Brownian dynamics investigation of the Boltzmann superposition principle for orthogonal superposition rheology

Vishal Metri (Corresponding Author), W. J. Briels (Corresponding Author)

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

The most general linear equation describing the stress response at time t to a time-dependent shearing perturbation may be written as the integral over the past history t′ of a time dependent relaxation modulus, depending on t - t′, multiplied by the perturbing shear rate at time t′. This is in agreement with the Boltzmann superposition principle, which says that the stress response of a system to a time dependent shearing deformation may be written as the sum of responses to a sequence of step-strain perturbations in the past. In equilibrium rheology, the Boltzmann superposition principle gives rise to the equality of the shear relaxation modulus, obtained from oscillatory experiments, and the stress relaxation modulus measured after a step-strain perturbation. In this paper, we describe the results of Brownian dynamics simulations of a simple soft matter system showing that the same conclusion does not hold when the system is steadily sheared in a direction perpendicular to the probing flows, and with a gradient parallel to that of the probing deformations, as in orthogonal superposition rheology. In fact, we find that the oscillatory relaxation modulus differs from the step-strain modulus even for the smallest orthogonal shear flows that we could simulate. We do find, however, that the initial or plateau levels of both methods agree and provide an equation relating the plateau value to the perturbation of the pair-function.

LanguageEnglish
Article number014903
JournalJournal of chemical physics
Volume150
Issue number1
DOIs
Publication statusPublished - 4 Jan 2019

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Rheology
rheology
Shearing
perturbation
shearing
Stress relaxation
Shear flow
plateaus
Linear equations
Shear deformation
shear
stress relaxation
linear equations
shear flow
Computer simulation
histories
Experiments
gradients
simulation

Cite this

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title = "Brownian dynamics investigation of the Boltzmann superposition principle for orthogonal superposition rheology",
abstract = "The most general linear equation describing the stress response at time t to a time-dependent shearing perturbation may be written as the integral over the past history t′ of a time dependent relaxation modulus, depending on t - t′, multiplied by the perturbing shear rate at time t′. This is in agreement with the Boltzmann superposition principle, which says that the stress response of a system to a time dependent shearing deformation may be written as the sum of responses to a sequence of step-strain perturbations in the past. In equilibrium rheology, the Boltzmann superposition principle gives rise to the equality of the shear relaxation modulus, obtained from oscillatory experiments, and the stress relaxation modulus measured after a step-strain perturbation. In this paper, we describe the results of Brownian dynamics simulations of a simple soft matter system showing that the same conclusion does not hold when the system is steadily sheared in a direction perpendicular to the probing flows, and with a gradient parallel to that of the probing deformations, as in orthogonal superposition rheology. In fact, we find that the oscillatory relaxation modulus differs from the step-strain modulus even for the smallest orthogonal shear flows that we could simulate. We do find, however, that the initial or plateau levels of both methods agree and provide an equation relating the plateau value to the perturbation of the pair-function.",
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Brownian dynamics investigation of the Boltzmann superposition principle for orthogonal superposition rheology. / Metri, Vishal (Corresponding Author); Briels, W. J. (Corresponding Author).

In: Journal of chemical physics, Vol. 150, No. 1, 014903, 04.01.2019.

Research output: Contribution to journalArticleAcademicpeer-review

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