Nonlinear microrheology with time-dependent forces -- Application to recoils in viscoelastic fluids

This work presents a theoretical analysis of the motion of a tracer colloid driven by a time-dependent force through a viscoelastic fluid. The recoil of the colloid after application of a strong force is determined. It provides insights into the elastic forces stored locally in the fluid and their weakening by plastic processes. We generalize the mode coupling theory of microrheology to include time-dependent forces. After deriving the equations of motion for the tracer correlator and simplifying to a schematic model we apply the theory to a switch-off force protocol that features the recoiling of the tracer after cessation of the driving. We also include Langevin dynamics simulations to compare to the results of the theory. A non-monotonic trend of the recoil amplitude is found in the theory and confirmed in the simulations. The linear-response approximation is also verified in the small-force regime. While the overall agreement between simulation and theory is good, simulation shows that the theory predicts a too strong non-monotonous dependence of the recoil distance on the applied force.