The viscous resistance to motion of a sphere falling through a sheared non-Newtonian liquid

Measurements have been made of the viscous resistance experienced by a solid sphere moving through a non-Newtonian liquid (poly-iso-butylene solution) which is simultaneously being sheared in a direction perpendicular to the line of motion of the particle. The resistive force can be calculated from Stokes' law using an appropriate `transverse viscosity' which decreases with increase of the primary shear rate. The decrease is considerably less than the corresponding decrease of viscosity measured conventionally. The transverse viscosity would be expected to control the rate of settlement of particles suspended in a fluid flowing through a pipe.