Inertia effects in rheometrical flow systems Part 2: The balance rheometer

spherical Bessel-function of the first kind and order n complex wave number (po~/2q) ~ wave number in a Hookean material non-negative integer spherical polar coordinate radius of plates of orthogonal rheometer radius of inner hemisphere of balance rheometer radius of outer hemisphere of balance rheometer time physical components of displacement physical components of velocity cartesian coordinates spherical Bessel-function of the second kind and order n integration constants force complex shear modulus shear modulus of a Hookean material Bessel-function of the first kind and order 1⁄2 couple associated Legendre-function (spherical harmonie) of the first kind, degree v and order # Legendre polynomial of degree n associated Legendre-function (spherical harmonie) of the second kind, degree v and order # S strain Y ~ ( z ) Bessel-function of the second kind and order 1⁄2 ;' r~/(d r 3) 6 loss angle angle between rotation axis of hemispheres q viscosity 0 spherical polar coordinate ). wave length A second Lamé-function p density r shear stress q5 spherical polar coordinate co angular velocity uJr, w0, ~o4, physical components of the spin tensor