Shear-wave speeds and elastic moduli for different liquids. Part 1. Theory

Abstract

In this paper we develop a theory for a rheometrical device for measuring the speed of shear waves into a region at rest. The device is a Couette apparatus with a narrow gap. The outer cylinder is moved impulsively and a time of transit is measured. The linearized theory governing this apparatus is reduced to a perturbation of Stokes’ first problem between parallel planes. A method for determining an effective shear modulus from measured values of the wave speed is discussed and various cases are analysed. An experimental apparatus based on this theory, together with tabular data, is discussed in a companion paper (Part 2, Joseph, Riccius & Arney 1986).

Thermal parameter identification for non-Fourier heat transfer from molecular dynamics

“…(8). This was a special model obtained after generalization of Boltzmann's equation of linear viscoelasticity [58], and was inspired by the work done by Maxwell [59] and Boltzmann [60]. Differentiating Eq.…”

Climbing constant, second-order correction of Trouton's viscosity, wave speed and delayed die swell for M1

“…The theory for the wave-speed meter is given in Joseph et al [19]. The apparatus and the measuring technique are described in Joseph et al [20] and in detail in Riccius [21].…”

Shear-wave speeds and elastic moduli for different liquids Part 3. Experiments-update

“…The concept of an effective modulus developed in [1] seems to be supported by measurements in [2], here and those of Fuller. Additional support for these ideas in a flow context come from recent measurements of delayed die swell [3].…”

“…In our earlier work we presented a theory [1] of effective wave-speeds for shear waves into regions at rest and developed the idea of an effective rigidity (shear modulus) and viscosity. A device, the wave-speed meter (U.S. patent 4,602,502), was described and used to measure wave speeds and effective rigidities in 51 liquids [2].…”

“…An effective-moduli theory for G (7, t -~) can be developed along exactly the same lines laid down in [1] and leads to effective rigidities Gc (i).…”