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Orientation in Large‐Amplitude Oscillatory Shear
Author(s) -
Schmalzer A. M.,
Giacomin A. J.
Publication year - 2015
Publication title -
macromolecular theory and simulations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.37
H-Index - 56
eISSN - 1521-3919
pISSN - 1022-1344
DOI - 10.1002/mats.201400058
Subject(s) - isotropy , viscoelasticity , shear flow , amplitude , mechanics , anisotropy , classical mechanics , newtonian fluid , harmonics , orientation (vector space) , shear stress , shear (geology) , spherical harmonics , physics , shear rate , nonlinear system , materials science , geometry , optics , rheology , thermodynamics , mathematics , quantum mechanics , voltage , composite material
We examine the simplest relevant molecular model for large‐amplitude oscillatory shear flow of a polymeric liquid: The dilute suspension of rigid dumbbells in a Newtonian solvent. We find explicit analytical expressions for the orientation distribution, and specifically for test conditions of frequency and shear rate amplitude that generate higher harmonics in the shear stress and normal stress difference responses. We solve the diffusion equation analytically to explore molecular orientation induced by oscillatory shear flow. We see that the orientation distribution is neither even nor odd. We find zeroth, first, second, third, and fourth harmonics of the orientation distribution, and we have derived explicit analytical expressions for these. We provide a clear visualization of the orientation distribution in large‐amplitude oscillatory shear flow in spherical coordinates all the way around one full alternant cycle. The Newtonian distribution is nearly isotropic, the linearly viscoelastic, only slightly anisotropic, and the nonlinear viscoelastic, highly anisotropic.