How are mobility and friction related in viscoelastic fluids?

Abstract

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.

Friction of a driven chain: role of momentum conservation, Goldstone and radiation modes

“…In the overdamped limit, the end of Brillouin zone is reached for ω0 γL ≈ 8, and the second term in equation ( 44 The different regimes are summarized in figure 3(c) which shows Γ as a function of ω0 /γ L for a fixed chain length N = 10 4 and different values of damping parameter γL . When ω0 ≪ γL (the overdamped limit), Γ exhibits a regime following equation (44) followed by saturation as one decreases ω0 beyond l L ≈ N. The radiation mode ( Γ = 1) is observed at the onset of the underdamped limit for γL ≪ 1 followed by the regime corresponding to the end of the Brillouin zone, where the friction coefficient is dominated by the bare friction of the driven bead, Γ = γL .…”

“…In time domain, Γ of equation (50) yields Γ(t) ∼ t 3/2 and the mean square displacement (MSD) ∼ t 1/2 . We omit here a detailed translation from friction to diffusion kernel [44].…”

Memory-induced alignment of colloidal dumbbells

“…As motion is prescribed, this description is useful in the presence of a (strong) optical trap. The connection between dynamics with trap on and trap off is non-trivial 12,13,21 , and we do not discuss it here for simplicity.…”

“…Therefore, pronounced memory effects (non-Markovian behavior) can be expected in such systems due to the slow relaxation of the fluid's mesoscopic microstructure and which has been confirmed using microrheological techniques [2][3][4][5][6][7][8][9] . In particular, so-called recoil experiments, where first a driving force is applied to a colloidal particle which is then suddenly removed, provide a useful method to explore how the motion of particles is modified when coupled to a slowly relaxing environment [10][11][12][13] . Previous studies have revealed rather general double-exponential recoil dynamics which can be quantitatively described by so-called bath particle models, where the response of the fluid is mimicked by harmonically coupled fictitious bath particles 12,14 .…”

Minimal model of diffusion with time changing Hurst exponent

“…This fact restricts some of its applications-crucially for us it makes it impossible to describe an increasing number of regime-switching anomalous diffusion systems in which the anomalous diffusion exponent and the diffusivity change as functions of time. Examples for such phenomena include the motion of a tracer in the changing viscoelastic environment of cells during their cycle [53] or in viscoelastic solutions under pressure and/or concentration changes [54,55], in actin gels with changing mesh size [56], the motion of lipid molecules in cooling bilayer membranes [35], passive and active intracellular movement after treatment with chemicals [37,57], or intra-and inter-daily variations in the movement dynamics of larger animals [58]. Quite abrupt changes of H and/or D may be effected by binding to larger objects or surfaces [41,59] or multimerization [59,60] of the tracer.…”