Flow of a simple non-newtonian fluid past a sphere

Summary Creeping flow past a sphere is solved for a limiting case of fluid behaviour: an abrupt change in viscosity.List of Symbols d_ij Component of rate-of-deformation tensor - F_d Drag force exerted on sphere by fluid - G^(d) Coefficients in expression for _ij in terms of d_ij - G_YOJK^(d) Coefficients in power series representing G^(d) - R Radius of sphere - r Spherical coordinate - V Velocity of fluid very far from sphere - v_i Component of the velocity vector - x Dimensionless radial distance, r/R - x_i Rectangular Cartesian coordinate - Dimensionless quantity defined by (26) - ^(d) Potential defined by (7) - Value of x denoting border between Regions 1 and 2 as a function of - ₁, ₂ Lower and upper limiting viscosities defined by (10) - Spherical coordinate - * Value of for which =1 - Value of denoting border between regions 1 and 2 as a function of x - Newtonian viscosity - _ij Component of the stress tensor - Spherical coordinate - ₁, ₂ Stream functions defined by (12) and (14) - Second and third invariants of the stress tensor and of the rate-of-deformation tensor, defined by (3)