Non-equilibrium dynamics of actively-driven viscoelastic networks

To maintain internal organization, living systems need to dissipate energy at the molecular level, thus operating far from thermodynamic equilibrium. At the larger scales, non-equilibrium behavior can be manifest through circulation in the phase space of mesoscopic coordinates and various techniques and measures have been developed to detect and quantify this circulation. It is however still not clear what these measures teach us about the physical properties of the system and how they can be employed to make useful predictions. In the following thesis, we will first review recent progress in detecting and quantifying mesoscopic currents in soft living systems; we will then employ minimal models of actively driven viscoelastic networks to understand how the non-equilibrium dynamics are affected by the internal mechanical structure. Finally, we will introduce a method of assessing non-equilibrium fluctuations in a tracking-free fashion via time-lapse microscopy imaging.Um ihre innere Organisation aufrechtzuerhalten, müssen lebende Systeme Energie auf molekularer Ebene dissipieren. Somit arbeiten sie weit entfernt vom thermodynamischen Gleichgewicht. Auf größeren Skalen kann sich Nichtgleichgewichtsverhalten in zirkulärer Bewegung im Phasenraum der mesoskopischen Koordinaten niederschlagen. Um diese Zirkulation zu erkennen und zu quantifizieren, wurden verschiedene Techniken und Methoden entwickelt. Es ist jedoch immer noch nicht klar, was diese Methoden über die physikalischen Eigenschaften des Systems aussagen und wie sie für nützliche Vorhersagen eingesetzt werden können. In dieser Arbeit werden wir zunächst die jüngsten Fortschritte bei der Erkennung und Quantifizierung mesoskopischer Ströme in Systemen aus weicher lebendender Materie untersuchen. Anschließend werden wir minimale Modelle aktiv getriebener viskoelastischer Netzwerke verwenden, um zu verstehen, wie die Nichtgleichgewichtsdynamik durch deren interne mechanische Struktur beeinflusst wird. Schließlich werden wir eine Methode zur Messung von Nichtgleichgewichtsfluktuationen aus Zeitraffermikroskopieaufnahmen, ohne tracking auskommt, einführen

Non-equilibrium dynamics of actively-driven viscoelastic networks

To maintain internal organization, living systems need to dissipate energy at the molecular level, thus operating far from thermodynamic equilibrium. At the larger scales, non-equilibrium behavior can be manifest through circulation in the phase space of mesoscopic coordinates and various techniques and measures have been developed to detect and quantify this circulation. It is however still not clear what these measures teach us about the physical properties of the system and how they can be employed to make useful predictions. In the following thesis, we will first review recent progress in detecting and quantifying mesoscopic currents in soft living systems; we will then employ minimal models of actively driven viscoelastic networks to understand how the non-equilibrium dynamics are affected by the internal mechanical structure. Finally, we will introduce a method of assessing non-equilibrium fluctuations in a tracking-free fashion via time-lapse microscopy imaging.Um ihre innere Organisation aufrechtzuerhalten, müssen lebende Systeme Energie auf molekularer Ebene dissipieren. Somit arbeiten sie weit entfernt vom thermodynamischen Gleichgewicht. Auf größeren Skalen kann sich Nichtgleichgewichtsverhalten in zirkulärer Bewegung im Phasenraum der mesoskopischen Koordinaten niederschlagen. Um diese Zirkulation zu erkennen und zu quantifizieren, wurden verschiedene Techniken und Methoden entwickelt. Es ist jedoch immer noch nicht klar, was diese Methoden über die physikalischen Eigenschaften des Systems aussagen und wie sie für nützliche Vorhersagen eingesetzt werden können. In dieser Arbeit werden wir zunächst die jüngsten Fortschritte bei der Erkennung und Quantifizierung mesoskopischer Ströme in Systemen aus weicher lebendender Materie untersuchen. Anschließend werden wir minimale Modelle aktiv getriebener viskoelastischer Netzwerke verwenden, um zu verstehen, wie die Nichtgleichgewichtsdynamik durch deren interne mechanische Struktur beeinflusst wird. Schließlich werden wir eine Methode zur Messung von Nichtgleichgewichtsfluktuationen aus Zeitraffermikroskopieaufnahmen, ohne tracking auskommt, einführen

Microviscosity, microdiffusivity, and normal stresses in colloidal dispersions

In active, nonlinear microrheology, a Brownian “probe” particle is driven through a complex fluid and its motion tracked in order to infer the mechanical properties of the embedding material. In the absence of external forcing, the probe and background particles form an equilibrium microstructure that fluctuates thermally. Probe motion through the medium distorts the microstructure; the character of this deformation, and hence its influence on probe motion, depends on the strength with which the probe is forced, F^(ext), compared to thermal forces, kT/b, defining a Péclet number, Pe = F^(ext)/(kT/b), where kT is the thermal energy and b is the characteristic microstructural length scale. Recent studies showed that the mean probe speed can be interpreted as the effective material viscosity, whereas fluctuations in probe velocity give rise to an anisotropic force-induced diffusive spread of its trajectory. The viscosity and diffusivity can thus be obtained by two simple quantities—mean and mean-square displacement of the probe. The notion that diffusive flux is driven by stress gradients leads to the idea that the stress can be related directly to the microdiffusivity, and thus the anisotropy of the diffusion tensor reflects the presence of normal stress differences in nonlinear microrheology. In this study, a connection is made between diffusion and stress gradients, and a relation between the particle-phase stress and the diffusivity and viscosity is derived for a probe particle moving through a colloidal dispersion. This relation is shown to agree with two standard micromechanical definitions of the stress, suggesting that the normal stresses and normal stress differences can be measured in nonlinear microrheological experiments if both the mean and mean-square motion of the probe are monitored. Owing to the axisymmetry of the motion about a spherical probe, the second normal stress difference is zero, while the first normal stress difference is linear in Pe for Pe≫1 and vanishes as Pe^4 for Pe≪1. The expression obtained for stress-induced migration can be viewed as a generalized nonequilibrium Stokes–Einstein relation. A final connection is made between the stress and an “effective temperature” of the medium, prompting the interpretation of the particle stress as the energy density, and the expression for osmotic pressure as a “nonequilibrium equation of state.

Smoothed profile method for direct numerical simulations of hydrodynamically interacting particles

A general method is presented for computing the motions of hydrodynamically interacting particles in various kinds of host fluids for arbitrary Reynolds numbers. The method follows the standard procedure for performing direct numerical simulations (DNS) of particulate systems, where the Navier-Stokes equation must be solved consistently with the motion of the rigid particles, which defines the temporal boundary conditions to be satisfied by the Navier-Stokes equation. The smoothed profile (SP) method provides an efficient numerical scheme for coupling the continuum fluid mechanics with the dispersed moving particles, which are allowed to have arbitrary shapes. In this method, the sharp boundaries between solid particles and the host fluid are replaced with a smeared out thin shell (interfacial) region, which can be accurately resolved on a fixed Cartesian grid utilizing a SP function with a finite thickness. The accuracy of the SP method is illustrated by comparison with known exact results. In the present paper, the high degree of versatility of the SP method is demonstrated by considering several types of active and passive particle suspensions