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Concentration-induced convection of a binary metal melt in a rectangular crucible has been studied numerically in the case of a mixture with a eutectic phase diagram. The calculations are performed for realistic parameters which correspond to the pair of metals Sn-Pb. A solid rod with non-wettable boundaries and a non-uniform longitudinal temperature distribution on the surface is immersed into the melt vertically at the center of the crucible. The condition of complete non-wetting allows us to consider the interface between the melt and the rod to be free. The temperature non-uniformity leads to inhomogeneity of the surface tension. As a result, the thermocapillary force generates a steady convective flow first on the surface of the rod and then in the volume. Due to this motion, the heavy component of the alloy is transferred along the rod’s surface to the butt-end. At the boundary patches with the excess of concentration it has been extracted into the volume by means of the desorption mechanism. In the presence of weak convection in the volume, this component is partially accumulated near the bottom of the crucible under the butt-end. Thus, there takes place a process of separation of heavy admixture for the two-component metal melts.

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.

Direct numerical simulation of the process of separation of binary low-melting metal melts in a thin nonuniformly heated inclined capillary is carried out. A physical model which describes the macroscopic motion in the melt and the process of separation of the liquid mixture in components is constructed on the basis of laws and equations valid for the multiphase hydrodynamic systems. The calculation results are compared with the experimental data. The separation time is compared for various angles of inclination of the layer, the characteristic concentration fork which demonstrates separation dynamics is reproduced, and the qualitative agreement with the experiment is obtained for the component concentrations in the cross-section. In the course of numerical simulation, that replicates the succession of experimental actions with the maximum precision, the presence of the specific maximum for the difference between the end-face concentrations at a certain angle of inclination of the channel is confirmed. The radical difference between the calculation results obtained within the framework of the model considered and the conclusions made earlier in explanation of the experiment by other authors is demonstrated.

The results of the flow structure visualization experiments conducted on the surface of a single bubble streamlined by uniform flow are presented. It is shown that, at certain critical values for bubble size, flow velocity, and contamination level, the axial symmetry of the surface flow loses its stability in a threshold manner, and the first instability mode in the form of two vortices appears. Below the threshold, the stationary flow on the bubble surface is impossible. The experimental results indicate that the assumption about the axial symmetry of the motion on the bubble surface containing surfactants, which is used in most theoretical and numerical studies, is invalid. Analysis of the results has revealed the most likely reason for the spiral form of the trajectory in the problem of a small rising bubble in the surrounding fluid. For the surfactant-free surface realized in the experiments with isopropyl alcohol, the rising trajectory was a straight line, and no vortex structures were observed on the bubble surface. In the experiments with water, a spiral rising trajectory was observed, and the first instability mode was formed on the bubble surface.

The structure and stability of the convective flow generated by a source located at the water surface containing an insoluble surfactant layer are experimentally investigated. Application of a few types of source, which differ in the force driving the interface, and two surfactants with different rheological properties made it possible to generalize the results and to develop a unified approach to describing the flow patterns observed in this study. It is shown that, regardless of source type and surfactant used, the problem under consideration can be completely described in terms of two non-dimensional parameters. The first is the elasticity number introduced earlier by Homsy and Meiburg (J. Fluid Mech., v.139, 1984). This parameter is the ratio of two shear stresses formed at the interface by surfactant and source, and it defines the formation of the convective zone at the center nearby the source and the size of the stagnant zone at the periphery. The second, called the surface Rayleigh number, is introduced for the first time in this paper. It is responsible for the appearance of the multi-vortex flow structure within the stagnant zone. We suppose that this structure occurs as a result of the mechanical equilibrium instability of the surfactant layer under the action of the momentum flux transported from the subphase by the viscous mechanism. Based on our results and those reported earlier by other researchers, we have determined the critical value of the surface Rayleigh number and analyzed the possibility and conditions for the occurrence of this instability, called by us the shear-driven surfactant layer (SDSL) instability, by addressing some problems of interfacial hydrodynamics., Comment: 27 pages, 11 figures

Objective: Collecting exhaled particles that represent small droplets of the alveolar lining fluid shows great promise as a tool for pulmonary surfactant (PS) sampling. For this purpose, we present a setup consisting of two modules, namely, a module for droplet collecting, called an electrostatic aerosol trapping (ESAT) system, and a measurement module for studying PS properties. We suggest the way how to extract numerical values from the experimental data associated with PS properties. Methods: The operating principle of ESAT is based on the electrostatic precipitation of exhaled particles. The native material was collected directly on the water surface, where an accumulated adsorbed film of PS was examined with tensiometric method. The modified capillary waves method adapted to study small volume samples was utilized. The efficiency of the setup was verified in the experiments with healthy subjects. Conclusion: The accumulation of PS components on the water surface in an amount sufficient for tensiometric study was reported. It was shown how to extract the numerical values from the experimental data characterizing PS properties. Significance: The idea underlying the new concept used in this study may give impetus to further development of point-of-care facilities for collecting PS samples and for their express analysis., 19 pages, 6 figures, submitted

We consider the effect of a partially contaminated interface on the steady thermocapillary flow developed in a two-dimensional slot of finite extent. The contamination is due to the presence of an insoluble surfactant which is carried away by the flow and forms a region of stagnant surface. This problem, first studied in the classical theoretical paper by Carpenter and Homsy (1985, J. Fluid Mech. 155, 429), is revisited thanks to new experimental data. We show that there is a qualitative agreement between above theory and our experiments: two different regions simultaneously coexist on the surface, one of which is free from surfactant and subject to vigorous Marangoni flow, while the other is stagnant and subject to creeping flow with the surface velocity smaller about two orders of magnitude. We found, however, significant disagreement between theory predictions for the extent of a stagnant surface region and newly obtained experimental data. In this paper, we provide an explanation for this discrepancy demonstrating that the surface temperature distribution is far from suggested earlier. Another effect, not previously taken into account, is a possible phase transition experienced by the surfactant. We obtain a correct analytic solution for the position of the edge of the stagnation zone and compare it with the experimental data.

Surface diffusion is an important mass transfer mechanism of surfactant molecules within adsorbed layers, which has to be taken into account in many fluid dynamics problems. Although considerable research has been devoted to studying the thermodynamic and rheological properties of surface films, rather less attention has been paid to surface diffusivity measurements. Current measurement methods, which are based on marking part of surfactant molecules in uniform motionless layers with the radiotracer or fluorescence technique, are well suited for use in quite condensed layers, but they do not work in rarefied layers due to increasing contribution of density fluctuations at an interface. In this study, we propose a method for measuring the surface diffusion coefficient in gaseous monolayers of an insoluble surfactant under dynamic conditions, i.e., in the presence of a flow at an interface. Our approach is based on measuring the velocity of thermocapillary flow on the water surface, which contains molecules of an insoluble surfactant. We show that under conditions of the balance between thermo- and solutocapillary tangential stresses the convective motion exists at an interface, which is caused by a blurring of the surface concentration gradient of surfactant molecules due to the surface diffusion mechanism. For calculations of the surface diffusion coefficient, we use the equation proposed earlier in the theoretical study [ Homsy , G. M.

In this paper, the mixing process of two solutions of inorganic salts in a continuous flow channel with Y-type micromixer is investigated. Due to different diffusivity rates of solutes the double-diffusion convection develops in the channel. To visualize convective flows and the distribution of mixing substances the shear interferometer technique and a fluorescent dye are used. The latter makes it possible to quantify the mixing degree. The mixing extent for different volume flow rates is calculated. The comparison of convection and pure diffusion mechanisms of mixing is provided.

The diffusion coefficients of aqueous solutions of lithium, sodium, potassium, and cesium hydroxide in a concentration range of 0 to 3.0 mol/L were obtained at 25 °C and normal pressure. The Fizeau interferometer and the spatial phase-shifting method were used to measure the spatial distribution of concentration of the investigated substances. The concentration dependence of the diffusion coefficient was determined from the Matano-Boltzmann analysis. The experimental setup and techniques, as well as the image and data processing procedure, were tested using an aqueous solution of nitric acid. The comparison made for lithium, sodium, and potassium hydroxides indicated good agreement between the obtained results and the data collected from the literature. The concentration dependence of the diffusion coefficient for cesium hydroxide in water was found experimentally for the first time.

Continuous-flow microfluidic devices are applied in the study of microorganisms, in genetic research, production of pharmaceutical substances, lab-on-a-chip technology, biomedicine etc. Some applications require continuous mixing of the solutions that flow through the devices. However, straight-line mechanical mixing methods cannot be used due to the small size of the channels. In this paper, we discuss from a theoretical and experimental point of view the prospects of using various mechanisms of natural or forced convection for efficient mixing of solutions entering a microfluidic chip. Different designs of micromixers operating on gravity-dependent instabilities of the Rayleigh-Taylor type, double diffusion convection, and surface-dependent Marangoni instability are considered. Micromixers, in which the fluid flow is controlled by an electro-osmotic mechanism and directional deformations of the channel walls, are considered as examples of forced convection. For each case, we will provide the assessment of the range of chip sizes in which this mixing mechanism works effectively. The examples of experimental implementation of different mixing principles are given.

Capillary waves are frequently used to measure the surface tension of liquids. However, this approach has not found wide application in the manufacture of modern commercial tensiometers because of the limitations imposed by capillary wave excitation techniques and the labor input associated with its practical implementation. In this paper we introduce a modified version of the capillary wave method which allows one to avoid the existing limitations and disadvantages. The distinguishing features of the proposed technique are as follows: acoustic wave generation and application of an interferometry technique for 3D surface profile reconstruction. A dynamic speaker with controlled vibration frequency and amplitude is used to produce acoustic vibrations. Application of a conventional Fizeau interferometer and the spatial phase shifting method makes it possible to perform surface form measurements with a high accuracy. For calculating wavelengths and the damping co-efficient, the surface profile is fitted with a decaying cylindrical wave equation. The accuracy of surface tension measurement by the modified capillary wave technique is 0.3 %. Owing to the non-contact way of wave generation and the small amounts of the examined fluid, the proposed method can be used in different studies.

In this work, experimental studies were carried out to investigate the structure of a surface flow and to understand potential mechanisms leading to the formation of this type instability. The surface flow was generated by feeding water through three sources: a lumped source with free upper boundary, a slot gap, and a lumped source for inducing a capillary-driven Marangoni flow. For flow visualization, a traditional light knife technique was used. The application of a method of spatial separation of the water volume into two isolated parts whose common surface remained unchanged and the realization of a reverse situation with a divided surface made it possible to study in detail the surface flow structure and to determine the conditions for the appearance of such hydrodynamic instability. It is shown that the formation of a vortex flow is caused by the interaction between the coordinate of the flow homogeneous along the transverse flow and the layer of a surface-active substance adsorbed at the interface. The obtained experimental results demonstrate the importance of setting different boundary conditions for potential and vortex velocity components of a convective flow in the region near the interface occupied by a surfactant.

The capillary wave method is a well-known classical technique to measure surface tension and surface rheological properties. Despite the large number of theoretical works devoted to capillary waves, this technique has serious difficulties associated with its implementation, and therefore, it is not widely used by researchers. In this paper, we introduce our modifications of the existing method to overcome its drawbacks. First, a capillary wave is excited by pressure fluctuations generated locally at the interface. Being contactless, the proposed method is suitable for any liquid irrespective of its electrical properties. Second, the application of optical interferometry together with the spatial phase shifting method allows to quantify the surface profile with high accuracy. A new data processing algorithm makes it possible to subtract the parasitic deformation of the surface caused by external perturbations avoiding, thereby the thorough vibroisolation procedure. The relative error for surface measurements and surface tension calculations is 0.3%. The results of surface tension measurements of several liquids obtained by the modified method are in good agreement with the data determined by the Wilhelmy plate technique. The main advantage of our method is that is well suited for measurements of low liquid volumes, which makes it of particular interest in biological and chemistry applications. Additionally, our version of the examined method allows one to extend the frequency range to 103–104 Hz, where only the quasi-elastic light scattering technique is currently applicable.

The occurrence of thermocapillary convection in a Hele-Shaw cell in the presence of the surfactant film on the free surface is experimentally investigated. It is shown that at certain values of the control parameter two different zones are formed on the surface – the zone free from impurities and the stagnant zone. In the first zone, the onset and development of an intense Marangoni convection is observed, while in the stagnant zone the velocity of the motion on the surface is lower by about two orders of magnitude. This study clearly demonstrates that the analysis of the temperature profile provides sufficient information about both the distribution of tangential stresses over the surface and the degree of compression of the surfactant film. In addition, due to a simple linear law of temperature variation on the surface of the stagnant zone, the distribution of the surfactant molecules over the surface can be predicted based on the known equation of state for the film of the examined surfactant. Thus, the application of a set of simple experimental techniques to the examined model problem allowed us to obtain complete information on the state of a complex system consisting of a liquid layer and a surface film of the surfactant, the structure of the volumetric flow, the velocity of the liquid at the surface, the distribution of shear stresses and surfactant molecules over the surface.

The effect of the universal acid-base indicator on the pattern formation and mass transfer in a two-layer system composed of two reactive miscible liquids in a vertical Hele-Shaw cell is studied experimentally. The reaction we study is a neutralization one. It turns out that the presence of the indicator leads to a change in the spatio-temporal characteristics of the system and even in the mass transfer mechanism near the reaction front—from diffusive to convective. The conditions, where the universal indicator does not affect the reaction and can be used as a visualizing mean, are reported.