Biomedical subjects

D M Heyes

Publications and source records attributed to D M Heyes.

8 recordsLinked to original sources

PubMed2006

Thermodynamic properties of inverse power fluids.

The local scaling behavior of the radial distribution function of the soft sphere or inverse power, r-n potential, fluid leads to a formula for the equation of state. From this formula different analytic forms for the compressibility factor, Z, have been derived. In the first, Z is expressed as a product of three functions, the hard sphere equation of state and two other functions incorporating the effects of the potential softness. In the second formula, the compressibility factor is cast in terms of the position and height of the first peak in the radial distribution function. In the final form, Z can be expressed as an exponential function which depends entirely on a combination of the virial coefficients. In each case Z is an explicit expression which has the correct low density limiting behavior and is accurate up to the freezing density for all packing fractions and circa n>or=12. Expressions are derived for the various component functions required for the different forms of Z, and relations between them are established. The compressibility factor manifests a maximum value or "ridge" when plotted as contours on the density-softness plane. It starts for the softer fluids at lower densities, increases with particle stiffness, and crosses the freezing line at n congruent with 33. From the compressibility factor other thermodynamic quantities can be obtained and the density-softness dependence of the infinite frequency limit elastic properties been determined. A self-consistent expression is derived for the effective hard sphere packing fraction (or equivalently, diameter), valid for all packing fractions and circa n>12. The effective hard-sphere diameter is compared with the formulas of Barker and Henderson, and Wheatley.

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PubMed2005

Memory function for a fluid of molecules interacting through steeply repulsive potentials.

Previous studies of the properties of fluids of molecules interacting through steeply repulsive central potentials are extended to the investigation of the memory function. It is assumed that collisions are dominated by binary collisions and a general formula previously derived by Miyazaki, Srinivas, and Bagchi [J. Chem. Phys. 114, 6276 (2001)] is applied to the present problem. It is shown that the equations of motion of a pair of molecules can be solved explicitly and substitution of the result into the formula leads to a closed explicit expression for the memory function which is easily evaluated for any given state. In the limit of hard spheres this result leads to Enskog's equation and represents a generalization of that formula to fluids with softer potentials. The results obtained from the formula are compared with those derived from the molecular dynamics simulation. The velocity autocorrelation function was calculated using the generalized soft sphere potential, phi(r) = epsilon (sigma/r)(n), where epsilon and sigma set the energy and size of the molecule, and the exponent, n, is a variable. The two approaches agree very well for a range of state points for n large, especially at short times.

Journal Article↗

PubMed2005

The influence of potential softness on the transport coefficients of simple fluids.

This study explores the effects of interaction softness on the transport properties of simple fluids. The transport coefficients of soft-sphere fluids in which the particles interact via the potential, phi(r)=epsilon(rsigma)(-n), with n in the range from 6 to 1152, have been calculated by molecular-dynamics computer simulation. The self-diffusion coefficient D shear viscosity eta(s), bulk viscosity eta(b), and thermal conductivity lambda were computed over a wide packing fraction range. It was found that the Batschinski-Hildebrand expressions, in which D, eta(s) (-1), eta(b) (-1), and lambda(-1) are assumed to have a linear dependence on the molar volume, represent the data quite well for all n, although least well for the thermal conductivity. The density for which, on extrapolation, each of these quantities is zero, increases with the softness of the interaction (or approximately n(-1)), suggesting that the effective hard-sphere diameter decreases with increasing softness in the small n limit. This treatment leads to simple empirical formulas for the effect of density and n on the effective hard-sphere diameter and packing fraction (in an intermediate range) and the four transport coefficients of these fluids.

Colloids↗

PubMed2004

Discrete-element method simulations: from micro to macro scales.

Many liquid systems encountered in environmental science are often complex mixtures of many components which place severe demands on traditional computational modelling techniques. A meso scale description is required to account adequately for their flow behaviour on the meso and macro scales. Traditional techniques of computational fluid dynamics and molecular simulation are not well suited to tackling these systems, and researchers are increasingly turning to a range of relatively new computational techniques that offer the prospect of addressing the factors relevant to multicomponent multiphase liquids on length- and time-scales between the molecular level and the macro scale. In this category, we discuss the off-lattice techniques of 'smooth particle hydrodynamics' (SPH) and 'dissipative particle dynamics' (DPD), and the grid-based techniques of 'lattice gas' and 'lattice Boltzmann' (LB). We highlight the main conceptual and technical features underpinning these methods, their strengths and weaknesses, and provide a few examples of the applications of these techniques that illustrate their utility.

Algorithms↗

PubMed2004

Analysis of the evolution of granular stress-strain and voidage states based on DEM simulations.

We review and discuss the results of our granular-dynamics simulations of the time evolution of the microstructure of compact granular beds as found in pouring, in hopper filling and discharge, and in a shear cell. These systems are mainly quasi-static. However, it is also common to encounter localized 'shear zones' with significant velocity/voidage fluctuations and high bulk-strain gradients. These narrow-banded zones are separated from near-static regions by sharp, discontinuous changes of bulk stress and voidage. Within these bands the granular assembly undergoes a transition from the quasi-static to the inertial state, where enduring particle contacts are increasingly replaced by collisional ones. We focus on the discrete particle origins of this inhomogeneous yield/flow behaviour. We show the usefulness of analysing the local evolution in terms of relative rotation of the grains which is observed to cause rapid local bulk dilation responsible for setting off avalanches near free-surface boundaries and protracted bulk-failure planes in confined static assemblies. We also present some evidence to suggest that allowing for effective continuous particle-particle interactions could approximate observed effects attributable to particle shape and surface roughness. Wavelet analyses have been applied successfully to generate the variations in periodicity and the relative sequence of evolution of the stress, strain-rate and voidage states in avalanching granular heaps and in the wall region of axially symmetric hopper flows.

Journal Article↗

PubMed2004

Time correlation functions of hard sphere and soft sphere fluids.

We explore the transition between soft particle fluids of increasing steepness to the hard sphere limit. We analyze the analytic forms of the time correlation functions used in determining transport coefficients in Green-Kubo formulas for fluids composed of particles interacting through a repulsive r(-n) potential. We focus on the steeply repulsive n--> infinity limit where the potential tends to the hard sphere interaction. Dufty [Mol. Phys. 100, 2331 (2002)] developed a theoretical framework that can be used to characterize the transition from a steeply repulsive continuous potential toward the hard sphere potential for the shear stress time correlation function. This function was shown to consist of a rapidly decaying contribution (which is singular in the steeply repulsive limit) and a slowly decaying nonsingular part which can be reasonably well represented by Enskog's prediction on times of order and in excess of the mean collision time. We extend this treatment to the bulk viscosity and thermal conductivity. We focus on the bulk viscosity (pressure) correlation function as it is purely singular for hard spheres, and has no kinetic or cross term contributions in this limit. There is no relaxation of this correlation function on the mean collision or Enskog time scale for hard spheres. We show that it is not possible to represent the steeply repulsive behavior of this function entirely in terms of a sech function, i.e., C(B)(t)=sech(a(n)t/tau(n)), where a(n) is a numerical factor, t is time, and tau(n) is a relaxation time proportional to n(-1). An additional singular function, which we call w(t), is required to obtain the correct short-time behavior of C(B)(t) and the Enskog value for the bulk viscosity. With this additional function, the value of a(n) in the n--> infinity limit is a(n)=square root of 2 which is consistent with the second moment of the time expansion of the time correlation function. We compute this function for large n and extrapolate it to n--> infinity, determining one possible analytic form. The shear stress correlation function also gives a(n)=square root of 2 in the hard sphere limit for the singular part when the sech and w functions are used. This function has a nonsingular component, even in the hard sphere limit. We explore various forms for the crossover function X(t/tau(n)) introduced by Dufty, which weights the limiting singular and nonsingular contributions to C(S)(t) particularly at intermediate times. The qualitative behavior for the heat flux time correlation function (used to obtain the thermal conductivity) is much the same as the shear case. The w(t) derived by several self-consistent extrapolations appears, within the simulation statistics, to be the same for the bulk and shear viscosity, and for the thermal conductivity cases.

Journal Article↗

PubMed1999

Algorithms for Brownian dynamics computer simulations: multivariable case.

Several Brownian numerical schemes for treating stochastic differential equations at the position Langevin level are analyzed from the point of view of their algorithmic efficiency for large-N systems. The algorithms are tested using model colloidal fluids of particles interacting via the Yukawa potential. Limitations in the conventional Brownian dynamics algorithm are shown and it is demonstrated that much better accuracy for dynamical and static quantities can be achieved with an algorithm based on the stochastic expansion and second-order stochastic Runge-Kutta algorithms. The importance of the various terms in the stochastic expansion is analyzed, and the relative merits of second-order algorithms are discussed.

Journal Article↗

PubMed1999

Effects of bead-bead interactions on the static and dynamical properties of model polymer solutions.

The effects of segment-segment interactions on the static and dynamical properties of model polymer solutions are examined by Brownian dynamics simulations in the free-draining limit over a wide concentration range. A bead-and-spring model is used to describe the polymer chains at a coarse-grained level, in which segment-segment interactions are represented by a bead-bead pair potential with a Gaussian analytic form, beta u(ev)(r)=A exp(-r(2)/2 sigma(2)), where beta=1/k(B)T and A and sigma are characteristic energy and distance scales, respectively. The chain dimensions, self-diffusion coefficient, and viscosity of the systems are studied as functions of number density of beads of the system, rho, at given excluded-volume potential parameters, A and sigma. Our results show that in the limit of infinite dilution even for short chains (N approximately 10) there is statistically significant scaling behavior in the static and dynamical properties. For a system with given values of A and sigma the change in polymer coil size shows a realistic trend as the concentration of the system increases. In the dilute and concentrated regions the coil size decreases as a result of increasing interchain repulsions, while in the highly concentrated region the coil size increases again, showing a return to Rouse-like behavior because the intrapolymer and interpolymer segment-segment interactions become effectively indistinguishable for an arbitrary bead and to a large extent are "balanced out." In the limit of infinite dilution, the self-diffusion coefficient of the center of mass, D(cm), depends on N only and not on the potential parameter A, while in contrast the specific viscosity eta(sp) depends on both N and A. As the concentration increases D(cm) decreases and eta(sp) increases consistent with the behavior of real polymers. When the system becomes highly concentrated, however, both D(cm) and eta(sp) unrealistically return to the Rouse limit. This suggests that from the concentrated region upward in concentration, the entanglement or the topological constraints caused by the physical connectivity of the chains significantly influence their dynamical behavior. The mean-field segment-segment interactions or excluded-volume effects incorporated in the current coarse-grained bead-spring approach cannot capture this entanglement effect, and therefore give rise to unrealistic dynamical behavior in the concentrated regime.

Journal Article↗