Thermodynamic relationships for shearing linear viscoelastic fluids

Daivis, Peter J.

doi:10.1016/j.jnnfm.2007.02.004

Cited by 20 publications

(23 citation statements)

References 13 publications

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“…We also created a variety of systems at a similar state point but different concentrations and induced the system to flow using the SLLOD equations of motion, given by Eqn. 19 and Eqn. 20.…”

Section: Transport Coefficientsmentioning

confidence: 99%

Deviations From Classical Hydrodynamic Theory in Highly Confined Planar Poiseuille Flow of a Polymer Solution

Menzel¹,

Daivis²,

Todd³

2017

CMST

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The behaviour of polymer solutions in highly confined geometries remains a subject of interest in rheology and fluid dynamics. In this paper, we investigate how well the classical hydrodynamic description based on the Navier-Stokes equations, Fourier's Law and Fick's Law describes the flow of a highly confined polymer solution. In particular, we examine the effects of depletion of polymer concentration at the wall-fluid interface and strain rate coupling to the heat flux. We present data from molecular dynamics simulations of a model polymer solution in explicit solvent undergoing planar Poiseuille flow for channel widths ranging from around 10 solvent atomic diameters to around 80 solvent atomic diameters. We find that the classical continuum approach works very well for channels wider than 20 solvent atomic diameters. For narrower channels, we observe deviations in the velocity, temperature and concentration profiles due to density oscillations near the walls, the polymer depletion effect, and possible weak strain rate coupling. For the narrowest channel, the wall effects extend to the centre of the channel but the underlying profiles are quite well described by the classical continuum picture. By allowing very long times of order 10 4 reduced time units for relaxation to the steady state and averaging over very long runs of order 10 5 reduced time units and 16 independent ensemble members, we are able to conclude that previously reported deviations from the classical continuum predictions (I.K. Snook, P.J. Daivis, T. Kairn, J. Physics-Condensed Matter 20, 404211 (2008)) were probably the result of insufficient equilibration time. Our results are also sufficiently accurate and precise to verify the expected quartic temperature profile predicted by classical hydrodynamic theory, with only a very small deviation which we can attribute to nonlinear coupling of the heat flux vector to the strain rate.

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Section: Transport Coefficientsmentioning

confidence: 99%

Deviations From Classical Hydrodynamic Theory in Highly Confined Planar Poiseuille Flow of a Polymer Solution

Menzel¹,

Daivis²,

Todd³

2017

CMST

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“…The simulations are conducted on the same system that was studied previously [4], for which there already exists a large body of data for verification. The system consists of N = 500 particles interacting via the truncated and shifted Lennard-Jones (LJ) interaction potential given by…”

Section: Simulationsmentioning

confidence: 99%

“…In a study of the thermodynamics of steady shear, Daivis [4] used the Green-Kubo relation to calculate the zero shear rate viscosity η 0 and a relationship derived from the retarded motion expansion by Coleman and Markovitz [5] to calculate the zero shear rate limit of the first normal stress coefficient 1,0 of a simple liquid from its stress relaxation modulus G(t). These quantities were also computed directly from nonequilibrium molecular dynamics simulations using the sllod [1] algorithm.…”

Section: Introductionmentioning

confidence: 99%

Effect of kinetic and configurational thermostats on calculations of the first normal stress coefficient in nonequilibrium molecular dynamics simulations

2012

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Thermostats for homogeneous nonequilibrium molecular dynamics simulations are usually designed to control the kinetic temperature, but it is now possible control any combination of many different types of temperature, including the configurational and kinetic temperatures and their directional components. It is well known that these temperatures can become unequal in homogeneously thermostatted shearing steady states. The microscopic expressions for these temperatures are all derived from equilibrium distribution functions, and it is pertinent to ask, what are the consequences of using these equilibrium microscopic expressions for temperature in thermostats for shearing nonequilibrium steady states? Here we show that the answer to this question depends on which properties are being investigated. We present numerical results showing that the value of the zero shear rate viscosity obtained by extrapolating results of nonequilibrium molecular dynamics simulations of shearing steady states is the same, regardless of the type of temperature that is controlled. It also agrees with the value obtained from the equilibrium stress autocorrelation function via the Green-Kubo relation. However, the values of the limiting zero shear rate first normal stress coefficient obtained from nonequilibrium molecular dynamics simulations of shearing steady states are strongly dependent on the choice of temperature being controlled. They also differ from the value of the first normal stress coefficient that is calculated from the equilibrium stress autocorrelation function. We show that even when all of the directional components of the kinetic and configurational temperatures are simultaneously controlled to the same value, the agreement with the result obtained from the equilibrium stress autocorrelation function is poor.

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“…Apart from a few detailed computational investigations for atomic fluids [27,28], this equation of state has received little attention, but it is possible to obtain one from the retarded motion expansion. Most derivations of the retarded motion expansion introduce the incompressibility assumption at an early stage [11,12,29], but it is possible to carry out the derivation without making this assumption.…”

Section: Retarded Motion Expansion For a Compressible Fluidmentioning

confidence: 99%

Nonlinear shear and elongational rheology of model polymer melts at low strain rates

Daivis

Matin

Todd

2007

Journal of Non-Newtonian Fluid Mechanics

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Thermodynamic relationships for shearing linear viscoelastic fluids

Cited by 20 publications

References 13 publications

Deviations From Classical Hydrodynamic Theory in Highly Confined Planar Poiseuille Flow of a Polymer Solution

Deviations From Classical Hydrodynamic Theory in Highly Confined Planar Poiseuille Flow of a Polymer Solution

Effect of kinetic and configurational thermostats on calculations of the first normal stress coefficient in nonequilibrium molecular dynamics simulations

Nonlinear shear and elongational rheology of model polymer melts at low strain rates

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