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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. [ABSTRACT FROM AUTHOR]

If, in a hard sphere fluid, a single (test) particle is fixed, the other particles display a density profile that possesses long-ranged oscillations. Surprisingly, one can show via classical density functional theory that it takes a simple, purely repulsive (external) potential with a finite range in addition to the fixed hard sphere that forces these oscillations to vanish completely. This can give rise to interesting phenomena; however, it gained little attention in the past. In this work, we use the potential in question as an inter-component interaction in a binary hard-sphere mixture, where it is shown that the effective interaction induced by one component resembles qualitatively the well-known Asakura–Oosawa–Vrij potential and can lead to a liquid–gas phase transition in the other component. [ABSTRACT FROM AUTHOR]