We study, both experimentally and theoretically, the fluid flow driven by a thermocapillary effect applied to a partially contaminated interface in a two-dimensional slot of finite extent. The contamination is due to the presence of an insoluble surfactant which is convected by the flow forming a stagnant zone by the colder edge of the interface. The thermocapillary surface stress is produced by a special optocapillary system, which makes it possible, first, to get an almost linear temperature profile along the interface and, second, to apply a surface pressure large enough to force the surfactant to experience a phase transition to a more condensed state. This enabled us for the first time since the release of the paper by Carpenter & Homsy (J. Fluid Mech., vol. 155, 1985, pp. 429–439) to test experimentally their theoretical predictions and obtain new results for the case when the contamination exists simultaneously in two phase states within the interface. We show that one part of the surface is free of surfactant and subject to vigorous thermocapillary flow, while another part is stagnant and subject to creeping flow with a surface velocity which is approximately two orders of magnitude smaller. We found that the extent of the stagnant zone theoretically predicted earlier does not coincide with the newly obtained experimental data. In this paper, we suggest analytical and numerical solutions for the position of the edge of the stagnation zone, which are in perfect agreement with the experimental data.

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A mathematical model has been developed to describe the process of a high-temperature silicification process in a carbon-carbon porous material. The statement of the problem is based on general equations describing the clogging of tubules in a porous medium with various kinds of impurities. In the problem under consideration, the cause of blockage is the condensation of gaseous silicon on the inner walls of the pores. Temperature dependences for the coefficients of condensation and evaporation are proposed, which characterize the intensity of this process. It is assumed that the diffusion of gas is the main mechanism of initial filling pores of the material. Numerical modeling was carried out by the finite difference method using an explicit scheme in the case of a constant value of the mobile concentration at the input and for imposed linear temperature distribution on the vertical boundaries of the sample. Such temperature distribution made it possible to describe a partially silicified region and to delimit from it the sample part that remains “dry” during this process. The dynamics of the main physical characteristics, i.e. porosity of the composite material and concentration of the immobile component in the volume, is analyzed. The external factors influencing the intensity of the condensation process are considered quantitatively, namely, the concentration of the mobile component in the volume is calculated as a function of time. For the characteristic time interval, the maximum change in the porosity of the medium is calculated, on the basis of which the time of complete saturation of the material is estimated, which, as it turned out, is equal about 2 hours. The results of numerical simulation for silicification time and weight gain of the product are in qualitative and quantitative agreement with the known experimental data.

The influence of high-frequency horizontal vibrations on convection in the Hele-Shaw cell located in a uniform gravity field is considered experimentally and theoretically. Nonlinear regimes of vibrational convection in the supercritical region are examined. It is shown that horizontal vibrations (directed toward the wide sides of the cell ) decrease the threshold of quasi-equilibrium stability. Regions of existence of one-and two-vortex steady flows are found, and unsteady regular and random regimes of thermal vibrational convection are considered. New random regimes in the Hele-Shaw cell are found, which result from nonlinear interaction of the "lower" modes responsible for the formation of regular supercritical convective regimes.Introduction. Convective flows in liquids and gases, which arise under conditions of spatial inhomogeneity of density in the gravity field, are wide-spread types of motion of liquids and gases in nature. Such flows are characterized by a wider range of structures, as compared to isothermal types of motion, whose role is taken into account in design of various engineering devices. Therefore, of significant interest is to consider conditions of origination of gravitational-convective flows and to study their stability and evolution in space and time in various situations, e.g., under the action of variable inertial acceleration, forced flow, porous media, nonuniform composition, magnetic field, or other complicating factors.Convective motion in a vertical Hele-Shaw cell under the action of high-frequency vibrations is considered in the present work both experimentally and theoretically. The Hele-Shaw cell is a cavity in the form of a rectangular parallelepiped with two linear scales much greater than the third one. The cavity is heated from below and is subjected to horizontal vibrations aligned with the wide sides of the cell. A typical feature of convective motion in the Hele-Shaw cell is that the planes of trajectories are aligned parallel to the wide edges in a wide range of angles of inclination of the cavity. Because of significant thermal and hydraulic resistance, the range of vibrational regimes in the Hele-Shaw cell is much closer to the basic level of instability than in a horizontal layer. For this reason, the Hele-Shaw cell is a convenient object for experimental (first of all, optical) methods of research and for theoretical calculations because the approximation of plane trajectories can be used. Free thermal convection in the Hele-Shaw cell was considered experimentally and theoretically in [1,2]. The boundaries of equilibrium stability were determined, the structure of steady flows was studied, and regular and some random vibrational regimes were described. It should be noted that the case with these vibrations was one of the first physical examples of the random behavior in simple hydrodynamic systems.The first theoretical study of vibrational convection in the Hele-Shaw cell in microgravity was performed by Braverman [3] who showed that vibrations induce convection eve...

The results of comparative experiments on the convection of magnetic fluids and molecular binary fluid mixtures in connected vertical channels heated from below are discussed. In both media, near the equilibrium stability threshold, flows in the form of specific swing oscillations are observed. The results of the experiment form a basis for a three-component model for magnetic fluid convection which takes into account the thermodiffusion separation of the dispersion medium components and the weak sedimentation of magnetic particles. The results of numerical simulation and experiment are compared.The specific low-frequency convective ferrofluid oscillations in connected vertical channels, described in [1], surprisingly turned out to be qualitatively similar to the binary mixture oscillations. In the medias of both types, near the equilibrium stability threshold, periodic changes in the channel flow direction were observed. The nature of the convective oscillations of molecular binary mixtures was established, the theory of the phenomenon was developed, numerical and analytical calculations were carried out, and the results were described in a series of papers [2][3][4]. It was revealed that in these oscillations the determining role is played by the positive thermodiffusion of a heavy molecular admixture.In order to understand the nature of the convective oscillations in ferrofluids, novel comparative experiments were carried out with ferrofluids and aqueous sodium sulfate solutions. The experimental results obtained make a basis for formulating equations that describe the convection of the magnetic fluid as a three-component fluid consisting of a binary carrier filled with magnetic particles.

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