David M. Heyes

Rheology of molecular liquids and concentrated suspensions by microscopic dynamical simulations

Abstract The rheology and the associated changes that arise in sheared molecular and colloidal liquids are investigated by Molecular and Brownian Dynamics Computer Simulation. Significant shear thinning and normal pressure effects occur in all liquids when the shear rate approximately equals an inverse characteristic relaxation time for the material. The shear and bulk moduli, and self-diffusion coefficients increase with shear rate for all liquids and stable dispersions. The importance for rheology of hydrodynamic coupling between macromolecule trajectories at high packing fractions is demonstrated. The infinite frequency moduli depend on the packing fraction to a power which is effectively the same for all materials, i.e. ca. 3.5, above a percolation transition at a packing fraction 0.25. The suspending fluid enhances the degree of shear thinning above that of the corresponding single component fluid consisting of pure macroparticles.

Correlation functions in Couette flow from group theory and molecular dynamics

We describe group theory statistical mechanics, GTSM, which enables us to predict new non-vanishing time correlation functions in fluids at steady state subjected to planar couette flow. These are by symmetry trivially zero at equilibrium. An ensemble average is treated using the rules of group theory in the laboratory XYZ frame and in the molecule-fixed xyz frame of the point group character tables. In this paper we determine the effect of couette flow on a range of ensemble averages by establishing the symmetry of the strain rate tensor in terms of the irreducible representations of the Rh (3) rotation reflection group in the XYZ frame. This symmetry, D (0) g + D (1) g + D (2) g , is the same as the pressure tensor, P and consists of an antisymmetric vorticity term, D (1) g and a symmetric strain rate component of symmetry D (0) g + D (2) g . This allows non-zero ensemble averages of the same symmetry in the XYZ frame. Depending on the number of off-diagonal elements in the strain rate tensor, up to six...

Combined shear and elongational flow by non-equilibrium molecular dynamics

We continue our development of group theory statistical mechanics applied to non-newtonian shear and elongational flow. We discuss some new aspects of shear flow discovered by non-equilibrium molecular dynamics, NEMD. We investigate the origins of time reversal asymmetry in newly discovered cross-correlation functions. Using the profile unbiased thermostat, PUT, shear flow algorithm we discover that the strong phase is stable in 3D, for typical system sizes considered by molecular dynamics. In addition, for the first time we apply NEMD, to simultaneous shear and elongational non-newtonian flow. New equations of motion are constructed to enforce the elongational flow. We apply transient flows to a model Lennard-Jones liquid and monitor the thermodynamics and mechanical response, directly, and from transient time correlation functions. The value of the shear viscosity can be increased or lowered by the presence of simultaneous shear and elongational flow, in which the main velocity flow directions are perpe...

Shear thinning of dense suspensions modelled by Brownian dynamics

Abstract Brownian dynamics computer simulations of model dense suspensions subjected to laminar flow reveal shear thinning behaviour as observed experimentally. It is associated with a shear-induced phase change of the dispersed particles into a lattice with long range translational order in the plane perpendicular to the streaming direction, also in agreement with experiment.

The nature of extreme shear thinning in simple liquids

The structural and dynamical changes that take place in simple liquids during extreme shear thinning are illuminated by Non-Equilibrium Molecular Dynamics. Long range order develops, which is characterized by linear lines of molecules spontaneously forming along the shear flow lines. These ‘strings’ of molecules pack into a triangular lattice, when viewed in a plane orthogonal to their length, and are very slow to drift en masse and appear stationary when viewed in cross-section over many Maxwell relaxation times. Computations were performed on cubic MD cells containing Lennard-Jones molecules at reduced densities close to the triple point for this pair potential. The transition from amorphous liquid to the ‘string phase’ takes place sharply at reduced shear rates of ˙γ = 2·3 ∓ 0·1. Increasing the shear rate leads to a decrease in recoverable shear strain, making a limiting shear stress a useful modelling parameter. Symmetry breaking structural distortions appear also at these shear rates. Calculations of...

Some physical consequences of large shear rates on simple liquids

The structural and dynamical changes that take place in simple liquids and glasses during extreme shear thinning are investigated by nonequilibrium molecular dynamics (NEMD). Simulations performed on the Lennard‐Jones liquid at states close to the triple point reveal long range order accompanying extreme shear thinning which is characterized by linear lines of molecules spontaneously forming along the shear flow lines. These ‘‘strings’’ of molecules pack into a triangular lattice. The density of strings increases with shear rate, as does the difference in density in various directions with respect to the flow field. Local structural asymmetry with lifetimes comparable to the simulation are observed at the highest shear rates considered, leading eventually to structural disorder via dislocations in the triangular lattice.

Molecular dynamics computer simulations of binary Lennard-Jones fluid mixtures: Thermodynamics of mixing and transport coefficients

Equilibrium (NVT) ensemble molecular dynamics are used to evaluate the transport coefficients of binary Lennard-Jones mixtures via Green-Kubo formulae. Time correlation and mean-square displacements are employed to determine the component self-diffusion and mutual-diffusion coefficients. Time correlation functions are used to evaluate the shear viscosity, thermal conductivity and the thermal diffusion coefficient (Soret-Dufour coefficient). The results are for the low fluid density regime (ρ → 0), where there are experimental data and analytic expressions for the transport coefficients based on kinetic theory. For Ar-Kr, the simulation transport coefficients extrapolate reasonably well to the experimental and the analytic expressions in the ρ → 0 limit. Agreement near the triple point with experiment and previous simulation is also good. The model Ar-Hg viscosity, thermal conductivity and mutual diffusion coefficient manifest more dramatic variations in the simulations as ρ → 0, suggesting deviations from...

Percolation cluster statistics of Lennard-Jones fluids

The percolation and cluster characteristics of the 3D Lennard-Jones, LJ, fluid have been determined by molecular dynamics computer simulation. The continuous nature of the LJ potential has a pronounced effect on the percolation threshold when compared with a nearest equivalent hard-sphere fluid. In the hard-core limit, percolation takes place at a higher equivalent hard-sphere density than for the hard-sphere fluid. In the soft-core regime the reverse trend is observed. The distribution of clusters is analysed using the cluster number distribution function, ns , above and below the percolation threshold. Its variation with density is statistically the same as for lattice percolation. The pair correlation within the percolating cluster is measured using the pair connectedness function, p(r). It can be used to obtain, at short range the coordination number within the cluster and at long range the fractal dimension, D f, of the percolating cluster. The radius of gyration, R g, of the non-percolating clusters...

Cluster analysis and continuum percolation of 3D square-well phases MC and PY solutions

An extensive study of the percolation threshold, ρp of three dimensional attractive and repulsive square well fluids is made by Monte Carlo computer simulation. We find that in the hard-core limit an attractive well decreases ρp below the high temperature limiting value. In contrast a hard shoulder potential produces the opposite trend. A numerical solution of the PY integral equations employing Hills concept of bound and unbound pairs gives results qualitatively in agreement with MC. The PY solution overestimates ρp especially in the hard-core limit and at high temperature. We examine the shapes of all the clusters at the percolation threshold, resolved as a function of the number of particles in a cluster, s. The asphericity parameter, A 3, describing the instantaneous shape of the cluster decays slowly from unity, typically only achieving ∼ 0·3 by s ∼ 100, close to the estimated universal value of 0·312.

Microscopic Simulation of Rheology: Molecular Dynamics Computations and Percolation theory

Abstract The rheology of any liquid can now, in principle, be predicted from first principles using the computer simulation technique of molecular dynamics. Computations on simple molecular fluids close to the solid phase co-existence line have revealed that shear thinning and shear thickening, as well as other non-Newtonian effects are manifest by all liquids at large enough shear rates. This discovery leads to simplifications in predicting non-Newtonian behaviour. The shear viscosity as a function of shear rate for a wide range of disparate experimental and simulated liquids fall on a “universal” curve, when normalised by internally derived parameters. The rheology of intermediate density fluids at volume fractions ca. 25% has not been studied by simulation with the same degree of interpretive success. We reveal that there is a close link between the rheology of this part of the phase diagram and microscopic parameters, using ideas borrowed from Percolation Theory. We establish this relationship directl...