Macromolecular Origins of Fifth Shear Stress Harmonic in Large-Amplitude Oscillatory Shear Flow

Journal of Non-Newtonian Fluid Mechanics

2017

Section: Amentioning

confidence: 95%

“…γ 0 (see Eq. (20) of [47]), its cause depends on the all orders of the orientation distribution expansion.…”

Section: Amentioning

confidence: 99%

Polymer orientation contributions in large-amplitude oscillatory shear flow

Gilbert

Journal of Non-Newtonian Fluid Mechanics

2017

“…For the steady uniaxial elongational viscosity, we compare the coefficients in Eqs. (8) and (12) to get:…”

Section: Materials Function Molecular Continuummentioning

confidence: 99%

Molecular continua for polymeric liquids in large-amplitude oscillatory shear flow

Saengow

2018

Mod. Phys. Lett. B

Self Cite

In this paper, we connect a molecular description of the rheology of a polymeric liquid to a continuum description, and then test this connection for large-amplitude oscillatory shear (LAOS) flow. Specifically, for the continuum description, we use the 6-constant Oldroyd framework, and for the molecular, we use the simplest relevant molecular model, the suspension of rigid dumbbells. By relevant, we mean predicting at least higher harmonics in the shear stress response in LAOS. We call this connection a molecular continuum, and we examine two ways of arriving at this connection. The first goes through the retarded motion expansion, and the second expands each of a set of specific material functions (complex, steady shear, and steady uniaxial extensional viscosities). Both ways involve in comparing the coefficients of expansions and then solve for the six constants of the continuum framework in terms of the two constants of the rigid dumbbell suspension. The purpose of a molecular continuum is that many well-known results for rigid dumbbell suspensions in other flow fields can also be easily obtained, without having to firstly find the orientation distribution function. In this paper, we focus on the recent result for the rigid dumbbell suspension in LAOS. We compare the accuracies of the retarded motion molecular continuum (RMMC) with the material function molecular continuum (MFMC). We find the RMMC to be the most accurate for LAOS.

“…(15) of [8]; Eq. (14.4-1) of [9]; see [10], [11], [12], [13], [14], [15] to explore diffusion equation and application; see also Table I. of [16], Table I.…”

Section: Introductionmentioning

confidence: 99%

Macromolecular tumbling and wobbling in large-amplitude oscillatory shear flow

Jbara

2019

Physics of Fluids

Self Cite

For a suspension of rigid dumbbells, in any simple shear flow, we recently solved for the diffusion equation for the orientation distribution function by a power series expansion in the shear rate magnitude. In this paper, we focus specifically on large-amplitude oscillatory shear flow (LAOS), for which we extend the orientation distribution function to the 6th power of the shear rate amplitude. We arrive at the Fourier solution for each harmonic contribution to the total orientation distribution function, separating each harmonic into its coefficients in and out-of-phase with cosnωt , ′ ψ n and ′′ ψ n , respectively. We plot, for the first time, the evolving normalized alternant macromolecular orientation. Moreover, to deepen our understanding of the macromolecular motions, we distinguish and study the two types of possible rotations, tumbling and wobbling.*Corresponding author (giacomin@queensu.ca) CONTENTS