Behavior of viscoelastic models with thermal fluctuations

Martien A. Hulsen,Markus Hütter,Mick A. Carrozza,Patrick D. Anderson

doi:10.1140/epje/i2020-11948-9

Martien A. Hulsen, Markus Hütter + Show 2 more

Open Access

https://doi.org/10.1140/epje/i2020-11948-9

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Abstract

.Fluctuating viscoelasticity for conformation-tensor-based models is studied at equilibrium, in simple-shear deformation, and in uniaxial extension. The models studied are the upper-convected Maxwell model, the FENE-P model with finite chain-extensibility, and the Giesekus model with anisotropic drag. Using numerical simulations, the models are compared in detail both with each other and with analytical predictions for the Maxwell model. At equilibrium, the models differ only marginally, both in terms of static and dynamic characteristics. When deformed, the average mechanical response of the Maxwell model is unaffected by the strength of thermal fluctuations, while the mechanical response of the FENE-P and Giesekus models show a slight decrease the stronger the fluctuations in simple shear, whereas the decrease in uniaxial extension is marginal. For all models, the standard deviation of the mechanical response increases with increasing strength of fluctuations, and the magnitude of the standard deviation relative to the average for given fluctuation strength generally decreases the stronger the deformation, this effect being stronger for uniaxial extension than for simple-shear deformation.Graphical abstract

Highlights

Thermal fluctuations in viscoelastic fluids become important if the length scales of observation and possibly confinement are of the same order of magnitude as the characteristic length scale of the, often meso-scale, constituents of the fluid
The models examined are the most standard and simple model of all (Maxwell), a model that accounts for non-linearity in terms of the thermodynamics (FENE-P, with finite chainextensibility), and a model accounting for anisotropic mobility (Giesekus)
From a non-equilibrium thermodynamics viewpoint, they are prototypical for a wide class of conformation-tensor–based models

Summary

Introduction

Thermal fluctuations in viscoelastic fluids become important if the length scales of observation and possibly confinement are of the same order of magnitude as the characteristic length scale of the, often meso-scale, constituents of the fluid. Either one can use a particle-based approach, related to e.g. molecular dynamics, dissipative particle dynamics or Brownian dynamics, or one prefers to adopt a field-theoretic approach, related to fluid dynamics The latter route is what is examined further in this paper. E (2020) 43: 24 generic approach and more flexibility in applications of fluctuating viscoelasticity This should include variations in the strength of the fluctuations, as well as a comparison of different rheological models, for unraveling the characteristic behavior. The goal of this paper is to examine in detail the behavior of three viscoelastic models with fluctuations, at equilibrium and in flow, by means of numerical simulation. Since free energy and mobility are the key ingredients for formulating complex-fluid models along non-equilibrium thermodynamic principles, these three models are considered prototypical, and will be studied in this paper. For all SDEs reported in this paper, it is understood that the Itointerpretation of stochastic calculus [20, 21] is used

General aspects

Thermodynamics for finite N

FENE-P model

Upper-convected Maxwell model

Analytical calculations and predictions

Equilibrium

Simple shear and uniaxial extension

Findings

Discussion and conclusions