Theoretical investigations as basis for a new rheometer which measures the non-linear mechanical properties of polymeric solutions or melts

Abstract

The theoretical and experimental studies of the isothermal flow of a second-order (non- Newtonian ) fluid in the annular region between two eccentric spheres are investigated . The study has been carried out in tenns of the three -dimensional bispherical coordinates (a, ,<p), where the inner sphere is rotating with angular velocity Q and the outer sphere is kept at rest .

A second-order stream-function\j/ 2 (a, ),through which the secondary flow field .!12 (a, ) can be determined , has been properly formulated by solving the three-dimensional inhomogenious biharmonic vector equation . On the basis of the obtained velocity field , the distribution of the

surface tractions on the boundaries are determined . The resultant forces acting on the boundaries as well as the resultant torques about the common axis of rotation , up to the second-order ,are calculated . Based on the previous calculations , the eccentric spheres rheometer IS designed which allows the determination of the combined second-order coefficient (a 2 + 2a 1) besides the viscosity coefficient f.L. The measurements of the viscosity coefficient f.L and the first normal stress difference coefficient(a 2 + 2a 1 ) of some polymeric solutions by the eccentric spheres rheometer have been carried out . The obtained results are compared with -t e other experimental data delivered by some other rheometers .