Numerical solutions to creeping flow equations. Part 1: Falling ball rheometry
Abstract
Numerical solutions are described for the velocity and stress fields in a viscous Newtonian liquid contained in a cylindrical vessel during the passage of a solid sphere settling under the influence of gravity. By taking advantage of the mathematical analogy between incompressible creeping flow of a Newtonian liquid and incompressible elasticity in a Hookean solid, we use advanced, finite element, computer programs developed for solid mechanics to perform creeping flow calculations. The drag on the sphere, in an unbounded fluid, would be given by Stokes' law. Using finite element stress codes we calculate the additional drag on the sphere due to the presence of the containing walls of the cylinder and the upper free surface of the liquid. Good agreement with experimental data and with analytical calculations is obtained for a range of ball sizes. Our findings indicate that the finite element method is an accurate computational technique for solving this class of multiphase hydrodynamics problems.
 Publication:

Presented at the 17th Annual Meeting of the Fine Particle Society
 Pub Date:
 1986
 Bibcode:
 1986fps..meet.....W
 Keywords:

 Creep Properties;
 Finite Element Method;
 Flow Equations;
 Hydrodynamics;
 Liquid Filled Shells;
 Stresses;
 Computation;
 Computer Programs;
 Falling;
 Liquids;
 Stress Distribution;
 Velocity;
 Viscosity;
 Fluid Mechanics and Heat Transfer