arXiv subjects

Andrew J. Archer

Publications and source records attributed to Andrew J. Archer.

53 records · Page 3Linked to original sources

arXiv2013

An Introduction to Microscopic Theories for Inhomogeneous Liquids: Getting Started with Density Functional Theory

Classical density functional theory (DFT) is a statistical mechanical theory for calculating the density profiles of the molecules in a liquid. It is widely used, for example. to calculate the density distribution of the molecules in the vicinity of a confining wall, the interfacial tension, the wetting behaviour and many other properties of nonuniform liquids. DFT can however be somewhat daunting to students entering the field, because of the many connections to other areas of liquid-state science that are required and used to develop the theories. Here we give an introduction to some of the key ideas, based on a lattice-gas (Ising) model fluid. This builds on knowledge covered in most undergraduate statistical mechanics and thermodynamics courses and so students can quickly get to the stage of calculating density profiles, etc for themselves. We derive a simple DFT for the lattice-gas and present some typical results that can readily be calculated using the theory.

cond-mat.stat-mech↗

arXiv2013

Sedimentation of a two-dimensional colloidal mixture exhibiting liquid-liquid and gas-liquid phase separation: a dynamical density functional theory study

We present dynamical density functional theory results for the time evolution of the density distribution of a sedimenting model two-dimensional binary mixture of colloids. The interplay between the bulk phase behaviour of the mixture, its interfacial properties at the confining walls, and the gravitational field gives rise to a rich variety of equilibrium and non-equilibrium morphologies. In the fluid state, the system exhibits both liquid-liquid and gas-liquid phase separation. As the system sediments, the phase separation significantly affects the dynamics and we explore situations where the final state is a coexistence of up to three different phases. Solving the dynamical equations in two-dimensions, we find that in certain situations the final density profiles of the two species have a symmetry that is different from that of the external potentials, which is perhaps surprising, given the statistical mechanics origin of the theory. The paper concludes with a discussion on this.

cond-mat.soft↗

arXiv2013

Note on the hydrodynamic description of thin nematic films: strong anchoring model

We discuss the long-wave hydrodynamic model for a thin film of nematic liquid crystal in the limit of strong anchoring at the free surface and at the substrate. We rigorously clarify how the elastic energy enters the evolution equation for the film thickness in order to provide a solid basis for further investigation: several conflicting models exist in the literature that predict qualitatively different behaviour. We consolidate the various approaches and show that the long-wave model derived through an asymptotic expansion of the full nemato-hydrodynamic equations with consistent boundary conditions agrees with the model one obtains by employing a thermodynamically motivated gradient dynamics formulation based on an underlying free energy functional. As a result, we find that in the case of strong anchoring the elastic distortion energy is always stabilising. To support the discussion in the main part of the paper, an appendix gives the full derivation of the evolution equation for the film thickness via asymptotic expansion.

physics.flu-dyn↗

arXiv2013

Localized states in the conserved Swift-Hohenberg equation with cubic nonlinearity

The conserved Swift-Hohenberg equation with cubic nonlinearity provides the simplest microscopic description of the thermodynamic transition from a fluid state to a crystalline state. The resulting phase field crystal model describes a variety of spatially localized structures, in addition to different spatially extended periodic structures. The location of these structures in the temperature versus mean order parameter plane is determined using a combination of numerical continuation in one dimension and direct numerical simulation in two and three dimensions. Localized states are found in the region of thermodynamic coexistence between the homogeneous and structured phases, and may lie outside of the binodal for these states. The results are related to the phenomenon of slanted snaking but take the form of standard homoclinic snaking when the mean order parameter is plotted as a function of the chemical potential, and are expected to carry over to related models with a conserved order parameter.

nlin.PS↗

arXiv2012

Modelling the formation of structured deposits at receding contact lines of evaporating solutions and suspensions

When a film of a liquid suspension of nanoparticles or a polymer solution is deposited on a surface, it may dewet from the surface and as the solvent evaporates the solute particles/polymer can be deposited on the surface in regular line patterns. In this paper we explore a hydrodynamic model for the process that is based on a long-wave approximation that predicts the deposition of irregular and regular line patterns. This is due to a self-organised pinning-depinning cycle that resembles a stick-slip motion of the contact line. We present a detailed analysis of how the line pattern properties depend on quantities such as the evaporation rate, the solute concentration, the Péclet number, the chemical potential of the ambient vapour, the disjoining pressure, and the intrinsic viscosity. The results are related to several experiments and to depinning transitions in other soft matter systems.

cond-mat.soft↗

arXiv2012

Thermodynamically consistent description of the hydrodynamics of free surfaces covered by insoluble surfactants of high concentration

In this paper we propose several models that describe the dynamics of liquid films which are covered by a high concentration layer of insoluble surfactant. First, we briefly review the 'classical' hydrodynamic form of the coupled evolution equations for the film height and surfactant concentration that are well established for small concentrations. Then we re-formulate the basic model as a gradient dynamics based on an underlying free energy functional that accounts for wettability and capillarity. Based on this re-formulation in the framework of nonequilibrium thermodynamics, we propose extensions of the basic hydrodynamic model that account for (i) nonlinear equations of state, (ii) surfactant-dependent wettability, (iii) surfactant phase transitions, and (iv) substrate-mediated condensation. In passing, we discuss important differences to most of the models found in the literature.

physics.flu-dyn↗

arXiv2011

Modelling fluids and crystals using a two-component modified phase field crystal model

A modified phase field crystal model in which the free energy may be minimised by an order parameter profile having isolated bumps is investigated. The phase diagram is calculated in one and two dimensions and we locate the regions where modulated and uniform phases are formed and also regions where localised states are formed. We investigate the effectiveness of the phase field crystal model for describing fluids and crystals with defects. We further consider a two component model and elucidate how the structure transforms from hexagonal crystalline ordering to square ordering as the concentration changes. Our conclusion contains a discussion of possible interpretations of the order parameter field.

cond-mat.soft↗

arXiv2011

Ratcheting of driven attracting colloidal particles: Temporal density oscillations and current multiplicity

We consider the unidirectional particle transport in a suspension of colloidal particles which interact with each other via a pair potential having a hard-core repulsion plus an attractive tail. The colloids are confined within a long narrow channel and are driven along by a DC or an AC external potential. In addition, the walls of the channel interact with the particles via a ratchet-like periodic potential. We use dynamical density functional theory to compute the average particle current. In the case of DC drive, we show that as the attraction strength between the colloids is increased beyond a critical value, the stationary density distribution of the particles loses its stability leading to depinning and a time dependent density profile. Attraction induced symmetry breaking gives rise to the coexistence of stable stationary density profiles with different spatial periods and time-periodic density profiles, each characterized by different values for the particle current.

cond-mat.soft↗

arXiv2010

On the interplay between sedimentation and phase separation phenomena in two-dimensional colloidal fluids

Colloidal particles that are confined to an interface effectively form a two-dimensional fluid. We examine the dynamics of such colloids when they are subject to a constant external force, which drives them in a particular direction over the surface. Such a situation occurs, for example, for colloidal particles that have settled to the bottom of their container, when the container is tilted at an angle, so that they `sediment' to the lower edge of the surface. We focus in particular on the case when there are attractive forces between the colloids which causes them to phase separate into regions of high density and low density and we study the influence of this phase separation on the sedimentation process. We model the colloids as Brownian particles and use both Brownian dynamics computer simulations and dynamical density functional theory (DDFT) to obtain the time evolution of the ensemble average one-body density profiles of the colloids. We consider situations where the external potential varies only in one direction so that the ensemble average density profiles vary only in this direction. We solve the DDFT in one-dimension, by assuming that the density profile only varies in one direction. However, we also solve the DDFT in two-dimensions, allowing the fluid density profile to vary in both the $x$- and $y$-directions. We find that in certain situations the two-dimensional DDFT is clearly superior to its one-dimensional counterpart when compared with the simulations and we discuss this issue.

cond-mat.soft↗

arXiv2010

Collective shuttling of attracting particles in asymmetric narrow channels

The rectification of a single file of attracting particles subjected to a low frequency ac drive is proposed as a working mechanism for particle shuttling in an asymmetric narrow channel. Increasing the particle attraction results in the file condensing, as signalled by the dramatic enhancement of the net particle current. Magnitude and direction of the current become extremely sensitive to the actual size of the condensate, which can then be made to shuttle between two docking stations, transporting particles in one direction, with an efficiency much larger than conventional diffusive models predict.

cond-mat.stat-mech↗

arXiv2010

Dynamical model for the formation of patterned deposits at receding contact lines

We describe the formation of deposition patterns that are observed in many different experiments where a three-phase contact line of a volatile nanoparticle suspension or polymer solution recedes. A dynamical model based on a long-wave approximation predicts the deposition of irregular and regular line patterns due to self-organised pinning-depinning cycles corresponding to a stick-slip motion of the contact line. We analyze how the line pattern properties depend on the evaporation rate and solute concentration.

physics.flu-dyn↗

arXiv2009

Solvent mediated interactions between model colloids and interfaces: A microscopic approach

We determine the solvent mediated contribution to the effective potentials for model colloidal or nano- particles dispersed in a binary solvent that exhibits fluid-fluid phase separation. Using a simple density functional theory we calculate the density profiles of both solvent species in the presence of the `colloids', which are treated as external potentials, and determine the solvent mediated (SM) potentials. Specifically, we calculate SM potentials between (i) two colloids, (ii) a colloid and a planar fluid-fluid interface, and (iii) a colloid and a planar wall with an adsorbed wetting film. We consider three different types of colloidal particles: colloid A which prefers the bulk solvent phase rich in species 2, colloid C which prefers the solvent phase rich in species 1, and `neutral' colloid B which has no strong preference for either phase, i.e. the free energies to insert the colloid into either of the coexisting bulk phases are almost equal. When a colloid which has a preference for one of the two solvent phases is inserted into the disfavored phase at statepoints close to coexistence a thick adsorbed `wetting' film of the preferred phase may form around the colloids. The presence of the adsorbed film has a profound influence on the form of the SM potentials.

cond-mat.soft↗

arXiv2009

Selectivity in binary fluid mixtures: static and dynamical properties

Selectivity of particles in a region of space can be achieved by applying external potentials to influence the particles in that region. We investigate static and dynamical properties of size selectivity in binary fluid mixtures of two particles sizes. We find that by applying an external potential that is attractive to both kinds of particles, due to crowding effects, this can lead to one species of particles being expelled from that region, whilst the other species is attracted into the region where the potential is applied. This selectivity of one species of particle over the other in a localized region of space depends on the density and composition of the fluid mixture. Applying an external potential that repels both kinds of particles leads to selectivity of the opposite species of particles to the selectivity with attractive potentials. We use equilibrium and dynamical density functional theory to describe and understand the static and dynamical properties of this striking phenomenon. Selectivity by some ion-channels is believed to be due to this effect.

cond-mat.soft↗

arXiv2008

Interfacial and wetting properties of a binary point Yukawa fluid

We investigate the interfacial phase behavior of a binary fluid mixture composed of repulsive point Yukawa particles. Using a simple approximation for the Helmholtz free energy functional, which yields the random phase approximation (RPA) for the pair direct correlation functions, we calculate the equilibrium fluid density profiles of the two species of particles adsorbed at a planar wall. We show that for a particular choice (repulsive exponential) of the wall potentials and the fluid pair-potential parameters, the Euler-Lagrange equations for the equilibrium fluid density profiles may be transformed into a single ordinary differential equation and the profiles obtained by a simple quadrature. For certain other choices of the fluid pair-potential parameters fluid-fluid phase separation of the bulk fluid is observed. We find that when such a mixture is exposed to a planar hard-wall, the fluid exhibits complete wetting on the species 2 poor side of the binodal, i.e. we observe a thick film of fluid rich in species 2 adsorbed at the hard-wall. The thickness of the wetting film grows logarithmically with the concentration difference between the fluid state-point and the binodal and is proportional to the bulk correlation length of the intruding (wetting) fluid phase. However, for state points on the binodal that are further from the critical point, we find there is no thick wetting film. We determine the accompanying line of first-order (pre-wetting) surface phase transitions which separate a thin and thick adsorbed film. We show that for some other choices of repulsive wall potentials the pre-wetting line is still present, but its location and extent in the phase diagram is strongly dependent on the wall-fluid interaction parameters.

cond-mat.soft↗

arXiv2007

Phase behavior of a fluid with competing attractive and repulsive interactions

Fluids in which the interparticle potential has a hard core, is attractive at moderate separations, and repulsive at greater separations are known to exhibit novel phase behavior, including stable inhomogeneous phases. Here we report a joint simulation and theoretical study of such a fluid, focusing on the relationship between the liquid-vapor transition line and any new phases. The phase diagram is studied as a function of the amplitude of the attraction for a certain fixed amplitude of the long ranged repulsion. We find that the effect of the repulsion is to substitute the liquid-vapor critical point and a portion of the associated liquid-vapor transition line, by two first order transitions. One of these transitions separates the vapor from a fluid of spherical liquidlike clusters; the other separates the liquid from a fluid of spherical voids. At low temperature, the two transition lines intersect one another and a vapor-liquid transition line at a triple point. While most integral equation theories are unable to describe the new phase transitions, the Percus Yevick approximation does succeed in capturing the vapor-cluster transition, as well as aspects of the structure of the cluster fluid, in reasonable agreement with the simulation results.

cond-mat.soft↗

arXiv2006

Dynamics in inhomogeneous liquids and glasses via the test particle limit

We show that one may view the self and the distinct part of the van Hove dynamic correlation function of a simple fluid as the one-body density distributions of a binary mixture that evolve in time according to dynamical density functional theory. For a test case of soft core Brownian particles the theory yields results for the van Hove function that agree quantitatively with those of our Brownian dynamics computer simulations. At sufficiently high densities the free energy landscape underlying the dynamics exhibits a barrier as a function of the mean particle displacement, shedding new light on the nature of glass formation. For hard spheres confined between parallel planar walls the barrier height oscillates in-phase with the local density, implying that the mobility is maximal between layers, which should be experimentally observable in confined colloidal dispersions.

cond-mat.soft↗

arXiv2004

Dynamical density functional theory for interacting Brownian particles: stochastic or deterministic?

We aim to clarify confusions in the literature as to whether or not dynamical density functional theories for the one-body density of a classical Brownian fluid should contain a stochastic noise term. We point out that a stochastic as well as a deterministic equation of motion for the density distribution can be justified, depending on how the fluid one-body density is defined -- i.e. whether it is an ensemble averaged density distribution or a spatially and/or temporally coarse grained density distribution.

cond-mat.stat-mech↗