Properties of a nonlinear bath: Experiments, theory, and a stochastic Prandtl-Tomlinson model

Abstract

A colloidal particle is a prominent example of a stochastic system, and, if suspended in a simple viscous liquid, very closely resembles the case of an ideal random walker. A variety of new phenomena have been observed when such colloid is suspended in a viscoelastic fluid instead, for example pronounced nonlinear responses when the viscoelastic bath is driven out of equilibrium. Here, using a micron-sized particle in a micellar solution, we investigate in detail, how these nonlinear bath properties leave their fingerprints already in equilibrium measurements, for the cases where the particle is unconfined or trapped in a harmonic potential. We find that the coefficients in an effective linear (generalized) Langevin equation show intriguing inter-dependencies, which can be shown to arise only in nonlinear baths: For example, the friction memory can depend on the external potential that acts only on the colloidal particle (as recently noted in simulations of molecular tracers in water in Phys. Rev. X 7, 041065 (2017)), it can depend on the mass of the colloid, or, in an overdamped setting, on its bare diffusivity. These inter-dependencies, caused by so-called fluctuation renormalizations, are seen in an exact small time expansion of the friction memory based on microscopic starting points. Using linear response theory, they can be interpreted in terms of microrheological modes of force-controlled or velocity-controlled driving. The mentioned nonlinear markers are observed in our experiments, which are astonishingly well reproduced by a stochastic Prandtl-Tomlinson model mimicking the nonlinear viscoelastic bath. The pronounced nonlinearities seen in our experiments together with the good understanding in a simple theoretical model make this system a promising candidate for exploration of colloidal motion in nonlinear stochastic environments.

arXiv comment14 pages, 12 figures changes v2: minor changes regarding abstract, and Fig. 11

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Cited by in corpus (9)

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• Two step micro-rheological behavior in a viscoelastic fluid
• How are mobility and friction related in viscoelastic fluids?
• Dynamics of a colloidal particle coupled to a Gaussian field: from a confinement-dependent to a non-linear memory
• Non-Gaussian fluctuations of a probe coupled to a Gaussian field
• Adjoint-based calibration of nonlinear stochastic differential equations
• Nonlinear Langevin functionals for a driven probe
• Memory-induced alignment of colloidal dumbbells
• Micro-rheology of a particle in a nonlinear bath: Stochastic Prandtl-Tomlinson model