In this article, we provide a brief review of some generalizations of the second grade fluid model. We discuss certain similarities between these fluids and fluids of higher grades, while also describing certain limitations of these models. The new models that we put forth are based upon some interesting experimental results which suggest that not only can normal stress coefficients depend upon the shear rate, but that this dependency is in fact not the same rate as that of shear viscosity variation with shear rate. We then discuss some steady flows of these generalized second grade fluid models.

On some generalizations of the second grade fluid model

The problem of flow between infinite eccentric disks rotating at different speeds is considered and a solution to the complete Navier-Stokes equations obtained. An approximate analytic solution is also presented.

Flow between eccentric disks rotating at different speeds: Inertia effects

A detailed account of the usefulness of a bodytensor formalism in rheology has been given byLodge (1975). Here, we outline some of the more important results concerning shear flows and motions with constant stretch history (M.C.S.H.). We then discuss the relation between M.C.S.H. and the concept of a “perpetual rheological history” (P.R.H.) introduced byOldroyd (1965) and conclude that they are equivalent. The body-tensor formalism is applied to specific situations of practical interest, including certain new rheometers and an important class of nearly-viscometric flows. In much of the work, we use suitably chosennon-orthogonal coordinate systems. New results include (i) a method for deciding whether any given flow is a M.C.S.H. or not, and (ii) a proof that ‘Balance Rheometer Flow’ is not a M.C.S.H.

Some examples of the use of body coordinate systems in the kinematics of continuous media

The linear time-dependent behaviour of elasticoviscous liquids may be determined by conventional rheometers, or by any one of a number of new rheometers which have recently appeared in which the test fluid is contained between two surfaces which rotate with the same angular velocity about axes which are not coincident. (The Orthogonal, Balance and Eccentric-Cylinder rheometers are perhaps the most well known examples of such instruments at the present time.) In this communication, we consider the more general situation in the new rheometers in which the angular velocities of the two surfaces are different.

D. G. Knight

Papers

Nearly viscometric flows in the new rheometers