a kink-rod structure which could clarify some recent puzzling experiments on actin.

cond-mat.stat-mech↗

arXiv1997

The scaling behaviour of screened polyelectrolytes

We present a field-theoretic renormalization group (RG) analysis of a single flexible, screened polyelectrolyte chain (a Debye-Hückel chain) in a polar solvent. We point out that the Debye-Hückel chain may be mapped onto a local field theory which has the same fixed point as a generalised $n \to 1$ Potts model. Systematic analysis of the field theory shows that the system is one with two interplaying length-scales requiring the calculation of scaling functions as well as exponents to fully describe its physical behaviour. To illustrate this, we solve the RG equation and explicitly calculate the exponents and the mean end-to-end length of the chain.

cond-mat.stat-mech↗