Nonequilibrium dynamics and magnetoviscosity of moderately concentrated magnetic liquids: A dynamic mean--field study

A mean-field Fokker-Planck equation approach to the dynamics of ferrofluids in the presence of a magnetic field and velocity gradients is proposed that incorporates magnetic dipole-dipole interactions of the colloidal particles. The model allows to study the combined effect of a magnetic field and dipolar interactions on the viscosity of the ferrofluid. It is found that dipolar interactions lead to additional non-Newtonian contributions to the stress tensor, which modify the behavior of the non-interacting system. The predictions of the present model are in qualitative agreement with experimental results, such as presence of normal stress differences, enhancement and different anisotropy of magnetoviscous effect and the dependence of the viscosity on the hydrodynamic volume fraction. A quantitative comparison of the concentration dependence of the magnetoviscosity shows good agreement with experimental results for low concentrations.Comment: 12 pages, 5 figure

The Divergence of the Viscosity of a Fluid of Hard Spheres as an Indicator for the Fluid-Solid Phase Transition

Solution of the Kirkwood-Smoluchowski equation for a hard sphere fluid yields an expression for the viscosity which shows a dramatic pretransitional increase and a divergence at a number density close to that one observed in computer simulations and in colloidal dispersions. The value for the transition density stems from a boundary condition at the surface of the hard sphere in the configurational relative pair-space and makes use of the density dependence of the pair-correlation function and of its derivative at the point of contact

On the Shock Front Thickness in Water and other Molecular Liquids

Theoretical explanations are presented for the deviation of the shock front thickness from linear hydrodynamics, as observed by W. Eisenmenger (1964) in water and several molecular liquids for large driving pressure differences. Two mechanisms are proposed, which are based on generalizations of the Maxwell relaxation equation for the friction pressure tensor. One is due to the spatial inhomogeneity and linked with piezo-electric or piezo-tetradic effects. The other is caused by nonlinearities which account for shear thickening

Construction And Test Of Thermostats And Twirlers For Molecular Rotations

The equations of motion are coupled with a dynamical variable, referred to as twirler, which randomizes the angular momentum. The equations are time-reversal invariant, just as those for the standard Gaussian, Nosé-Hoover and configurational thermostats. The derivation of the basic equations is outlined. Test calculations are performed for the two-dimensional isotropic harmonic oscillator and for a nonlinear elastic dumbbell, used as a simple model to study properties of polymer molecules. Graphs of characteristic quantities and orbits, some of which are rather intriguing, are displayed. As applications, the rotational diffusion and the influence of a shear flow on the angular velocity and the deformation of the model polymer are analyzed.DFG, SFB 448, Mesoskopisch strukturierte Verbundsystem

Flow Velocity and Effective Viscosity of a Fluid Containing Rigid Cylindrical Inclusions

The determination of the flow properties of a fluid containing a cylindrical inclusion with its long axis oriented parallel to the vorticity direction is a 2-dimensional problem which is treated as a special case in a calculation of the corresponding D-dimensional problem. The velocity and pressure are obtained from the solution of the equations of hydrodynamics where D-dimensional multipole potential tensors are used. The effective viscosity of a dilute suspension is evaluted via the entropy production, as suggested by Einstein, and via an effective stress tensor. The relative change of the viscosity is proportional to the volume fraction. For D = 2 the proportionality factor Z is found to be 2 and 3 when the inclusion rotates with an angular velocity equal to the vorticity and when the inclusion does not rotate, repectively. The corresponding results for D=3 are the well known number Z = 2.5 and Z = 4

Squeeze-Flow in the Presence of a Temperature Gradient: Effective Attraction between Asperites in the Friction Zone of Two Solids

Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG geförderten) Allianz- bzw. Nationallizenz frei zugänglich.This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively.The equations of hydrodynamics are solved for a slow squeeze-Oow in the presence of a gradient of the viscosity which, in turn, is caused by a temperature gradient. The gradient induces an asymmetry of the spreading velocity and a drift of the center of mass towards the direction where the viscosity is decreasing. Due to this phenomenon, adjacent asperites in the friction zone between two solids sliding over each other experience an effective attraction.DFG, SFB 605, Elementarreibereigniss

Derivation and Application of an Algorithm for the Numerical Calculation of the Local Orientation of Nematic Liquid Crystals

Starting from a relaxation equation for the alignment tensor, an algorithm is derived which allows the numerical calculation of the dynamic and static behavior of the director field n with the correct nematic symmetry property, where n and - n are equivalent. As a first application, a two-dimensional problem is treated where the typical nematic defects with half-integer winding numbers only occur when the algorithm with the correct nematic symmetry property is used. Furthermore, the method is applied to the static and dynamic behavior of a Frederiks cell with strong and weak anchoring.DFG, SFB 335, Anisotrope Fluid

Pressure and Isotropic-Nematic Transition Temperature of Model Liquid Crystals

The pressure in the gaseous, the isotropic liquid and nematic liquid crystalline states, as well as the isotropic-nematic transition temperature are calculated for a model system composed of non-spherical particles. The potential is a generalization of the Lennard-Jones interaction where the attractive part depends on the relative orientations of the particles and the vector joining their centers of mass. Point of departure is an augmented van der Waals approach. It involves a modified Carnahan-Starling expression associated with the repulsive part of the interaction, and an orientation dependent second virial coefficient, as well as the orientational distribution functions of a pair of particles, linked with the attractive part of the potential. In a high temperature approximation, and for a special choice of model parameters, results are presented and displayed graphically.DFG, SFB 448, Mesoskopisch strukturierte Verbundsystem

Shear-stress controlled dynamics of nematic complex fluids

Based on a mesoscopic theory we investigate the non-equilibrium dynamics of a sheared nematic liquid, with the control parameter being the shear stress $\sigma_{\mathrm{xy}}$ (rather than the usual shear rate, $\dot\gamma$). To this end we supplement the equations of motion for the orientational order parameters by an equation for $\dot\gamma$, which then becomes time-dependent. Shearing the system from an isotropic state, the stress- controlled flow properties turn out to be essentially identical to those at fixed $\dot\gamma$. Pronounced differences when the equilibrium state is nematic. Here, shearing at controlled $\dot\gamma$ yields several non-equilibrium transitions between different dynamic states, including chaotic regimes. The corresponding stress-controlled system has only one transition from a regular periodic into a stationary (shear-aligned) state. The position of this transition in the $\sigma_{\mathrm{xy}}$-$\dot\gamma$ plane turns out to be tunable by the delay time entering our control scheme for $\sigma_{\mathrm{xy}}$. Moreover, a sudden change of the control method can {\it stabilize} the chaotic states appearing at fixed $\dot\gamma$.Comment: 10 pages, 11 figure

Monte Carlo Simulation of the Director Field of a Nematic Liquid Crystal with Three Elastic Coefficients

In this article, a Monte Carlo simulation is presented, which generates the equilibrium director field of a nematic liquid crystal under the influence of an external field and fixed boundary conditions. The liquid crystal is characterized by a set of directors on a spatially fixed lattice. The simulation is based on an expression for the Frank free energy with three elastic coefficients. The chosen discretisation conserves the nematic symmetry, which means n and - n are equivalent. The results for several Frederiks geometries with homogeneous and spatially modulated external fields are shown, as well as an investigation of a capillary with homeotropic boundary conditions. Further we compare our method with the Lebwohl-Lasher model and introduce an extension of the latter which distinguishes between splay-, twist-and bend-configurations.DFG, SFB 335, Anisotrope Fluid