We study the unsteady motion of a sphere immersed in a Stokes fluid and subject to an elastic force. The equations of motion for the sphere lead to an integro-differential equation, whose solution we study asymptotically. We prove that the position of the sphere reaches its equilibrium point with a power-law, t-gamma, with gamma = 1/2, 3/2, depending on the initial conditions. This behavior is due to the memory effect of the surrounding fluid.
ON THE APPROACH TO EQUILIBRIUM FOR A PENDULUM IMMERSED IN A STOKES FLUID / Cavallaro, Guido; Marchioro, Carlo. - In: MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. - ISSN 0218-2025. - STAMPA. - 20:11(2010), pp. 1999-2019. [10.1142/s0218202510004854]
ON THE APPROACH TO EQUILIBRIUM FOR A PENDULUM IMMERSED IN A STOKES FLUID
CAVALLARO, GUIDO;MARCHIORO, Carlo
2010
Abstract
We study the unsteady motion of a sphere immersed in a Stokes fluid and subject to an elastic force. The equations of motion for the sphere lead to an integro-differential equation, whose solution we study asymptotically. We prove that the position of the sphere reaches its equilibrium point with a power-law, t-gamma, with gamma = 1/2, 3/2, depending on the initial conditions. This behavior is due to the memory effect of the surrounding fluid.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
