New problems of particle transfer in ferrocolloids: Magnetic Soret effect and thermoosmosis

The paper deals with critical reviewing of the experiments on thermodiffusion in ferrocolloids. The observed magnetic Soret effect is much stronger than that predicted theoretically. It is shown that the main reason of that is the influence of the magnetic field on mass diffusion. Besides, some measurements are affected by uncontrolled thermal and solutal magnetic convection. In porous media, when macroscopic convection is suppressed, thermodiffusion is accompanied by thermoosmosis as well as by a microconvective mass transfer induced by particle magnetophoresis on filter grains.     

Influence of isotopic substitution on the diffusion and thermal diffusion coefficient of binary liquids

The mutual mass diffusion coefficient (D) and the thermal diffusion coefficient ( D _T) of the liquids acetone, benzene, benzene-d ₁, benzene-d ₃, benzene-d ₅, benzene-d ₆, benzene- ¹³C₆, n-hexane, toluene, 1, 2, 3, 4-tetrahydronaphtalene, isobutylbenzene, and 1, 6-dibromohexane in protonated and perdeuterated cyclohexane have been measured with a transient holographic grating technique at a temperature of 25 ^°C. The mass diffusion coefficient shows a pronounced concentration dependence. Perdeuteration of cyclohexane only leads to marginal changes of the mass diffusion coefficient. The Stokes-Einstein equation describes the limiting tracer diffusion coefficients well if the solute molecule is smaller than the solvent. It is not capable to describe the small isotope effect of a few percent. On the other hand, the isotope effect, which is independent of concentration, is in agreement with the Enskog theory, that does not provide the absolute value of the mass diffusion coefficient of the liquid mixtures. The thermal diffusion coefficient of all the binary mixtures shows a moderate and almost linear concentration dependence. Its isotope effect, which is the change of D _T upon deuteration of cyclohexane, varies with mole fraction. The thermophoretic force acting on any tracer molecule in cyclohexane changes by the same amount when cyclohexane is perdeuterated, irrespective of the magnitude of the thermophoretic force before deuteration. This change of the thermophoretic force is equal but of opposite sign to the difference between the thermophoretic forces acting on cyclohexane and perdeuterated cyclohexane as tracers in any of the above liquids.     

Single-particle thermal diffusion of charged colloids: Double-layer theory in a temperature gradient

The double-layer contribution to the single-particle thermal diffusion coefficient of charged, spherical colloids with arbitrary double-layer thickness is calculated and compared to experiments. The calculation is based on an extension of the Debye-Hückel theory for the double-layer structure that includes a small temperature gradient. There are three forces that constitute the total thermophoretic force on a charged colloidal sphere due to the presence of its double layer: i) the force F _W that results from the temperature dependence of the internal electrostatic energy W of the double layer, ii) the electric force F _el with which the temperature-induced non-spherically symmetric double-layer potential acts on the surface charges of the colloidal sphere and iii) the solvent-friction force F _sol on the surface of the colloidal sphere due to the solvent flow that is induced in the double layer because of its asymmetry. The force F _W will be shown to reproduce predictions based on irreversible-thermodynamics considerations. The other two forces F _el and F _sol depend on the details of the temperature-gradient-induced asymmetry of the double-layer structure which cannot be included in an irreversible-thermodynamics treatment. Explicit expressions for the thermal diffusion coefficient are derived for arbitrary double-layer thickness, which complement the irreversible-thermodynamics result through the inclusion of the thermophoretic velocity resulting from the electric- and solvent-friction force.     

Transient oscillations in Soret-driven convection in a colloidal suspension

We present measurements of the transient stage of Soret-driven convective instability. The sample is a diluted colloidal suspension of silica spheres in water with an unusually large negative Soret coefficient S_T. A large temperature gradient (heating from above) is rapidly applied over the sample, while a shadowgraph imaging technique provides images of the convective flow. From the processing of the variance of the intensity of the images we are able to recover the time evolution of the overall intensity of the convective flow. A typical evolution of such signal exhibits, after a latency time, a peak followed by some damped oscillations leading to a steady-state value. Both the onset time _p (the temporal position of the first peak), and the oscillation period _osc show a power law dependence as a function of the solutal Rayleigh number R_s. The exponents found are compared with predictions from existing models.     

Transient-state method for coupled evaluation of Soret and Fick coefficients,and related tortuosity factors,using free and porous packed thermodiffusion cells: Application to CuSO4 aqueous solution ( 0.25M)

The measurement of Soret coefficients in liquids is not easy and usually not very precise because the resulting concentration gradient is small and moreover can be perturbed by undesired convection currents. In order to suppress, or to drastically reduce these convection currents, the use of a porous medium is sometimes suggested. The question arises as to whether the Soret coefficient is the same in free fluid and in porous medium. This is the aim of this paper. To this end, for a given liquid mixture, the time evolution of the vertical concentration gradient is experimentally measured in the same thermodiffusion cell filled first with the free liquid and next with a porous medium followed by saturation by the liquid mixture. Both the isothermal diffusion (Fick) coefficient and the Soret coefficient can be deduced, providing that a correct working equation is used. The proposed equation results from integration of the general mass conservation equation with realistic boundary conditions (zero mass flux at the boundaries) and some simplifying assumptions rendering this equation more tractable than the one proposed some decades ago by Bierlein (J.A. Bierlein, J. Chem. Phys. 23, 10 (1955)). The method is applied here to an electrolytic solution (CuSO4, 0.25 M) at a mean temperature of 37^°C. The Soret coefficients in free and porous medium (zircon microspheres in the range of 250- 315 ^. 10^-6m) may be considered to be equal ( S_T = 13.2±0.5 ^. 10^-3 K^-1) and the tortuosity factors for the packed medium are the same relative to thermodiffusion and Fick coefficients ( = 1.51±0.02).     

Importance of direction of vibration on the onset of Soret-driven convection under gravity or weightlessness

This paper considers the influence of the direction of vibration on the stability threshold of two-dimensional Soret-driven convection. The configuration is an infinite layer filled with a binary mixture, which can be heated from below or from above. The limiting case of high-frequency and small-amplitude vibration is considered for which the time-averaged formulation has been adopted. The linear stability analysis of the quasi-mechanical equilibrium shows that the problem depends on five non-dimensional parameters. These include the thermal Rayleigh number ( Ra_T), the vibrational parameter (R), the Prandtl number ( Pr), the Lewis number (Le), the separation ratio (S) and the orientation of vibration with respect to the horizontal heated plate (). For different sets of parameters, the bifurcation diagrams are plotted Ra_c = f (S) and k_c = g(S), which are the critical thermal Rayleigh and the critical wave numbers, respectively. Our results indicate that, relative to the classical case of static gravity, vibration may affect all regions in Ra_c-S stability diagram. In the case of mono-cellular convection, by using a regular perturbation method, a closed-form relation for the critical Rayleigh number is found. Several physical situations in the presence or in the absence of gravity (micro-gravity) are discussed.     

The role of heat-conducting walls in the measurement of heat and mass transport in transient grating experiments

We present a two-dimensional model to account for the role of heat-conducting walls in the measurement of heat transport and Soret-effect-driven mass transport in transient holographic grating experiments. Heat diffusion into the walls leads to non-exponential decay of the temperature grating. Under certain experimental conditions it can be approximated by an exponential function and assigned an apparent thermal diffusivity D_{th, app} < D_{th, s}, where D_th,s is the true thermal diffusivity of the sample. The ratio D_{th, app}/D_{th, s} depends on only three dimensionless parameters, d /l_s, κ_s/κ_w, and D_{th, s}/D_{th, w}. d is the grating period, l_s the sample thickness, κ_s and κ_w the thermal conductivities of sample and wall, respectively, and D_th,w the thermal diffusivity of the wall. If at least two measurements are performed at different d /l_s, both D_th,s and κ_s can be determined. Instead of costly solving PDEs, D_th,s can be obtained by finding the zero of an analytic function. For thin samples and large grating periods, heat conduction into the walls plays a predominant role and the concentration grating in binary mixtures is no longer one-dimensional. Nevertheless, the normalized heterodyne diffraction efficiency of the concentration grating remains unaffected and the true thermal and collective diffusion coefficient and the correct Soret coefficient are still obtained from a simple one-dimensional model.     

Cooperative motions in a finite size model of liquid silica: an anomalous behavior

Finite size effects on dynamical heterogeneity are studied in liquid silica with Molecular Dynamics simulations using the BKS potential model. When the system size decreases relaxation times are found to increase in accordance with previous results in finite-size simulations and confined liquids. It has been suggested that this increase may be related to a modification of the spatially heterogeneous dynamics in confined liquids. In agreement with this hypothesis we observe a decrease of the spatially heterogeneous dynamics when the size decreases. The spatially heterogeneous dynamics is usually characterized by the dynamical aggregation of the most or the least mobile atoms. However we find that the decrease of the dynamical aggregation associated to the least mobile atoms is much more important than the decrease associated to the most mobile atoms when the size decreases. This result associated with a slowing down of the liquid is surprising as it is expected that the dynamical aggregation of the least mobile atoms should increase the slowing down of the liquid dynamics. The decrease of the heterogeneous behaviour is also in contradiction with the increase of the spatially heterogeneous dynamics observed in liquids confined inside nanopores. However, an increase of the non-Gaussian parameter appears both for the confinement inside nanopores and for the finite size simulations. As the non-Gaussian parameter is usually associated with the heterogeneous dynamics, the increase of the non-Gaussian parameter together with a decrease of the spatially heterogeneous dynamics is also surprising.     

Anomalous viscosity exponent in a discretized model for a chain diffusion in one dimension

We present a one-dimensional Monte Carlo simulation for the diffusion motion of a chain of N beads. We found that the scaling exponent for the viscosity can be smaller or greater than 3. This anomalous behavior cannot be attributed to the diffusivity scaling or the length fluctuations but is due to the chain dynamics details during diffusion in which the end beads play the key role. The viscosity exponent 3 and its expected relation with the diffusivity exponent are recovered in the asymptotic regime (N ↦∞). Received 24 September 2001 and Received in final form 28 January 2002     

Diffusion and rheology in a model of glassy materials

We study self-diffusion within a simple hopping model for glassy materials. (The model is Bouchaud's model of glasses (J.-P. Bouchaud, J. Phys. I France 2, 1705 (1992)), as extended to describe rheological properties (P. Sollich, F. Lequeux, P. Hébraud, M.E. Cates, Phys. Rev. Lett. 78, 2020 (1997)).) We investigate the breakdown, near the glass transition, of the (generalized) Stokes-Einstein relation between self-diffusion of a tracer particle and the (frequency-dependent) viscosity of the system as a whole. This stems from the presence of a broad distribution of relaxation times of which different moments control diffusion and rheology. We also investigate the effect of flow (oscillatory shear) on self-diffusion and show that this causes a finite diffusivity in the temperature regime below the glass transition (where this was previously zero). At higher temperatures the diffusivity is enhanced by a power law frequency dependence that also characterises the rheological response. The relevance of these findings to soft glassy materials (foams, emulsions etc.) as well as to conventional glass-forming liquids is discussed. Received 31 August 1998 and Received in final form 25 January 1999     

Thermophoresis as persistent random walk

In a simple model of a continuous random walk a particle moves in one dimension with the velocity fluctuating between +v and −v. If v is associated with the thermal velocity of a Brownian particle and allowed to be position dependent, the model accounts readily for the particle's drift along the temperature gradient and recovers basic results of the conventional thermophoresis theory.     

Monte-Carlo analysis of tracer diffusion mechanisms in YBa2Cu3O6+c

A method for estimating, via the Monte-Carlo simulation, the most often realized diffusion mechanisms in 2D ordered structures is presented. Taking as an example the diffusion of oxygen ions in high temperature superconductor we propose several diffusion mechanisms and show to what extent they depend on the temperature and concentration of the diffusing particles. Our results are compared with the ones proposed earlier on the basis of energy arguments. We find also additional trajectories, different from those earlier reported in that system. Received 9 November 1998     

Segregation in desiccated sessile drops of biological fluids

It is shown here that concurrence between advection and diffusion in a drying sessile drop of a biological fluid can produce spatial redistribution of albumen and salt. The result gives an explanation for the patterns observed in the dried drops of the biological fluids.     

The nonlinear Fokker-Planck equation with state-dependent diffusion - a nonextensive maximum entropy approach

Nonlinear Fokker-Planck equations (e.g., the diffusion equation for porous medium) are important candidates for describing anomalous diffusion in a variety of systems. In this paper we introduce such nonlinear Fokker-Planck equations with general state-dependent diffusion, thus significantly generalizing the case of constant diffusion which has been discussed previously. An approximate maximum entropy (MaxEnt) approach based on the Tsallis nonextensive entropy is developed for the study of these equations. The MaxEnt solutions are shown to preserve the functional relation between the time derivative of the entropy and the time dependent solution. In some particular important cases of diffusion with power-law multiplicative noise, our MaxEnt scheme provides exact time dependent solutions. We also prove that the stationary solutions of the nonlinear Fokker-Planck equation with diffusion of the (generalized) Stratonovich type exhibit the Tsallis MaxEnt form. Received 26 February 1999     

Interfacial roughness in a near-critical binary fluid mixture: X-ray reflectivity and near-specular diffuse scattering

Measurements are presented of the X-ray specular reflectivity and near-specular diffuse scattering of the interface in a near-critical mixture of hexane and perfluorohexane. A lineshape analysis of the scattered intensity at each temperature yields values for the interfacial tension and interfacial width. The temperature variation of the tension and width so-obtained are consistent with current understanding of this interface, which holds that there is, firstly, an intrinsic width over which the fluid density varies smoothly from one coexistence composition to the other, and, secondly, that the interface acquires an additional and larger statistical interfacial width as a result of capillary fluctuations. Received 1 April 1998     

Characterization of magnetic colloids by means of magnetooptics

A new, efficient method for the characterization of magnetic colloids based on the Faraday effect is proposed. According to the main principles of this technique, it is possible to detect the stray magnetic field of the colloidal particles induced inside the magnetooptical layer. The magnetic properties of individual particles can be determined providing measurements in a wide range of magnetic fields. The magnetization curves of capped colloids and paramagnetic colloids were measured by means of the proposed approach. The registration of the magnetooptical signals from each colloidal particle in an ensemble permits the use of this technique for testing the magnetic monodispersity of colloidal suspensions.     

The influence of surface forces on shear-induced tracer diffusion in mono and bidisperse suspensions

The shear-induced self-diffusivity of tracer particles of radius a _t = λa in a suspension of particles having a radius, a , is calculated by Stokesian dynamics for different values of the size ratio, λ , both in 2 and 3 dimensions in the binary-collision regime. The self-diffusion is found to decrease strongly when the size ratio becomes quite different from unity. On the other hand, for the same average distance of contact between two spheres, the presence of a soft force always increases greatly the diffusion compared to the effect of a hard shell which is used to model the roughness. This is particularly true for tracer particles smaller than the bath particles, where the shear-induced diffusion can be increased by many order of magnitudes in the presence of a soft force. For suspensions of monodisperse particles we show that, for low volume fraction, the diffusion coefficient is much smaller than the one predicted by the binary collision model, due to the existence of a layered structure. On the contrary at higher volume fraction, many-body collisions strongly enhance the diffusion and it appears that the value of the diffusion is quite sensitive to the presence of clusters of particles which are themselves determined by the range of interparticle forces.     

Depletion from a hard wall induced by aggregation and gelation

Diffusion-limited cluster aggregation and gelation of hard spheres is simulated using off-lattice Monte Carlo simulations. A comparison is made of the wall-particle correlation function with the particle-particle correlation function over a range of volume fractions, both for the initial system of randomly distributed spheres and for the final gel state. For randomly distributed spheres the correlation functions are compared with theoretical results using the Ornstein-Zernike equation and the Percus-Yevick closure. At high volume fractions (φ > 40%) gelation has little influence on the correlation function, but for φ < 10% it is a universal function of the distance normalized by correlation length (ξ) of the bulk. The width of the depletion layer is about 0.5ξ. The concentration increases as a power law from the wall up to r ≈ ξ, where it reaches a weak maximum before decreasing to the bulk value.     

Scattering from solutions of star polymers

We study the scattering intensity of dilute and semi-dilute solutions of star polymers. The star conformation is described by a model introduced by Daoud and Cotton. In this model, a single star is regarded as a spherical region of a semi-dilute polymer solution with a local, position dependent screening length. For high enough concentrations, the outer sections of the arms overlap and build a semi-dilute solution (a sea of blobs) where the inner parts of the actual stars are embedded. The scattering function is evaluated following a method introduced by Auvray and de Gennes. In the dilute regime there are three regions in the scattering function: the Guinier region (low wave vectors, ) from where the radius of the star can be extracted; the intermediate region () that carries the signature of the form factor of a star with f arms: ; and a high wavevector zone () where the local swollen structure of the polymers gives rise to the usual q ^-5/3 decay. In the semi-dilute regime the different stars interact strongly, and the scattered intensity acquires two new features: a liquid peak that develops at a reciprocal position corresponding to the star-star distances; and a new large wavevector contribution of the form q ^-5/3 originating from the sea of blobs. Received: 3 September 1997 / Revised: 13 January 1988 / Accepted: 31 March 1998