Unsteady motion of a Maxwellian fluid droplet in a Maxwellian medium under the action of monotonic and periodic forces

Unsteady motion of a Maxwellian fluid droplet, which arises in a quiescent Maxwellian medium under the action of monotonic and periodic forces, is considered. In the initial period of time smaller than the relaxation time, the droplet is affected by elastic forces on the part of the fluid; moreover, the droplet itself is a viscoelastic material. A solution of the problem in the first approximation is found. The dependence of the amplitude of droplet velocity and the shift of the phase of oscillations on the relaxation time of the external and internal media and also on the frequency of oscillations of the driving force is analyzed. The passage to the limit in terms of density and viscosity of the internal medium is performed.