Continuum Mechanics in a Space of Any Dimension : IV. Viscometric Flows of General Fluids

Abstract

The viscometric flows of the incompressible general fluids in n-dimensional space are investigated, where n takes 2, 3, 4 and 5, and the determinate stress of the fluids is determined by the relative deformation history. It is shown that the characteristic matrices of the viscometric flow have one rate of shear for n＝2 and 3, and two for n＝4 and 5. The general fluids in the flow are represented by the viscometric functions. There are one shear stress function for n＝2, 3, 4 and 5, one normal stress difference function for n＝2, and two for n＝3, 4 and 5. The approximation forms of the viscometric functions are obtained in the case of a small magnitude of rate of shear. The generalized steady curvilinear flow is also investigated, and it is proved that the flow is a special case of the viscometric flow.