Propagation of Transverse Waves in Viscoelastic Media

Abstract

In calculating elastic constants of viscoelastic media from transverse wave propagation, it has been customary heretofore to assume a plane disturbance in a medium of infinite extent. Equations have now been derived for conditions which approach much more closely the experimental arrangement, namely, propagation from a finite source plate in a rectangular cell, and representative numerical calculations have been made. The new theory shows that the finite dimensions of cell and source should have very little influence on the wave-length as determined from observations of strain double refraction, but the attenuation should be perceptibly different from that of the plane wave case. Experimental data confirm these conclusions. Nevertheless, the simple plane theory is adequate within present experimental error for the majority of cases. Only in certain specified ranges of mechanical consistency will it be necessary to apply corrections taking into account the sizes of the cell and source.

Bulk rheometry at high frequencies: a review of experimental approaches

“…Consider an oscillatory in-plane movement of a surface with velocity u 0 (t) = U 0 • e j 2πf t , which induces a shear wave (Adler et al 1949;Thurston 1959) travelling in a direction normal to the plane of motion. The velocity profile in this normal (z) direction can be obtained by solving the one-dimensional wave equation (Adler et al 1949;Schrag et al 1965), or from the Navier-Stokes equations for irrotational flow (Deen 1998), as follows:…”

Extensions of the Ferry shear wave model for active linear and nonlinear microrheology

“…A classical [6, 8, 1] method for linear viscoelastic characterization of gels and polymer solutions is based upon measurements of the unidirectional propagation of shear waves induced by an oscillating plate. The experimental technique and associated modeling and analysis are extensively discussed in the literature [30, 7, 2, 13, 14].…”

Molecular simulation and continuum mechanics investigation of viscoelastic properties of fluids confined to molecularly thin films

“…The importance of these shear wave propogation effects on the experimental determination of dynamic rheological properties has been pointed out in the literature. [22][23][24][25] Using the theory of waves, Schrag and co-workers [23][24][25] have presented expressions for the velocity and shear rate profiles ͑as functions of time and position͒ in the fluid when these inertial effects play an important role. Here we present a brief outline of an alternate derivation of these expressions starting from the equation of motion of the fluid.…”