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General solution of the particle momentum equation in unsteady Stokes flows. (English) Zbl 0935.76018
The aim is to give an analytical method for determining the general solution of the particle momentum equation for unsteady Stokes flows. The method is based on applying a fractional differential operator to the first-order integro-differential equation of motion in order to transform the original equation into a second-order nonhomogeneous equation. This equation is finally solved by the method of variation of parameters. The analytical method is applied to some particular problems. The first one corresponds to the gravitationally induced motion of a particle through an otherwise quiescent fluid. The second problem describes the motion of a particle caused by a background velocity field that accelerates the particle linearly in time, and finally, the third problem describes the motion of a particle in a fluid that undergoes an impulsive acceleration. In each case, the analytical solution is compared to other solutions available in the literature.
MSC:
76D07Stokes and related (Oseen, etc.) flows