Behavior of concentrated polymer solutions under periodic stresses

Abstract

Synopsis.Experimental methods for measuring the mechanical properties of concentrated polymer solutions and other viscoelastic systems under periodically varyiny stresses are reviewed. These include direct measurements of stress and strain, measurements of response at resonance frequencies determined by the inertia of the apparatus, propagation of waves in extended media, and measurements of resonance vibrations. The conditions for the suitability of each method are discussed, and equations for the interrelation of the various quantities measured are given. Examples are shown to illustrate the fitting of experimental data to the calculated behavior of mechanical models, in order to obtain frequency-independent mechanical constants which can be interpreted in terms of molecular behavior.It may be equally well represented by a frequency-dependent capacity in parallel with a frequencydependent resistance, the frequency variation of these units following certain simple relations (Debye, Polar Molecules, 1923). The latter model facilitates interpretation of the phenomenon in terms of orientation of dipoles, while the former leads to interpretation in terms of a heterogeneous system of two dielectric solids. notation is regretted, but it is hoped that the present notation, which has been chosen with care, will serve better for a variety of experimental methods and a variety of mechanical models.

Stress communication and filtering of viscoelastic layers in oscillatory shear

“…The full model (1)(2)(3)(4) reduces to the following closed system of partial differential equations for the remaining unknowns (v x , p, xx , yy ), which are functions of the gap height (y) and time:…”

“…In [4], a complete solution of this problem is derived resting on the observation that v x and xy decouple into a linear hyperbolic system once yy is negligible, and then the remnant of non-linearity from the upper convective derivative reduces to the solution of (8) with known functions for the velocity and shear stress. The 2 × 2 system (7, 9, satisfying BC1 and BC2) is solved, in the H = ∞ limit by Ferry et al [1][2][3], and generalized to any finite H by the authors [4]:…”

“…We recall the formulation developed in [4,5], which is a generalization of the Ferry shear wave model [1][2][3] to finite depth layers and non-linear constitutive laws. We summarize the key elements from these references in order to describe the present focus on boundary stress signals in oscillatory strain experiments.…”

The viscoelastic properties of concentrated suspensions

“…The simplest one which shows the same characteristics as our data, is the retarded Maxwell element, first described by Ferry et al [15] and shown in figure 6. It consists of a Maxwell element, ~p G ~s Fig.…”

A Penetroviscosimeter for Newtonian and Visco-Plastic Fluids

“…This method was extended to the dynamic frequency analysis of linear viscoelastic solutions of polymers. (21)(22) This survey of the literature shows that the penetration test has received moderate attention from researchers. Many semiempirical equations have been proposed to relate measurements (i.e., strength of penetration or velocity) to rheological properties.…”