TY - JOUR

T1 - Brownian dynamics investigation of the Boltzmann superposition principle for orthogonal superposition rheology

AU - Metri, Vishal

AU - Briels, W. J.

PY - 2019/1/4

Y1 - 2019/1/4

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85059629260&partnerID=8YFLogxK

U2 - 10.1063/1.5080333

DO - 10.1063/1.5080333

M3 - Article

C2 - 30621405

AN - SCOPUS:85059629260

VL - 150

JO - Journal of chemical physics

JF - Journal of chemical physics

SN - 0021-9606

IS - 1

M1 - 014903

ER -