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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., Comment: 17 pages, 12 figures

The motion of a colloidal probe in a viscoelastic fluid is described by friction or mobility, depending on whether the probe is moving with a velocity or feeling a force. While the Einstein relation describes an inverse relationship valid for Newtonian solvents, both concepts are generalized to time-dependent memory kernels in viscoelastic fluids. We theoretically and experimentally investigate their relation by considering two observables: the recoil after releasing a probe that was moved through the fluid and the equilibrium mean squared displacement (MSD). Applying concepts of linear response theory, we generalize Einstein's relation and thereby relate recoil and MSD, which both provide access to the mobility kernel. With increasing concentration, however, MSD and recoil show distinct behaviors, rooted in different behaviors of the two kernels. Using two theoretical models, a linear two-bath particle model and hard spheres treated by mode-coupling theory, we find a Volterra relation between the two kernels, explaining differing timescales in friction and mobility kernels under variation of concentration., Comment: 12 pages, 7 figures