Siegfried Hess

On the theory of irreversible processes in molecular liquids and liquid crystals, nonequilibrium phenomena associated with the second and fourth rank alignment tensors

A theory for nonequilibrium phenomena primarily associated with the molecular orientation in liquids and liquid crystals is developed within the framework of irreversible thermodynamics. The alignment tensors of rank 2 and 4 are taken into consideration as additional macroscopic variables. With appropriate assumptions concerning the dependence of the internal energy, specific volume and the entropy on the alignment, a dynamic Landau theory is obtained. Nonlinear relaxation equations are derived for the alignment tensors. They possess zero and nonzero stable stationary solutions corresponding to the isotropic and nematic phases of a liquid crystal when the temperature is above or below the transition temperature. Some further applications of the relaxation equations are discussed, in particular fluctuations of the intensity of the depolarized component of scattered light.

Similarities and differences in the nonlinear flow behavior of simple and of molecular liquids

After the introduction of viscosity coefficients describing the non-Newtonian flow behavior and the normal pressure differences in a plane Couette symmetry, methods for the calculation of these coefficients are presented and some remarks on the connection with the linear viscoelasticity are made. The nonlinear flow behavior stems from the influence of the vorticity of the flow field and of the symmetric traceless shear rate tensor on the primary shear-rate-induced anisotropy of molecular distribution functions. In the case of molecular liquids the orientational distribution of the molecular axes (alignment) is the most relevant quantity; in simple liquids it is the pair-correlation function. Results are presented which can be inferred from an extended version of irreversible thermodynamics of molecular liquids; from a Fokker-Planck equation approach and for simple liquids, from a kinetic equation of Kirkwood-Smoluchowski type for the pair-correlation function. Finally, some modifications are discussed which lead to a nonanalytic shear-rate and frequency dependence as observed for the viscosity coefficients in the computer simulations.

Stokes-Maxwell relations for the distorted fluid microstructure☆

Abstract Relationships between the coefficients of the expansion of the pair correlation function for a fluid subjected to a shear are derived from a model kinetic equation. They equate a relaxation time with the viscosity and shear modulus of the fluid. Nonlinear phenomena are considered. The results are tested using nonequilibrium molecular dynamic simulation data for a soft sphere system close to freezing. Agreement between the theory and the simulations is satisfactory.

Diffusion in a laminar flow: Shear rate dependence of correlation functions and of effective transport coefficients

The diffusionequation for independent Brownian particles suspended in a fluid undergoing plane Couetteshear flow is solved in Fourier space by means of the Campbell–Baker–Hausdorff expansion for the product of exponentials of noncommuting operators. Explicit solutions are derived and numerically evaluated for an initial Gaussian distribution with no source and for a continuous stationary source with a Gaussian spatial distribution. For the latter problem, the tensor describing the curvature of the steady‐state distribution at the origin is analyzed in some detail and is shown to possess a dependence on shear rate very similar to that of the pressure tensor obtained in computer simulations of simple liquids under shear by Hanley and Evans.

Nonlinear flow behavior of the Boltzmann gas

A nonlinear inhomogeneous relaxation equation for the friction pressure is derived from the Boltzmann equation with the help of the moment method. Nonlinear terms emerge from both the flow term and the quadratic part of the Boltzmann collision operator. The importance of the latter contributions is characterized by coefficients which are expressed in terms of Chapman-Cowling collision integrals and can thus be evaluated for various collision models. Rheological consequences are analysed for stationary viscous flows in special geometries, viz. plane Couette flow, four-roller flow and uniaxial elongational flow. The resulting non-Newtonian viscosity and similar coefficients associated with normal pressure differences (viscometric functions) are discussed and displayed graphically as functions of the shear rate or the elongation rate.

Decay of bcc-structure and of bond-orientational order in a fluid

The decay of an initially prepared bcc structure and the bond-orientational order (anisotropy of the first coordination shell) are studied in a non-equilibrium molecular dynamics simulation for a fluid of 1024 particles interacting with a repulsive r-12 potential. Data are presented for pair-correlation functions and order parameters associated with an angle dependence described by cubic harmonics of the ranks 4, 6 and 8. These cubic pair-correlation functions and cubic order parameters are defined by the expansion of the pair-correlation function and of the bond orientational distribution function with respect to Cartesian tensors. The relaxation of the local anisotropy shows a pretransformational slowing down for densities approaching the freezing point.

Diffusio birefringence in colloidal suspensions and macromolecular liquids

Abstract The constitutive law for diffusio birefringence is introduced. Theoretical results are reported for the characteristic coefficient determining the size of this new effect in a colloidal suspension or a macromolecular liquid.

A solvable weak-potential model of a non-Newtonian fluid

A theoretical model is developed for a non-Newtonian fluid of spherical molecules interacting with a weak potential. The Kirkwood-Smoluchowski equation for planar Couette flow reduces in leading order in potential strength to a shear-diffusion equation with an inhomogeneous source term. The pressure tensor elements are calculated and, for a Gaussian potential, reduce to one-dimensional integrals which are evaluated numerically. The model reproduces several qualitative features of non-Newtonian liquids and the computer simulations of Evans and Hanley. These features include shear thinning, shear dilatancy, normal pressure differences, and dependence on shear rate to a half-integer power.

Computer simulation of stress relaxation in fluids

Abstract The viscoelastic properties of fluids - time correlation functions, shear moduli and values for relaxation time and viscosity coefficients — are obtained by the simulation of stress relaxation. Some specific results are presented for a Lennard-Jones liquid and a soft sphere fluid.

Nonlinear flow behavior of gases

Abstract Computer simulation results for a dilute Lennard-Jones gas subjected to a shear are compared with theoretical predictions from an approximate solution of the Boltzmann equation. Nonlinear, nonnewtonian characteristics are observed in the gas, including the existence of normal pressure differences. Agreement between the simulations and kinetic theory is satisfactory.