Vibrational Measurements with Large Amplitudes

Abstract

Using a new instrument, the influence of the shear amplitude s0 on the dynamic behavior of polymer solutions up to 700% shear was investigated. At amplitudes <∼100% shear, the dynamic viscosity η1 remained constant, as required by linear viscoelasticity; however, the shear storage modulus G′ decreased considerably. The steady-state flow curve forms the envelope of curves measured with different amplitudes and frequencies, predominantly in the range of higher rates of shear. The more complete analysis of the results is forthcoming.

Large amplitude oscillatory shear of pseudoplastic and elastoviscoplastic materials

“…frequency and amplitude { , 0 }. These two parameters define an experimental test space in which results can be compactly represented, which is now known as the Pipkin diagram (Pipkin (1972) Methods for analyzing LAOS include Lissajous curves (Philippoff (1966); Tee and Dealy (1975)), Fourier transform rheology (e.g. Wilhelm (2002)), Stress decomposition (Cho et al (2005); Ewoldt et al (2008); Yu et al (2009)), computation of viscoelastic moduli (Hyun et al (2002); Ewoldt et al (2008)), decomposition into characteristic waveforms (Klein et al (2007)), and analysis of parameters related to Fourier transform rheology (Debbaut and Burhin (2002); Hyun and Wilhelm (2009)).…”

Nonlinear Viscoelastic Behavior of Concentrated Xanthan Gum Systems in Large Amplitude Oscillatory Shear (LAOS) Flow Fields : Stress Waveform and Lissajous Pattern Analysis

“…Although this manner produces a lot of visuable informations concerning both the linear and nonlinear rheological properties of complex fluids, it may not be effective to interpret the relationship between stress As an early attempt to evaluate the nonlinear characteristics of stress responses with a graphical method, a Lissajous pattern (or Figure) displaying stress versus strain loop had been introduced by Philippoff [61] in the middle of 1960's. This Lissajous pattern shows a circular form for a purely Newtonian viscous liquid because stress and strain are out of phase.…”

Strain-rate frequency superposition in large-amplitude oscillatory shear

“…Our definition of the moduli [Eqs. (2)] and resulting calculations do not account for higher harmonics in the strain signal. In Fig.…”

“…Most LAOS studies to-date have been restricted to the study of stress-strain curves [2,5,8,11] or the ratios of the harmonics of the stress amplitude spectrum [4,6,7]. In occasional studies [9], the harmonic moduli have been calculated in a strain amplitude or an angular frequency sweep test.…”

“…In order to probe their linear viscoelastic response, materials are frequently subject to small-amplitude oscillatory shear, wherein an applied sinusoidal strain γ(t) = γ 0 sin(ωt) (here γ 0 is the strain amplitude, ω is the angular frequency, t is the time) results in a stress response σ(t; ω) = γ 0 [G [1], and are functions of the angular frequency. By contrast, the resultant stress from a large-amplitude oscillatory shear (LAOS) [2][3][4][5][6][7][8][9][10][11] test contains higher harmonics which may be interpreted in terms of harmonic moduli G ′ n and G ′′ n (subscript n refers to the n-th harmonic, see Section III(A) for the definition), which are functions of both the strain amplitude and the angular frequency. The moduli G ′′ 1 may be physically interpreted [7] in terms of the energy dissipated per unit volume per cycle of strain oscillation (see Section III(E) below).…”