Active and passive microrheology with large tracers in hard colloids
2023-10-10, Orts Gómez, Francisco José, Maier, Manuel, Fuchs, Matthias, Ortega, Gloria, Garzón, Ester Martin, Puertas López, Antonio Manuel
The dynamics of a tracer particle in a bath of quasi-hard colloidal spheres is studied by Langevin dynamics simulations and mode coupling theory (MCT); the tracer radius is varied from equal to up to seven times larger than the bath particles radius. In the simulations, two cases are considered: freely diffusing tracer (passive microrheology) and tracer pulled with a constant force (active microrheology). Both cases are connected by linear response theory for all tracer sizes. It links both the stationary and transient regimes of the pulled tracer (for low forces) with the equilibrium correlation functions; the velocity of the pulled tracer and its displacement are obtained from the velocity auto-correlation function and the mean squared displacement, respectively. The MCT calculations give insight into the physical mechanisms: At short times, the tracer rattles in its cage of neighbours, with the frequency increasing linearly with the tracer radius asymptotically. The long-time tracer diffusion coefficient from passive microrheology, which agrees with the inverse friction coefficient from the active case, arises from the transport of transverse momentum around the tracer. It can be described with the Brinkman equation for the transverse flow field obtained in extension of MCT, but cannot be recovered from the MCT kernel coupling to densities only. The dynamics of the bath particles is also studied; for the unforced tracer the dynamics is unaffected. When the tracer is pulled, the velocity field in the bath follows the prediction of the Brinkman model, but different from the case of a Newtonian fluid.
Emergence of Long-Ranged Stress Correlations at the Liquid to Glass Transition
2017-12-29, Maier, Manuel, Zippelius, Annette, Fuchs, Matthias
A theory for the nonlocal shear stress correlations in supercooled liquids is derived from first principles. It captures the crossover from viscous to elastic dynamics at an idealized liquid to glass transition and explains the emergence of long-ranged stress correlations in glass, as expected from classical continuum elasticity. The long-ranged stress correlations can be traced to the coupling of shear stress to transverse momentum, which is ignored in the classic Maxwell model. To rescue this widely used model, we suggest a generalization in terms of a single relaxation time τ for the fast degrees of freedom only. This generalized Maxwell model implies a divergent correlation length ξ∝τ as well as dynamic critical scaling and correctly accounts for the far-field stress correlations. It can be rephrased in terms of generalized hydrodynamic equations, which naturally couple stress and momentum and furthermore allow us to connect to fluidity and elastoplastic models.
Stress auto-correlation tensor in glass-forming isothermal fluids : From viscous to elastic response
2018-08-28, Maier, Manuel, Zippelius, Annette, Fuchs, Matthias
We develop a generalized hydrodynamic theory, which can account for the build-up of long-ranged and long-lived shear stress correlations in supercooled liquids as the glass transition is approached. Our theory is based on the decomposition of tensorial stress relaxation into fast microscopic processes and slow dynamics due to conservation laws. In the fluid, anisotropic shear stress correlations arise from the tensorial nature of stress. By approximating the fast microscopic processes by a single relaxation time in the spirit of Maxwell, we find viscoelastic precursors of the Eshelby-type correlations familiar in an elastic medium. The spatial extent of shear stress fluctuations is characterized by a correlation length ξ which grows like the viscosity η or time scale τ ∼ η, whose divergence signals the glass transition. In the solid, the correlation length is infinite and stress correlations decay algebraically as r−d in d dimensions.
Stressfluctuations in glass-forming liquids
2018, Maier, Manuel
A model for the transverse shear stress in isothermal incompressible supercooled liquids was derived. The model shows damped transverse soundwaves and anisotropic long ranged long lived stress correlations in the solid-like state and exhibits anisotropic shear stress correlations in the liquid state. The conservation of mass and momentum are used within the Zwanzig-Mori projection operator formalism to decompose the shear stress tensor. The appearing memory kernel contains the full complexity of the problem. Based on the Zwanzig-Mori approach, the arising memory kernel is approximated using Maxwell's model for viscoelasticity with a single relaxation time. Within this approximation two characteristic scales could be identified the correlation length and the relaxation time. The correlation length characterizing the spatial extend of the solid-like region and grows proportionally to the relaxation time. In the elastic long time limit both the correlation length and the relaxation time diverge. The transverse shear stress tensor is the linear response to small amplitude oscillatory shear strain. The computed spectra depend on the wavevector direction even in the limit of vanishing wavevectors and show a damped resonance at the frequency of the transverse soundwave. The model can be rephrased in terms of generalized hydrodynamic equations. For overdamped dynamics, addressing colloidal dispersions, the spectra show an arresting peak in the loss modulus dependent on the wavevector direction.