USE OF THE FALLING BALL VISCOMETER TO OBTAIN FLOW CURVES FOR INELASTIC, NON-NEWTONIAN FLUIDS

This paper reports on a numerical study of the drag force on a sphere moving at constant velocity in inelastic non-Newtonian fluids. The intended application of this work is in the use of the falling ball viscometer to determine flow curves for these fluids. Numerical solutions were obtained for the case of the sphere moving along the axis of a cylinder and ratios of cylinder to sphere diameter from 10 to 40 were examined. In obtaining the solutions inertia was neglected. To represent the fluid's flow curve the modified power law model was used. This model produces Newtonian behavior as the shear rate approaches zero and power law behavior as the shear rate becomes large. A control volume finite difference method was used to calculate the flow field and drag force. Solutions were obtained for values of the power law index from 1.0 to 0.35. Results are compared with others' calculated results in the power law limit and with published experimental data in the transition region of the flow curve. Two methods of using the falling ball viscometer to determine the flow curves of non-Newtonian fluids are presented. The first assumes that sphere drag data cover the Newtonian and power law limits. The second uses an apparent flow index, and an average shear rate and the corresponding shear stress. This is an extension of an approach used by others. © 1990.