Accelerating motion of a sphere in a maxwell fluid

摘要

The translatory accelerating motion of a sphere due to an arbitrarily applied force in an unlimited Maxwell fluid is considered. The exact solutions for the velocity of the sphere for three particular types of accelerating motion are presented. The first is for a falling sphere; the second is for the decelerating motion of a sphere after the force which maintains the sphere with a constant velocity is removed; the third is for the motion of the sphere subjected to an impulsive force. The exact solutions are expressed in terms of real, regular, definite integrals which can be evaluated by numerical technique. Also presented are the asymptotic solutions for the velocity of the sphere in all three cases which are valid for small values of time.