Lattice Boltzmann simulation of a binary fluid with different phase viscosities and its application to fingering in two dimensions

A thermodynamically consistent lattice Boltzmann scheme for simulating the flow of a binary fluid is extended to allow the fluid components to have different viscosities. The approach is tested for the shear and Poiseuille flow of layered immiscible fluids and for the dispersion relation and the damping of a capillary wave. We then consider the fingering that results when a fluid is displaced by a less viscous fluid in a two-dimensional channel. The finger widths obtained match the results of Reinelt and Saffman [#!Reinelt85!#], but differ somewhat from those of Halpern and Gaver [#!Halpern94!#] for capillary numbers above 2. A limiting finger width close to 1/2 is obtained for high capillary numbers and high viscosity ratios. Received 25 May 1999 and Received in final form 19 November 1999     

Spin tunneling properties in mesoscopic magnets: effects of a magnetic field

The tunneling of a giant spin at excited levels is studied theoretically in mesoscopic magnets with a magnetic field at an arbitrary angle in the easy plane. Different structures of the tunneling barriers can be generated by the magnetocrystalline anisotropy, the magnitude and the orientation of the field. By calculating the nonvacuum instanton solution explicitly, we obtain the tunnel splittings and the tunneling rates for different angle ranges of the external magnetic field ( θ _H = π/2 and π/2 < θ _H < π). The temperature dependences of the decay rates are clearly shown for each case. It is found that the tunneling rate and the crossover temperature depend on the orientation of the external magnetic field. This feature can be tested with the use of existing experimental techniques. Received 12 March 2001 and Received in final form 18 October 2001     

Statics and dynamics of a single ferrofluid-peak

We consider a single peak of a ferrofluid resulting from the Rosensweig instability for a small fluid container. Minimizing the total energy of the system by a variational method we determine the shape of the peak in a static field as well as the characteristics of the subcritical bifurcation leading to its formation. The latter are in very good agreement with experiment. Generalizing the approach to dynamic situations we qualitatively reproduce the complicated subharmonic response of the peak to an oscillating part in the external magnetic field found in recent experiments. Received 14 December 1999 and Received in final form 31 May 2000     

Hydrodynamic vector potentials

Solving the Navier-Stokes equation for incompressible fluids is greatly simplified by the solution of the vorticity equation. To accomplish this for three-dimensional flows requires vector potentials. These potentials are not only useful to take care of the incompressibility. Their modes are suitable also as test functions since the familiar Galerkin procedure does not work. The new method is checked by examples with known results and its relation to the classical approach with the stream function is clarified. The principle demonstration, however, concerns the transition to turbulence in plane shear flows. A simple layer of long rolls with axes parallel to the basic flow incites the transition. Received 20 August 2001     

Undulation instability in two-dimensional foams of magnetic fluid

Two-dimensional magnetic fluid foams are cellular structures whose framework is made of magnetic fluid. The features of these equilibrated patterns are driven by a control parameter: the amplitude of the applied magnetic field. When the latter is rapidly increased, an instability occurs: the walls between cells undulate. Such an instability has also been observed in other 2D cellular structures, which exist for instance in Langmuir monolayers or in magnetic garnets thin films. In this paper we give a theoretical analysis of this instability, the issues of which are shown to be well confirmed by experiments and numerical simulations. Received: 13 October 1997 / Received in final form: 28 January 1998 / Accepted: 9 March 1998     

Nanoparticles superficial density of charge in electric double-layered magnetic fluid: A conductimetric and potentiometric approach

We analyze potentiometric and conductimetric measurements simultaneously performed on Electric Double-Layer Magnetic Fluid based on cobalt ferrite nanoparticles, in order to obtain the pH-dependence of the particle surface charge density. We propose a mechanism for the charging of the particle surface. This model considers the ferrofluid solution as a mixture of strong and weak diprotic acids. We show how an exact analytical treatment involving proton transfer between the particle surface and the bulk solution allows the construction of a speciation diagram of the charged superficial sites. The saturation value of the superficial density of charge is found to be equal to 0.326 ± 0.065 C m^-2. Received 9 May 2001 and Received in final form 17 July 2001     

Minimum description of the onset of pipe turbulence

To demonstrate essentials of the mechanism for the onset of turbulence in a pipe at Re=2000, 48 degrees of freedom are enough. The derivation from the Navier-Stokes equation uses a novel type of modes which guarantee linear stability. For the reduction of the nonlinear interactions, the modes are grouped in 3 blocks. Facilitated by these simplifications the interdependence between linear and nonlinear processes is analysed, however, just for a special example. A phenomenon resembling backflow is identified. Received 20 October 1997     

Paradoxical magnetic cooling in a structural transition model

In contrast to the experimentally widely used isentropic demagnetization process for cooling to ultra-low temperatures we examine a particular classical model system that does not cool, but rather heats up with isentropic demagnetization. This system consists of several magnetite particles in a colloidal suspension, and shows the uncommon behavior of disordering structurally while ordering magnetically in an increasing magnetic field. For a six-particle system, we report an uncommon structural transition from a ring to a chain as a function of magnetic field and temperature. Received 5 September 2000     

Nanoparticle chain-like formation in electrical double-layered magnetic fluids evidenced by small-angle X-ray scattering

Small-angle X-ray scattering (SAXS) was performed on a series of Electric Double-Layered Magnetic Fluids (EDL-MF) composed of ferrite type-- CoFe₂O₄, MnFe₂O₄, ZnFe₂O₄, NiFe₂O₄ and CuFe₂O₄--nanoparticles of different crystalline sizes ( D _XR ranging from 40 to 139?, as determined by X-ray diffraction). The information concerning the scattering objects was obtained through the analysis of the distance distribution function p(r) and of the size distribution function D(R), both retrieved from SAXS data. The results show that EDL-MF, in the absence of an applied magnetic field, are composed of small magnetic particle aggregates in solution. These agglomerates are elongated in one direction (chain-like) with the longest dimension varying from 240 to 330?. The cross-section size is of the order of D _XR. The data also demonstrate that the maximum dimension of these aggregates is independent of the ferrite type. On the other hand, the number of aggregated magnetic particles is nanoparticle-size-dependent. Accordingly, larger ferrite-type nanoparticles as those with D _XR = 139? form aggregates composed of 2-3 magnetic particles, whereas smaller ones with D _XR 40? form agglomerates of about 6 magnetic particles in solution. As the nanoparticle size is reduced, it might increase the particle surface defects. Such occurrence would affect the particle surface charge density, which could reduce the electrostatic screening, favoring the agglomeration phenomenon. Received 28 February 2000 and Received in final form 28 August 2000     

Quasi-equilibrium lattice Boltzmann method

A general lattice Boltzmann method for simulation of fluids with tailored transport coefficients is presented. It is based on the recently introduced quasi-equilibrium kinetic models, and a general lattice Boltzmann implementation is developed. Lattice Boltzmann models for isothermal binary mixtures with a given Schmidt number, and for a weakly compressible flow with a given Prandtl number are derived and validated.     

Dilution series approach for investigation of microstructural properties and particle interactions in high-quality magnetic fluids

The aim of the paper is to study the deviation of magnetic properties of the magnetic fluids prepared for this study, from ideal (Langevin) behaviour, i.e. to estimate particle interaction influence and dimensions and influence of particle aggregates, as well as to explain the related effects observed. We also determine the particle coupling parameter, the particle nonmagnetic layer thickness, and the particle distribution, which are fundamental for sample characterization. A comparison of the studied magnetic fluids with each other, with respect to microstructure formation and particle interaction strength is finally done. For these purposes, a concentration dependence study, following the proposed “dilution series approach”, is performed. Three series of dilutions of three types of magnetic fluids were prepared and analyzed. Received 27 August 2001     

Implementation of diffuse reflection boundary conditions in a thermal lattice Boltzmann model with flux limiters

We discuss three new implementation versions of diffuse reflection boundary conditions in a thermal lattice Boltzmann model. Their accuracy is investigated in the case of Couette flow by considering the slip regime. The best results are recovered with versions 2 and 3, which rely on outgoing fluxes to express the particle distribution functions in the ghost nodes outside the flow domain. Version 2 is found to be more economical since it involves no interpolation procedure. This version was thereafter used to investigate the temperature profile in Couette flow for various values of Prandtl number, as well as the capability of the thermal LB model to capture the Knudsen minimum in Poiseuille flow.     

Lattice Boltzmann scheme for simulating thermal micro-flow

Gaseous flow and heat transfer in micro-channels are simulated by the lattice Boltzmann method (LBM). Thermal LB model with viscous heat dissipation has been adopted in the simulation. A new boundary treatment is proposed based on macro variables in order to capture the velocity slip and temperature jump. The numerical results show the velocity and temperature profiles are in agreement with the analytic results in different cases, which exhibits the availability of this model and boundary treatment in describing thermal micro-flow with viscous heat effect. The variation rules of temperature jump with different parameters are also discussed in this study.     

Surface waves in ferrofluids under vertical magnetic field

We present here new experimental results about the waves at the horizontal free surface of a magnetic fluid submitted to a normal magnetic field. The waves are generated by a small modulation at frequency of the vertical field . Using a shadowgraph method, we are able to measure the wavevector k of the 2D waves for a given value of and . The dispersion relation of the surface waves is established experimentally. On the other hand, we propose a theoretical derivation of the dispersion equation which includes a more complete treatment of the magnetic term than the previous works. Finally, we conclude that a linear and inviscid analysis is sufficient to fit well the experimental data, except in the vicinity of the critical field where a surface instability occurs. Received 11 May 1998     

Acoustic instabilities in thin polymer films

The spatial confinement of a fluctuation spectrum leads to forces at the confining boundaries. While electromagnetic (EM) fluctuations lead to the well-known dispersion forces, the acoustic analogy has widely been neglected. We show that the strength of the forces resulting from confined acoustic modes may be of the same order of magnitude as van der Waals forces. Additionally, the predicted scaling behavior is identical to the non-retarded case of the EM fluctuations. Our results suggest that dewetting experiments using polymer films are strongly influenced by the acoustic dispersion forces. Received 5 March 2002 and Received in final form 21 May 2002     

Alternating magneto-birefringence of ionic ferrofluids in crossed fields

A dynamic probing of magnetic liquids is performed experimentally, using a static magnetic field modulated by another smaller field, normal and alternating. The optical magneto-birefringence under these crossed magnetic fields is recorded as a function of the frequency for different field intensities and different sizes of the magnetic nanoparticles. A general reduced behavior is found for the in-phase and the out-of-phase optical response which is well-described by a simple mechanical model. Depending on the value H _ani of the anisotropy field of the nanoparticles, we can distinguish two different high magnetic field regimes: - a rigid dipole regime (large anisotropy energy with respect to k _B T) for cobalt ferrite nanoparticles with a relaxation time inversely proportional to the field intensity H _C(H _C < H _ani), - a soft dipole regime (anisotropy energy of the order of k _B T) for maghemite nanoparticles with a relaxation time independent of the field intensity H _C(H _C > H _ani). Received 5 June 2000 and Received in final form 8 January 2001     

A minimal model for vorticity and gradient banding in complex fluids

A general phenomenological reaction-diffusion model for flow-induced phase transitions in complex fluids is presented. The model consists of an equation of motion for a nonconserved composition variable, coupled to a Newtonian stress relation for the reactant and product species. Multivalued reaction terms allow for different homogeneous phases to coexist with each other, resulting in banded composition and shear rate profiles. The one-dimensional equation of motion is evolved from a random initial state to its final steady state. We find that the system chooses banded states over homogeneous states, depending on the shape of the stress constitutive curve and the magnitude of the diffusion coefficient. Banding in the flow gradient direction under shear rate control is observed for shear-thinning transitions, while banding in the vorticity direction under stress control is observed for shear-thickening transitions. Received 1 April 2001 and Received in final form 16 June 2001     

Radioactive ions for solid-state investigations at magnetic surfaces and interfaces

Hyperfine interactions observed at isomeric states of radioactive probe nuclei are used as a tool for solid-state investigations. This method is sensitive to atomic-scale properties. In recent years surface and interface investigations using radioactive probes delivered many results which can hardly be achieved by any other method. Several groups, e.g., from Konstanz, Leuven, Groningen, Aarhus, Uppsala, Tel Aviv, Pennsylvania, contributed to this field. Our group studies magnetic properties at surfaces and interfaces performing perturbed angular correlation (PAC) measurements in the UHV chamber ASPIC (Apparatus for Surface Physics and Interfaces at CERN). We take advantage of the enhanced variety of PAC probes delivered by the on-line mass separator ISOLDE. First, we report on measurements of magnetic hyperfine fields ( B _hf) at Se adatoms on a ferromagnetic substrate using ⁷⁷Se as a PAC probe. The investigation of induced magnetic interactions in nonmagnetic materials is a further subject of our studies. Here the nonmagnetic 4d element Pd is investigated, when it is in contact with ferromagnetic nickel. An outlook will be given on studies to be done in the future. The experiments were performed at the HMI, Berlin, and at CERN, Geneva. Received: 1 May 2001 / Accepted: 4 December 2001     

Dynamics of a single peak of the Rosensweig instability in a magnetic fluid

To describe the dynamics of a single peak of the Rosensweig instability a model is proposed which approximates the peak by a half-ellipsoid atop a layer of magnetic fluid. The resulting nonlinear equation for the height of the peak leads to the correct subcritical character of the bifurcation for static induction. For a time-dependent induction the effects of inertia and damping are incorporated. The results of the model show qualitative agreement with the experimental findings, as in the appearance of period doubling, trebling, and higher multiples of the driving period. Furthermore, a quantitative agreement is also found for the parameter ranges of frequency and induction in which these phenomena occur.