Steady flow of a slightly viscoelastic fluid between rotating spheres
In equations (1.2), (i = 1, 2, 3) denote the velocity components in the xt coordinate system. The coefficients in the tensor polynomial Pa are scalar invariants of the kinematic tensors, the coefficient of ATM vanishing when all the invariants vanish. The polynomial Pa may be assumed to have no term of degree zero, for any such term could be incorporated into the undetermined pressure p. One type of flow considered in the previous paper was that generated solely by rigid walls in steady motion parallel to themselves, the fluid mass having no bounding surfaces other than rigid walls and no body forces being applied to the fluid. It was shown that flows of this type can be investigated quantitatively by the following procedure: (i) A solution (v' , p') to the equations of motion for an incompressible Newtonian fluid with viscosity m is calculated neglecting inertia subject to the boundary condition that the fluid velocity at the walls match the velocity of the walls; (ii) the solution (y' , p') calculated in (i) is introduced into the equations of motion for the incompressible viscoelastic fluid described above, and the body forces required to support this solution are calculated neglecting inertia; (in) a solution (v'/ , p") to the equations of motion for an incompressible Newtonian fluid under the action of the body forces calculated in (ii) is calculated neglecting inertia, subject to the boundary condition of vanishing velocity on all the boundaries of the fluid mass;