A simple microswimmer model inspired by the general equation for nonequilibrium reversible-irreversible coupling

A simple mean-field microswimmer model is presented. The model is inspired by the nonequilibrium thermodynamics of multi-component fluids that undergo chemical reactions. These thermodynamics can be rigorously described in the context of the GENERIC (general equation for the nonequilibrium reversible-irreversible coupling) framework. More specifically, this approach was recently applied to non-ideal polymer solutions [T. Indei and J. D. Schieber, J. Chem. Phys. 146, 184902 (2017)]. One of the species of the solution is an unreactive polymer chain represented by the bead-spring model. Using this detailed description as inspiration, we then make several simplifying assumptions to obtain a mean-field model for a Janus microswimmer. The swimmer model considered here consists of a polymer dumbbell in a sea of reactants. One of the beads of the dumbbell is allowed to act as a catalyst for a chemical reaction between the reactants. We show that the mean-squared displacement (MSD) of the center of mass of this Janus dumbbell exhibits ballistic behavior at time scales at which the concentration of the reactant is large. The time scales at which the ballistic behavior is observed in the MSD coincide with the time scales at which the cross-correlation between the swimmer's orientation and the direction of its displacement exhibits a maximum. Since the swimmer model was inspired by the GENERIC framework, it is possible to ensure that the entropy generation is always positive, and therefore, the second law of thermodynamics is obeyed.

Nonequilibrium thermodynamics of dilute polymer solutions in flow

Modern materials processing applications and technologies often occur far from equilibrium. To this end, the processing of complex materials such as polymer melts and nanocomposites generally occurs under strong deformations and flows, conditions under which equilibrium thermodynamics does not apply. As a result, the ability to determine the nonequilibrium thermodynamic properties of polymeric materials from measurable quantities such as heat and work is a major challenge in the field. Here, we use work relations to show that nonequilibrium thermodynamic quantities such as free energy and entropy can be determined for dilute polymer solutions in flow. In this way, we determine the thermodynamic properties of DNA molecules in strong flows using a combination of simulations, kinetic theory, and single molecule experiments. We show that it is possible to calculate polymer relaxation timescales purely from polymer stretching dynamics in flow. We further observe a thermodynamic equivalence between nonequilibrium and equilibrium steady-states for polymeric systems. In this way, our results provide an improved understanding of the energetics of flowing polymer solutions.

Irreversible dynamics, Onsager-Casimir symmetry, and an application to turbulence

Irreversible contributions to the dynamics of nonequilibrium systems can be formulated in terms of dissipative, or irreversible, brackets. We discuss the structure of such irreversible brackets in view of a degeneracy implied by energy conservation, where we consider different types of symmetries of the bracket corresponding to the Onsager and Casimir symmetries of linear irreversible thermodynamics. Slip and turbulence provide important examples of antisymmetric irreversible brackets and offer guidance for the more general modeling of irreversible dynamics without entropy production. Conversely, turbulence modeling could benefit from elucidating thermodynamic structure. The examples suggest constructing antisymmetric irreversible brackets in terms of completely antisymmetric functions of three indices. Irreversible brackets without well-defined symmetry properties can arise for rare events, causing big configurational changes.

Bridging length and time scales in sheared demixing systems: from the Cahn-Hilliard to the Doi-Ohta model

We develop a systematic coarse-graining procedure which establishes the connection between models of mixtures of immiscible fluids at different length and time scales. We start from the Cahn-Hilliard model of spinodal decomposition in a binary fluid mixture under flow from which we derive the coarse-grained description. The crucial step in this procedure is to identify the relevant coarse-grained variables and find the appropriate mapping which expresses them in terms of the more microscopic variables. In order to capture the physics of the Doi-Ohta level, we introduce the interfacial width as an additional variable at that level. In this way, we account for the stretching of the interface under flow and derive analytically the convective behavior of the relevant coarse-grained variables, which in the long wavelength limit recovers the familiar phenomenological Doi-Ohta model. In addition, we obtain the expression for the interfacial tension in terms of the Cahn-Hilliard parameters as a direct result of the developed coarse-graining procedure. Finally, by analyzing the numerical results obtained from the simulations on the Cahn-Hilliard level, we discuss that dissipative processes at the Doi-Ohta level are of the same origin as in the Cahn-Hilliard model. The way to estimate the interface relaxation times of the Doi-Ohta model from the underlying morphology dynamics simulated at the Cahn-Hilliard level is established.

Flow properties of immiscible blends: Doi-Ohta model with active advection

The interface between two immiscible fluids both is influenced (advected) by the imposed flow and influences (perturbs) it. The perturbation then changes the advection. This phenomenon is taken into account in an extended Doi-Ohta model of rheological behavior of immiscible blends. The agreement of the rheological predictions with experimental data is improved.

Thermodynamically consistent incorporation of the Schneider rate equations into two-phase models

We formulate a solid-liquid two-phase model including viscous stresses, heat conduction in the two phases, as well as heat exchange through the interface, and a phase change in the structure of nonequilibrium thermodynamics described by a general equation for the nonequilibrium reversible-irreversible coupling (GENERIC). The evolution of the microstructure is studied in terms of the Schneider rate equations introducing the nucleation rate and the radial growth rate of the solid phase. The application of the GENERIC structure shows that this radial growth factor is not an additional, independent material function but is to be expressed in terms of the difference in the chemical potentials, in the temperatures, and in the pressures between the two phases. The contribution due to the pressure difference appears in conjunction with the surface tension in such a way, that a driving force results only if deviations from a generalized version of the Laplace equation occur. Furthermore, it is found that for conditions under which the radial growth rate is zero, the nucleation rate must vanish.

Derivation of a two-generator framework of nonequilibrium thermodynamics for quantum systems

Starting from the quantum description of isolated systems on the microscopic level we derive the two-generator formulation of nonequilibrium thermodynamics by means of the projection-operator technique. As a generalized canonical ensemble is employed, we obtain a convenient starting point for practical calculations in nonequilibrium thermodynamics; in particular, also in the classical limit. All dynamical material properties are contained in a canonical nonequilibrium correlation. However, the generalized canonical approach is inappropriate for systems with large fluctuations; possible steps toward a suitable generalization for quantum systems are discussed.