Simulation of the motion of a sphere through a viscous fluid

Abstract

We have designed a friendly program to help students, in the first courses of physics and engineering, to understand the motion of objects through fluids. In this paper we present a simulation of the dynamics of a sphere of arbitrary but relatively small radius through an incompressible viscous fluid. The external forces acting on the sphere are gravity, friction, a stochastic force that simulates microscopic interactions and buoyancy. The Reynolds numbers are small enough to assure unseparated and symmetrical flow around the sphere. The numerical analysis is carried out by solving the equation of motion using the Verlet algorithm. Besides the numerical results, the program includes an interactive animation of the physical phenomenon. Although originally conceived for teaching, the program may be used in research to investigate, among other things, the motion of raindrops or pollutants in the atmosphere.