arXiv subjects

J. M. Brader

Publications and source records attributed to J. M. Brader.

At least 19 recordsLinked to original sources

arXiv2026

Hard disks confined within a narrow channel

We employ inhomogeneous integral equation theory to investigate the equilibrium properties of hard disks confined to a channel of width $L$ by hard parallel walls. If the channel width is narrowed below two disk diameters, then the system enters a quasi one-dimensional regime for which the particles cannot move past each other. In the limit when $L$ is equal to one particle diameter the system reduces to the one-dimensional bulk along the center of the channel. We study first the dimensional crossover properties of the inhomogeneous Percus-Yevick (PY) integral equation as $L$ is reduced and then investigate the behaviour of a quasi one-dimensional system as the packing of the particles is increased for a fixed value of $L$. We find that the inhomogeneous PY equation is highly accurate for situations of quasi one-dimensional confinement and that it predicts the onset of a structural transition to a zigzag state at higher packing. The excellent performance of this integral equation method and the ease with which it handles confinement-induced dimensional crossover is a consequence of the improved resolution which comes from treating explicitly the inhomogeneous two-body correlation functions.

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arXiv2026

Routes to the density profile and structural inconsistency

Classical density functional theory (DFT) is the primary method for investigations of inhomogeneous fluids in external fields. It requires the excess Helmholtz free energy functional as input to an Euler-Lagrange equation for the one-body density. A variant of this methodology, the force-DFT, uses instead the Yvon-Born-Green equation to generate density profiles. It is known that the latter are consistent with the virial route to the thermodynamics, while DFT is consistent with the compressibility route. In this work we will show an alternative DFT scheme using the Lovett-Mou-Buff-Wertheim (LMBW) equation to obtain density profiles, that are shown to be also consistent with the compressibility route. However, force-DFT and LMBW DFT can both be implemented using a closure relation on the level of the two-body correlation functions. This is proven to be an advantageous feature, opening the possibility of an optimisation scheme in which the structural inconsistency between different routes to the density profile is minimized. (Structural inconsistency is a generalization of the notion of thermodynamic inconsistency, familiar from bulk integral equation studies.) Numerical results are given for the density profiles of two-dimensional systems of hard-core Yukawa particles with a repulsive or an attractive tail, in planar geometry.

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arXiv2025

Combining integral equation closures with force density functional theory for the study of inhomogeneous fluids

Classical density functional theory (DFT) is a powerful framework to study inhomogeneous fluids. Its standard form is based on the knowledge of a generating free energy functional. If this is known exactly, then the results obtained by using standard DFT or its alternative, recently developed version, force-DFT, are the same. If the free energy functional is known only approximately then these two routes produce different outcomes. However, as we show in this work, force-DFT has the advantage that it is also implementable without knowledge of the free energy functional, by using instead liquid-state integral equation closures. This broadens the range of systems that can be explored, since free energy functionals are generally difficult to approximate. In this paper we investigate the utility of using inhomogeneous integral equation closures within force-DFT thus demonstrating the versatility and accuracy of this approach.

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arXiv2024

Superadiabatic dynamical density functional theory for colloidal suspensions under homogeneous steady-shear

The superadiabatic dynamical density functional theory (superadiabatic-DDFT) is a promising new method for the study of colloidal systems out-of-equilibrium. Within this approach the viscous forces arising from interparticle interactions are accounted for in a natural way by treating explicitly the dynamics of the two-body correlations. For bulk systems subject to spatially homogeneous shear we use the superadiabatic-DDFT framework to calculate the steady-state pair distribution function and the corresponding viscosity for low values of the shear-rate. We then consider a variant of the central approximation underlying this superadiabatic theory and obtain an inhomogeneous generalization of a rheological bulk theory due to Russel and Gast. This paper thus establishes for the first time a connection between DDFT approaches, formulated to treat inhomogeneous systems, and existing work addressing nonequilibrium microstructure and rheology in bulk colloidal suspensions.

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arXiv2023

Superadiabatic dynamical density functional study of Brownian hard-spheres in time-dependent external potentials

Superadiabatic dynamical density functional theory (superadiabatic-DDFT), a first-principles approach based on the inhomogeneous two-body correlation functions, is employed to investigate the response of interacting Brownian particles to time-dependent external driving. Predictions for the superadiabatic dynamics of the one-body density are made directly from the underlying interparticle interactions, without need for either adjustable fit parameters or simulation input. The external potentials we investigate have been chosen to probe distinct aspects of structural relaxation in dense, strongly interacting liquid states. Nonequilibrium density profiles predicted by the superadiabatic theory are compared with those obtained from both adiabatic DDFT and event-driven Brownian dynamics simulation. Our findings show that superadiabatic-DDFT accurately predicts the time-evolution of the one-body density.

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arXiv2022

First-principles superadiabatic theory for the dynamics of inhomogeneous fluids

For classical many-body systems subject to Brownian dynamics we develop a superadiabatic dynamical density functional theory (DDFT) for the description of inhomogeneous fluids out-of-equilibrium. By explicitly incorporating the dynamics of the inhomogeneous two-body correlation functions we obtain superadiabatic forces directly from the microscopic interparticle interactions. We demonstrate the importance of these nonequilibrium forces for an accurate description of the one-body density by numerical implementation of our theory for three-dimensional hard-spheres in a time-dependent planar potential. The relaxation of the one-body density in superadiabatic-DDFT is found to be slower than that predicted by standard adiabatic DDFT and significantly improves the agreement with Brownian dynamics simulation data. We attribute this improved performance to the correct treatment of structural relaxation within the superadiabatic-DDFT. Our approach provides fundamental insight into the underlying structure of dynamical density functional theories and makes possible the study of situations for which standard approaches fail.

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arXiv2022

Force density functional theory in- and out-of-equilibrium

When a fluid is subject to an external field, as is the case near an interface or under spatial confinement, then the density becomes spatially inhomogeneous. Although the one-body density provides much useful information, a higher level of resolution is provided by the two-body correlations. These give a statistical description of the internal microstructure of the fluid and enable calculation of the average interparticle force, which plays an essential role in determining both the equilibrium and dynamic properties of interacting fluids. We present a theoretical framework for the description of inhomogeneous (classical) many-body systems, based explicitly on the two-body correlation functions. By consideration of local Noether-invariance against spatial distortion of the system we demonstrate the fundamental status of the Yvon-Born-Green (YBG) equation as a local force-balance within the fluid. Using the inhomogeneous Ornstein-Zernike equation we show that the two-body correlations are density functionals and, thus, that the average interparticle force entering the YBG equation is also a functional of the one-body density. The force-based theory we develop provides an alternative to standard density functional theory for the study of inhomogeneous systems both in- and out-of-equilibrium. We compare force-based density profiles to the results of the standard potential-based (dynamical) density functional theory. In equilibrium, we confirm both analytically and numerically that the standard approach yields profiles that are consistent with the compressibility pressure, whereas the force-density functional gives profiles consistent with the virial pressure. The structure of the theory offers deep insights into the nature of correlation in dense and inhomogeneous systems.

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arXiv2021

Fundamental measure theory of inhomogeneous two-body correlation functions

For the three-dimensional hard-sphere model we investigate the inhomogeneous two-body correlations predicted by Rosenfeld's fundamental measure theory. For the special cases in which the density has either planar or spherical symmetry we provide analytic formulae for the Hankel and Legendre transforms, respectively, of the inhomogeneous two-body direct correlation function as explicit functionals of the density. When combined with the Ornstein-Zernike relation our analytical results allow for rapid calculation of inhomogeneous hard-sphere density correlations in real-space. These provide not only information about the packing structures of the hard-sphere system, but also form an essential building-block for constructing perturbation theories of more realistic models.

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arXiv2020

Mean-Field Theory of Inhomogeneous Fluids

The Barker-Henderson perturbation theory is a bedrock of liquid-state physics, providing quantitative predictions for the bulk thermodynamic properties of realistic model systems. However, this successful method has not been exploited for the study of inhomogeneous systems. We develop and implement a first-principles 'Barker-Henderson density functional', thus providing a robust and quantitatively accurate theory for classical fluids in external fields. Numerical results are presented for the hard-core Yukawa model in three dimensions. Our predictions for the density around a fixed test particle and between planar walls are in very good agreement with simulation data. The density profiles for the free liquid vapour interface show the expected oscillatory decay into the bulk liquid as the temperature is reduced towards the triple point, but with an amplitude much smaller than that predicted by the standard mean-field density functional.

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arXiv2019

Escape rate of transiently active Brownian particle in one dimension

Activity significantly enhances the escape rate of a Brownian particle over a potential barrier. Whereas constant activity has been extensively studied in the past, little is known about the effect of time-dependent activity on the escape rate of the particle. In this paper we study the escape problem for a Brownian particle that is transiently active; the activity decreases rapidly during the escape process. Using the effective equilibrium approach we analytically calculate the escape rate, under the assumption that the particle is either completely passive or fully active when crossing the barrier. We perform numerical simulations of the escape process in one dimension and find good agreement with the theoretical predictions.

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arXiv2017

Shear-induced migration in colloidal suspensions

Using Brownian dynamics simulations we perform a systematic investigation of the shear-induced migration of colloidal particles subject to Poiseuille flow in both cylindrical and planar geometry. We find that adding an attractive component to the interparticle interaction enhances the migration effect, consistent with recent simulation studies of platelet suspensions. Monodisperse, bidisperse and polydisperse systems are studied over a range of shear rates, considering both steady states and the transient dynamics arising from the onset of flow. For bidisperse and polydisperse systems size segregation is observed.

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arXiv2017

Local phase transitions in driven colloidal suspensions

Using dynamical density functional theory and Brownian dynamics simulations we investigate the influence of a driven tracer particle on the density distribution of a colloidal suspension at a thermodynamic statepoint close to the liquid side of the binodal. In bulk systems we find that a localized region of the colloid-poor phase, a 'cavitation bubble', forms behind the moving tracer. The extent of the cavitation bubble is investigated as a function of both the size and velocity of the tracer. The addition of a confining boundary enables us to investigate the interaction between the local phase instability at the substrate and that at the particle surface. When both the substrate and tracer interact repulsively with the colloids we observe the formation of a colloid-poor bridge between the substrate and the tracer. When a shear flow is applied parallel to the substrate the bridge becomes distorted and, at sufficiently high shear-rates, disconnects from the substrate to form a cavitation bubble.

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arXiv2016

Escape rate of active particles in the effective equilibrium approach

The escape rate of a Brownian particle over a potential barrier is accurately described by the Kramers theory. A quantitative theory explicitly taking the activity of Brownian particles into account has been lacking due to the inherently out-of-equilibrium nature of these particles. Using an effective equilibrium approach [Farage et al., Phys. Rev. E 91, 042310 (2015)] we study the escape rate of active particles over a potential barrier and compare our analytical results with data from direct numerical simulation of the colored noise Langevin equation. The effective equilibrium approach generates an effective potential which, when used as input to Kramers rate theory, provides results in excellent agreement with the simulation data.

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arXiv2016

Green-Kubo approach to the average swim speed in active Brownian systems

We develop an exact Green-Kubo formula relating nonequilibrium averages in systems of interacting active Brownian particles to equilibrium time-correlation functions. The method is applied to calculate the density-dependent average swim speed, which is a key quantity entering coarse grained theories of active matter. The average swim speed is determined by integrating the equilibrium autocorrelation function of the interaction force acting on a tagged particle. Analytical results are validated using Brownian dynamics simulations.

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arXiv2015

Effective Interactions in Active Brownian Suspensions

Active colloids exhibit persistent motion, which can lead to motility-induced phase separation (MIPS). However, there currently exists no microscopic theory to account for this phenomenon. We report a first-principles theory, free of fit parameters, for active spherical colloids, which shows explicitly how an effective many-body interaction potential is generated by activity and how this can rationalize MIPS. For a passively repulsive system the theory predicts phase separation and pair correlations in quantitative agreement with simulation. For an attractive system the theory shows that phase separation becomes suppressed by moderate activity, consistent with recent experiments and simulations, and suggests a mechanism for reentrant cluster formation at high activity.

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arXiv2014

Dynamics and rheology of active glasses

Within the framework of mode-coupling theory, we present a simple model for describing dense assemblies of active (self-propelled) spherical colloidal particles. For isotropic suspensions, we demonstrate that the glass transition is shifted to higher volume fraction by the addition of activity, in agreement with recent Brownian dynamics simulations. Activity-induced changes in the static structure factor of the fluid are predicted. The mechanical response of an active glass to applied strain is shown to be softer than the corresponding passive glass; both the nonergodicity parameter and the yield stress reduce with increasing activity.

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arXiv2014

Microrheology close to an equilibrium phase transition

We investigate the microstructural and microrheological response to a tracer particle of a two- dimensional colloidal suspension under thermodynamic conditions close to a liquid-gas phase bound- ary. On the liquid side of the binodal, increasing the velocity of the (repulsive) tracer leads to the development of a pronounced cavitation bubble, within which the concentration of colloidal parti- cles is strongly depleted. The tendency of the liquid to cavitate is characterized by a dimensionless colloidal cavitation number. On the gas side of the binodal, a pulled (attractive) tracer leaves behind it an extended trail of colloidal liquid, arising from downstream advection of a wetting layer on its surface. For both situations the velocity dependent friction is calculated.

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arXiv2013

Normal-stress coefficients and rod climbing in colloidal dispersions

We calculate tractable microscopic expressions for the low-shear normal-stress coefficients of colloidal dispersions. Although restricted to the low rate regime, the presented formulas are valid for all volume fractions below the glass transition and for any interaction potential. Numerical results are presented for a system of colloids interacting via a hard-core attractive Yukawa potential, for which we explore the interplay between attraction strength and volume fraction. We show that the normal-stress coefficients exhibit nontrivial features close to the critical point and at high volume fractions in the vicinity of the reentrant glass transition. Finally, we exploit our formulas to make predictions about rod-climbing effects in attractive colloidal dispersions.

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