Hans Christian Öttinger

Dynamics and thermodynamics of complex fluids. I. Development of a general formalism

We recognize some universal features of macroscopic dynamics describing the approach of a well-established level of description (that is, successfully tested by experimental observations) to equilibrium. The universal features are collected in a general equation for the nonequilibrium reversible-irreversible coupling (abbreviated as GENERIC). In this paper we formulate a GENERIC, derive properties of its solutions, and discuss their physical interpretation. The relation of the GENERIC with thermodynamics is most clearly displayed in a formulation that uses contact structures. The GENERIC is also discussed in the presence of noise. In applications we either search for new governing equations expressing our insight into a particular complex fluid or take well-established governing equations and cast them into the form of a GENERIC. In the former case we obtain the governing equations as particular realizations of the GENERIC structure; in the latter case we justify the universality of the GENERIC and derive some properties of solutions. Both types of applications are discussed mainly in the following paper [Phys. Rev. E 56, 6633 (1997)].

Calculation of viscoelastic flow using molecular models: the connffessit approach

Abstract A new method for numerical calculation of viscoelastic flow based on simulation of molecular models of polymers is presented. The CONNFFES-SIT ( C alculation o f N on- N ewtonian F low: F inite E lements and S tochastic S imulation T echnique) approach directly combines standard finite element methods as currently used in the calculation of viscoelastic flow with stochastic simulations of polymer dynamics and thus obviates the need for a rheological constitutive equation to describe the fluid. The stresses are obtained from the molecular configurations rather than from constitutive equations. As an illustration of the method, the time development of plane Couette flow is studied for the upper-convected Maxwell, Oldroyd-B, FENE-P and FENE fluids. For the upper-convected Maxwell, Oldroyd-B and FENE-P models comparisons with analytical and existing numerical solutions are presented. Significant deviations between the behavior of the FENE-P and FENE models for the start-up of plane Couette flow are found.

Minimal entropic kinetic models for hydrodynamics

We derive minimal discrete models of the Boltzmann equation consistent with equilibrium thermodynamics, and which recover correct hydrodynamics in arbitrary dimensions. A new discrete velocity model is proposed for the simulation of the Navier-Stokes-Fourier equation and is tested in the setup of Taylor vortex flow. A simple analytical procedure for constructing the equilibrium for thermal hydrodynamics is established. For the lattice Boltzmann method of isothermal hydrodynamics, the explicit analytical form of the equilibrium distribution is presented. This results in an entropic version of the isothermal lattice Boltzmann method with the simplicity and computational efficiency of the standard lattice Boltzmann model.

A detailed comparison of various FENE dumbbell models

Abstract The rheological behaviour of dilute solutions of finitely extensible non-linear elastic (FENE) dumbbells in both steady state and transient shear and simple elongational flow is investigated. Three dumbbell models are compared: the original FENE model with the Warner spring force, which is treated by brownian dynamics simulations, and the FENE-P model based on the Peterlin approximation and the FENE-CR model as suggested by Chilcott and Rallison, which are treated by standard numerical techniques. It is shown that in the linear viscoelastic limit and in steady state flows the behaviour is similar, except for the FENE-CR dumbbell in shear flow, modelling a Boger fluid. In transient flows larger differences appear.

Brownian configuration fields and variance reduced CONNFFESSIT

Stochastic simulation techniques, such as Brownian dynamics, provide us an extremely powerful tool for solving the usually nonlinear equations describing polymer dynamics in solutions and melts [1]. However, the most challenging problems (e.g. the investigation of the universal behaviour of long polymer chains, or the flow calculation based on stochastic simulation techniques) involve a very large number of degrees of freedom and hence require an enomous amount of computer time. In order to solve such problems on currently available computers it is therefore necessary to develop strategies to drastically suppress the level of the fluctuations in the simulations. The purpose of this note is to show that the recently proposed concept of Brownian configuration fields [2] in viscoelastic flow calculations can be regarded as an extremely powerful extension of variance reduction techniques based on parallel process simulation.

A thermodynamically admissible reptation model for fast flows of entangled polymers. II. Model predictions for shear and extensional flows

Numerical predictions of a previously proposed thermodynamically consistent reptation model for linear entangled polymers are presented for shear and extensional flows. Comparisons with experimental data and two alternative molecular-based models are given in detail. The model studied in this paper incorporates the essence of double reptation, convective constraint release, and chain stretching, and it avoids the independent alignment approximation. Here, no use is made of the ingredient of anisotropic tube cross sections of the previously proposed model. Simulation results reveal that the model at a highly simplified level with few structural variables, i.e., four degrees of freedom, is able to capture qualitatively all features of the available experimental observations and is highly competitive with recently proposed models in describing nonlinear rheological properties of linear entangled polymers.

A thermodynamically admissible reptation model for fast flows of entangled polymers

The primary purpose of this paper is to introduce the effect of chain stretching into a previously developed, thermodynamically admissible reptation model incorporating anisotropic tube cross sections, double reptation, and convective constraint release, while avoiding the independent alignment approximation. A second goal is the detailed illustration of the thermodynamic modeling approach. Two versions of the model with different stretching mechanisms are proposed, and the simpler one sheds new light on thermodynamically admissible reptation models without independent alignment. The stochastic reformulation of the new model, its simulation, its linear viscoelastic properties, its predictions for rapid double-step shear strains, and the model parameters are discussed in detail.

Model Reduction and Coarse-Graining Approaches for Multiscale Phenomena

Model reduction and coarse-graining are important in many areas of science and engineering. How does a system with many degrees of freedom become one with fewer? How can a reversible micro-description be adapted to the dissipative macroscopic model? These crucial questions, as well as many other related problems, are discussed in this book. Specific areas of study include dynamical systems, non-equilibrium statistical mechanics, kinetic theory, hydrodynamics and mechanics of continuous media, (bio)chemical kinetics, nonlinear dynamics, nonlinear control, nonlinear estimation, and particulate systems from various branches of engineering. The generic nature and the power of the pertinent conceptual, analytical and computational frameworks helps eliminate some of the traditional language barriers, which often unnecessarily impede scientific progress and the interaction of researchers between disciplines such as physics, chemistry, biology, applied mathematics and engineering. All contributions are authored by experts, whose specialities span a wide range of fields within science and engineering

A model of dilute polymer solutions with hydrodynamic interaction and finite extensibility. I: Basic equations and series expansions

A bead-spring chain model is used to describe dilute polymer solutions. Two important effects, the hydrodynamic interaction between the beads of a single chain and the finite extensibility of the springs connecting the beads, are treated in a self-consistently averaged form. For the resulting model, a rheological equation of state, a third-order retarded-motion expansion, and a second-order codeformational memory-integral expansion are derived. Furthermore, the parameters characterizing the model and the limit of infinitely long chains are discussed in great detail.

Generalized Zimm model for dilute polymer solutions under theta conditions

The consistent averaging approximation for the hydrodynamic interaction is applied to linear chains with Gaussian chain statistics in order to improve the well‐known Zimm model, which is based on the preaveraged hydrodynamic interaction. For the resulting generalized Zimm model a rheological equation of state is derived which is then used as a starting point for the derivation of a codeformational memory integral expansion and a retarded motion expansion as well as for numerical investigations. The material functions predicted by the generalized Zimm model for steady shear flow and for small amplitude oscillatory shear flow are discussed in great detail. Finally, the limit of infinitely long chains is thoroughly studied by analytical and numerical techniques.