Volume 25, Issue 3-4

The Stokes flow of an incompressible viscous fluid over a spherical porous particle is considered as a problem in the framework of non-equilibrium thermohydrodynamics. The boundary conditions at the interface between the particle and a fluid for various types of porous media are provided and the general solution of the problem is constructed in the form of a series expansion inside and outside the particle.

We describe the continuous excitation of standing gravity surface waves in the free surface of a volatile silicone oil contained in a cylindrical heated vessel (crucible). Resonant coalescence occurred under certain conditions between the fluid in the vessel and a volume of condensed oil which forms at the lower end of a cold copper cylinder in contact from above with the center of the oil surface. The expected continuous coalescence between the cold and the hot fluid volumes does not occur if the cold cylinder is raised above a critical height from the fluid surface forming a free-standing liquid column (meniscus). The standing waves frequency is fixed by the geometry and repeated partial coalescence events are triggered by the standing wave. The thermal Marangoni effect during the partial coalescence events leads to resonant wave amplification.

A comparison is made between the traditional stress-tensor based approach to the local pressure in a curved liquid-vapor interface and a novel purely thermodynamic approach. While both approaches are equivalent for planar interfaces, the stress-tensor based approach becomes ambiguous on a molecular scale for curved interfaces. We illustrate how the value of the surface tension and the location of the surface of tension can be obtained from the thermodynamic approach when the pressure profile of a spherical interface is computed within a molecular dynamics simulation.

In this paper the effect of Marangoni convection on mass transfer for the partially miscible isobutanol/water system is analysed. Comparisons are made between the predictions for interfacial stability and mass transfer fluxes, and the experimental results obtained for the transfer of isobutanol into water when the water phase is pure, and when it is “contaminated” with surfactants. The interfaces have been visualised with the aid of a Schlieren optical system and concentration profiles obtained with a Mach-Zehnder interferometer. The presence in the system of the ionic surfactants investigated has been found to increase further the Marangoni convection observed in the clean system and to enhance the initial mass transfer fluxes. However, interfacial convection is suppressed with the addition of the non-ionic surfactant studied and a reduction in the mass transfer fluxes is measured.

We outline generalized separation of variables as applied to nonlinear second-order partial differential equations (PDEs). In this context, we suggest a method for constructing exact solutions of nonlinear PDEs. The method involves searching for transformations that “reduce the dimensionality” of the equation. New families of exact solutions of 3D nonlinear elliptic and parabolic equations that govern processes of heat and mass transfer in inhomogeneous anisotropic media are described. Moreover, the method makes it possible to construct exact solutions of nonlinear wave equations. We also present solutions for three families of equations with logarithmic heat sources; the solutions are obtained by nonlinear separation of variables.

A simplification down to twenty six reaction steps of twenty species from the Gyorgyi, Turanyi and Field model (GTF) with eighty steps and twenty six species of the Belousosv-Zhabotinsky reaction is shown to be enough to account for recently available experimental results obtained by Rouff in a batch reactor. The bromate concentration was used as the control parameter for the system. Upon variation of this parameter we see the evolution of the system from an excitable steady-state to a limit cycle, then to a subsequent hyperchaotic regime through crisis, and back to a steady-state.

We have studied the dilational viscoelasticity of the surface of various surfactant solutions by using an excited capillary waves technique. We find that the dilational viscosity is negative in some cases, depending on the surfactant chain length, ionic strength, pH, bulk concentration and frequency of the waves. We have investigated the linearity of the response of the monolayer, and the possible influence of surface modes coupling. A correlation with phase behavior in the monolayer is discussed.

The oxidation of CO on a palladium support catalyst under normal pressure in a continuous flow reactor was observed. For experimental work an X type zeolite loaded with 0.5 weight % palladium was used as catalyst. The palladium salt was inserted into the zeolite by ion exchange and then reduced under hydrogen flow. Palladium particles with an average diameter of 4 nm were formed under these conditions. The conversion rate shows a dynamic behaviour with self-affine pattern of excursions to a smaller conversion rate on a time scale of some seconds. The influence of the flow rate upon the dynamics of the CO conversion pattern was studied. Increasing flow rate causes increasing of frequency of maximum excursions, increasing of smaller excursions, increasing of complexity of the pattern and decreasing of maximum conversion (base line). The system was simulated by a time and space discrete automaton. The model is a considerable extension of that described by Liauw et al. [7]. For example, in the extended model the temperature of palladium particles (non-isothermic conditions), the flow rate and the distribution of particle size is introduced. The temperatures of the palladium particles have an important influence upon the velocities of reaction, oxidation and reduction. Arrhenius equations were used to describe the influence of temperature. To obtain self-affine patterns, the coupling of oscillators with very different frequencies are necessary. These were obtained by different self-organised ‘operating temperatures’ of the palladium particles in the active state. During the catalytic oxidation of CO, the heat production and the heat loss for each model palladium particle equilibrate very fast and a temporary maximum ‘operating temperature’ occurs for each of them. This operating temperature of each model palladium particle depends upon the size of each particle.

We present an experimental study of the influence of long range molecular forces on the 2D-foam microgeometry. It is shown that the disjoining pressure effect cause the Plateau angles to deviate from 120°C.

Thermal lens oscillations, and associated hot-wire experiments, pertain to a class of instabilities produced when the free surface of a liquid is locally heated from below, generalizing to some extent the classical Bénard-Marangoni instabilities [1–8]. They provided a host of original observations, including what is seemingly the first evidence of a type-II intermittency in hydrodynamical experiments or the discovery of a new kind of propagating waves exhibiting a significant 1D-character. After two decades of study, this class of instabilities now receives a rather classical aspect [9] and deserves a review, which is presented in this paper. Beside the presentation of what is known and understood nowadays, the opportunity is taken to stress unsolved issues, therefore opening the way to future studies. This review completes and up-to-dates a previous one published one decade ago [10].

A linear analysis of oscillatory thermocapillary instability associated with deformation of the free surface in a finite-depth horizontal liquid layer heated from above is carried out. First, we numerically solve the problem and determine the conditions of marginal stability. Then, assuming that Galileo and Marangoni numbers are large enough while the capillary number is small enough, which corresponds to the time scales of transverse and longitudinal oscillations related to the free surface being much smaller than the characteristic viscous and thermal time scales, we construct an asymptotic solution of the problem. Two high-frequency overstable modes—transverse (capillary-gravity waves) and longitudinal—are identified and analyzed. Mode-mixing occurring at their possible resonance is also studied.