Continuum Mechanics in a Space of Any Dimension : III. Stokes Fluids

Abstract

The behavior of the Stokes fluid in a space of any dimension is investigated. The linear approximation of the constitutive equations with respect to the stretching is obtained, and compressible and incompressible Navier-Stokes fluids are defined. In a space of more than one-dimension the former has two viscosity coefficients and the latter has one. In a space of one-dimension the former has a viscosity coefficient but the latter reduces to a rigid body. The general curvilinear flow is studied. In a space of dimension of more than two, the Stokes fluid has two viscometric functions, i.e., the shear-stress function and the normal-stress difference function. In a space of twodimension the fluid has only the shear-stress function. It is proved that the curvilinear flow in a space of any dimension is equivalent to a pure shearing flow, if the motion is observed by an appropriately rotated coordinate system. The simple shearing flow with a rate of shear is also analyzed.