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The article analyzes the communication environment of higher education institutions (HEIs). It was found out that the development of the communication environment of higher education institutions should be aimed at increasing the share of students involved in academic mobility programs, which will allow to obtain in the future highly qualified specialists with international experience. It is specified that the current level of integration of digital technologies into the working and personal space of everyone, its daily growth puts forward new requirements for the mass communication means. One of the most influential factors in the level of communication of higher education institutions is the active promotion of all web resources of HEIs on the Internet, taking into account the specifics (professional, age, gender, etc.) of the target audience. Under these conditions, the relevance of the analysis of the communication environment of higher education institutions is growing. It is noted that the analysis of communication contacts of universities, academies, institutes with students, applicants and their parents and stakeholders using social networks indicates that all HEIs have pages on social networks Instagram and Facebook. The social network Twitter was not so popular with universities for communication. However, Ukrainian universities, which are considered «flagship ones», add all the possibilities to communication, which is why each of them has a sufficient number of followers in all popular social networks. It is concluded that today there is an unconditional relationship between the number of subscribers of HEIs in social networks and its rating indicators. Comparison of the quantitative characteristics of social network activity in the three separated groups of HEIs leads to the further conclusions. Leading universities in Ukraine do not ignore the possibilities provided by the latest technologies, the total number of followers in all social networks of each of them amounts to tens of thousands. The highest rates are in Kharkiv National University named after Karazin (over 20000 Instagram and Facebook and nearly 1000 on Twitter). The number of subscribers of all other HEIs differ insignificantly and is largely due to the number of students of the relevant institutions and in most cases does not exceed the mark of 3000-5000 participants

The research object is a pneumatic spring of a modern rolling stock. Using a two - mass calculation scheme, the diagrams “force-deformation” of a pneumatic spring are designed at driving speed of 160-200 km/h and high-speed driving of 201-250 km/h. It is determined that when the diameter of the connecting pipeline is changed from 20 to 35 mm, the inclination angle of the diagram “force - deformation” of the pneumatic spring is changed at speed driving from 32 degrees up to 57 deg.; at high-speed driving from 30 deg. up to 48 deg. It is proposed to determine a pneumatic spring operation coefficient using the forms of the designed diagrams “force - deformation.” Studying the specified coefficient in the speed range from 160 to 250 km/h, and the connecting pipeline diameter from 20 to 35 mm showed that the values of the pneumatic spring operation coefficient vary from 0.089 to 0.24, and the dependencies are nonlinear. Using the pneumatic spring operation coefficient will make it possible to further evaluate the pneumatic spring suspension system operation depending on the operating conditions of the railway vehicle.

The article is aimed at developing a theoretical and methodical approach to assessing the demand for higher education in Ukraine. Educational qualification levels, characterized by a specific range of information users, are analyzed. Accordingly, it is natural for every user to form a certain information environment, which can be useful and interesting for one level, but not in demand for another. Therefore, when learning environment coordinators develop a communication strategy, it is necessary to clearly understand, which level it is designed for. Thus, the issue of establishing a classification of learning environment coordinators, who will provide training for education seekers at different levels, is relevant. It is noted that the concept of demand for higher education should be differentiated between the demand in society and the demand among i education seekers. The choice of "fashionable" specialties without taking into account the needs of the labor market leads to increase in the disparity of the workload per vacancy for certain professional groups. In order to quantify the demand for higher education, it is proposed to use the coefficient of demand for higher education in society (CDHES). Necessity to take into account many factors influencing the demand for higher education in society has led us to choosing an integrated method, which is normally used to measure the impact of factors in multiplicative, index, additive index models. The coefficients suggested, in our opinion, will be important for higher education institutions (HEIs) wishing to develop a communication strategy for both the short and long term. The importance of such coefficients can be explained by the fact that the patterns and trends identified during the study of their dynamics can serve as an information field for the HEI management service when outlining key aspects in developing a new communication strategy or improving the existing one. The fundamental difference between the proposed coefficients and the already existing ones lies in the fact that the former take into account not only the dynamics of the labor market and employment opportunities, but also the economic feasibility of education costs, and calculation of the payback prospects of receiving higher education.

According to the purpose of the article, which is aimed at substantiating the compliance of the acquired competencies of higher education applicants in the field of economics and entrepreneurship with the content and the amount of program knowledge in mathematical statistics, a number of publications on this issue are analyzed. The existing competency-based approaches and peculiarities of training mathematics, as well as the essence of propedeutic knowledge and requirements for their subject matter are highlighted. The narrowed application of propedeutic knowledge and the lack of a systematic approach, taking into account interdisciplinary connections, are indicated. On the basis of the educational and professional program «Entrepreneurship, trade and exchange activities» the content of the working program of the discipline «Quality Management, standardization and certification» is analyzed. The essential tasks of the discipline are determined using statistical methods for the control and management of quality of products and services that require deep knowledge about mathematical statistics. The mechanism of establishing compliance of basic knowledge of the subject matter in mathematical statistics with applied tasks of quality management is proposed. The authors have elaborated the algorithms of systematization, evaluation and analysis of sampled data together with determination of type and parameters of their statistical distribution, corresponding to the main tasks of mathematical statistics. The presented algorithm of research is accompanied by visual diagrams, which step by step reflect the course of solving statistical tasks with the relevant formulas, tables and recommendations, which contributes to better and more conscious assimilation of the material. On the example of studying a particular professional discipline, a systematic methodical approach to the formation of propedeutic knowledge of an interdisciplinary nature with the setting of tasks in certain types of economic activity is substantiated. It is proposed to extend the use of developed approaches to other areas of knowledge in the sphere of education.

In accordance with the task of substantiating the economic-mathematical model and the method of optimizing the main directions of investment to maintain the raw-materials and technology base of a mining and dressing enterprise, their current status and problematic issues of production are analyzed. The main areas of investment activity are highlighted and their connection with the major resource and technological facilities of the enterprise’s production infrastructure is displayed. A stochastic factor analysis is carried out and the closeness of investment investments by the areas with the main economic indicators of the enterprise as a whole is determined. The most acceptable effective indicator for the working conditions of a particular enterprise is substantiated. Correlations between net profit and volumes of investment in technical rearmament, major repairs to machinery and equipment and capital construction are determined. The nature and degree of joint influence of directions of investments on net profit are analyzed. A criterion for evaluating the efficiency of investment use is proposed and an economic and mathematical model is developed. The method of optimizing the structure of directions, which is the method of dynamic programming, is substantiated. The model is adapted and implemented in the working conditions of a typical mining and dressing enterprise. The results of the efficiency of implementation of the optimal structure of investment directions are presented. For the working conditions of a particular mining and dressing enterprise, an optimal structure is determined that, in comparison with the actual, allowed to get a significant increase in net profit. The possibility of expanding the application area of economic-mathematical models together with the methods of optimization of this type to solve other production tasks has been indicated.

The deterioration common crossing elements increase the need for the maintenance of crossings and significantly reduce the reliability, availability and safety of railway traffic. The present paper introduces the results of experimental investigation of common crossing monitoring while its deterioration during the lifecycle of crossing. The conventional methods of common crossing condition estimation with time-based features like maximal accelerations, etc. are low appropriate as statistically significant condition indicators. The proposed multifractal analysis enables to extract the significant features from acceleration measurements. The extracted features are fused together with information about the train velocities and longitudinal position of wheels impact with the Lasso regularisation and multivariate linear regression. A ranking of feature importance is done and the redundant features are identified. The developed condition indicator has good correlation to the crossing lifetime and is simple for interpretation.

The article is devoted to problems of state regulatory policy of stimulation of economic growth, increase of efficiency of activity of industrial branches of the country. It considers examples of foreign experience in the part of state support of domestic manufacturers. It shows possible variants of integration of co-operation between CIS countries on the basis of specialisation, co-operation and joint activity for achieving economic growth of economies. It demonstrates an automated system of mass servicing of customers, which is offered to be used in the structure of associations of trade enterprises. It offers ways of achievement of competitive advantages of domestic enterprises under conditions of globalisation by means of introduction of clusters of the consumer market enterprises. The article reveals their shortcomings and possibilities of development in the territory of Ukraine under conditions of limited financial resources. It acknowledges that measures of the fiscal policy should be directed, first of all, at support of creation of associations of medium enterprises of the light and other branches of industry and agriculture, which have development potential. It identifies main elements of creation of state programmes of support and development of the cluster form of organisation of the light and other branches of industry, agriculture and trade.

Investigation of damages of the subgrade slope in combination with its overwetting and rolling stock loading, which significantly affects safety traffic of the railway transport, has been carried out. The complex method of slope stability estimation of the subgrade is developed, which includes calculation of loads and vibration action of rolling stock on the main site of the subgrade, as well as the dynamic model of vibrations propagation in the body of the subgrade embankment and the model of plastic deformations accumulation. Dynamic and nonlinear plastic models are based on a finite-element model of the cross section of the subgrade. The plastic model takes into account the characteristics of soil strength of the subgrade, depending on the area of the vibration load impact. The developed method allows to carry out the estimation of external and internal factors impact on occurrence of subgrade destruction, which is of practical value for safety state estimation of the railway transport.

The article considers growth of expenditures of enterprise operation, resource nationalism, necessity of a complex development of the Earth interiors as important factors of prospective development of the mining industry of Ukraine. It justifies that development of the mining industry in future should be accompanied with strengthening of the regulatory role of the state. It states that Ukraine should make maximum efforts for creation of favourable conditions for business within the state and stimulate return of capital into the national economy. Only this would help to avoid economic dependence, to become an equal player in the world market of metal intensive products, to protect national interests and to preserve the existing resource potential for future generations.Рассматриваются рост расходов эксплуатации предприятий, ресурсный национализм, необходимость комплексного освоения недр как существенные факторы перспективного развития горнорудной промышленности Украины. Обосновано, что развитие горнорудной промышленности в дальнейшем должно сопровождаться усилением регуляторной роли государства. Высказано убеждение, что Украина должна приложить максимум усилий для создания благоприятных условий для бизнеса в пределах государства и стимулировать возвращение капиталов в национальную экономику. Только при этом условии можно предотвратить экономическую зависимость, стать равноправным игроком на мировом рынке металлоемкой продукции, защитить национальные интересы и сохранить имеющийся ресурсный потенциал для будущих поколений.

The problem of the interaction of rolling stock with the rail track has been analyzed in the present paper. It has been established that in the process of transport science development a number of methods for determining the causes of wheel pairs derailment are developed, which, in a varying degree, take into account the peculiarities of their interaction. The problem of choosing the most accurate method for estimating the causes of rolling stock derailment becomes more complicated because of the lack of sufficient experimental data that would allow us to verify the adequacy of the models. The indicators of stability of the wheel against derailment, which are used on the railways of Ukraine and Europe, have been examined. Their dependences on the speed of movement were derived. It has been established that the increase of the speed of motion leads to the increase of the interaction power of the rolling stock with the rail track, which may, under certain operational parameters, provoke its derailment. As a result of the calculations, it has been shown that the use of norms for car design and calculation used on Ukrainian railways can lead to an inadequate estimation of traffic safety parameters, since it does not take into account the unevenness of the railway track. It has been established that the requirements of BS EN 14363: 2005 European norms are stricter in comparison with the norms for calculation and evaluation of the bearing elements strength and dynamic qualities of motor-vehicle rolling stock used on Ukrainian railways. A comparison of the experimentally and theoretically calculated values of the stability margin coefficient against wheel derailment of the first wheel pair of the diesel train car was carried out.

During recent years, great progress has been made in understanding the adsorption of surfactants at liquid interfaces. In addition to tensiometry, new efficient methodologies have been developed, in particular interfacial selective optical methods which allow direct access to the adsorbed amounts and interfacial layer compositions. In addition to these new experimental tools, the thermodynamic description by equations of state now allows one to provide a quantitative picture of surfactant interfacial layers. This is most notable for surfactant layers at water/oil interfaces. Additional knowledge about the structure of interfacial layers was gained through different types of molecular modeling. Improved interrelationships between these three aspects are the challenges for current and future work. Particular attention must be paid to dilational interfacial rheology studies, as these mechanical quantities are much more sensitive to small changes in the interfacial composition and structure.

The paper deals with relationships between the individual transmembrane fluxes of binary electrolyte solution components and the experimentally measurable quantities describing rates of transfer processes, namely, the electric current, the transmembrane volume flow and the rates of concentration changes in the solutions adjacent to the membrane. Also, we collected and rigorously defined the kinetic coefficients describing the membrane selective and electrokinetic properties. A set of useful relationships between these coefficients is derived. An important specificity of the proposed analysis is that it does not use the Irreversible Thermodynamic approach by analyzing no thermodynamic forces that generate the fluxes under consideration. Instead, all the regularities are derived on the basis of conservation and linearity reasons. The terminology "Kinematics of Fluxes" is proposed for such an analysis on the basis of the analogy with Mechanics where Kinematics deals with regularities of motion by considering no mechanic forces. The only thermodynamic steps of the analysis relate to the discussion on the partial molar volumes of electrolyte and ions that are the equilibrium thermodynamic parameters of the adjacent solutions. These parameters are important for interrelating the transmembrane fluxes of the solution components and the transmembrane volume flow. The paper contains short literature reviews concerned with the partial molar volumes of electrolyte and ions: the methods of measurement, the obtained results and their theoretical interpretations. It is concluded from the reviews that the classical theories should be corrected to make them applicable for sufficiently concentrated solutions, 1 M or higher. The proposed correction is taken into account in the kinematic analysis., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2023. Published by Elsevier B.V.)

Experimental data for tridecyl dimethyl phosphine oxide (C 13 DMPO) adsorption layers at the water/air interface, including equilibrium surface tension and surface dilational viscoelasticity, are measured by bubble and drop profile analysis tensiometry at different solution concentrations and surface area oscillation frequencies. The results are used to assess the applicability of a multistate model with more than two possible adsorption states. For the experiments with single drops, the depletion of surfactant molecules due to adsorption at the drop surface is taken into account. For the assessment, the same set of model parameters is used for the description of all obtained experimental dependencies. The agreement between the proposed model and the experimental data shows that for the nonionic surfactant C 13 DMPO, the description of the adsorption layer behavior by three adsorption states is superior to that with only two adsorption states.

The theoretical description of the adsorption of surfactants at interfaces between aqueous solutions and oil was based over a very long time on models derived for the solution/air interface. Thus, most of the experimentally observed peculiarities could not be specifically considered but were merely interpreted in terms of a penetration of oil molecules into the alkyl chain layer of the adsorbed surfactant molecules. These penetrating oil molecules enhance the surfactant adsorption as compared to the water/air interface. Later on, for the special situations at water/oil interfaces a competitive adsorption of surfactant and oil molecules was postulated, allowing a much better description of experimental data. This picture, however, was unable to explain why the interfacial tension of the water/oil interface decreases very quickly when extremely small amounts of surfactants are added to the water. This effect cannot be of competitive nature, but a cooperativity of surfactant and oil molecules forming a mixed adsorption layer is required instead. This cooperative effect means that already few surfactant molecules adsorbed at the interface can induce a significant ordering of oil molecules in the interfacial layer. This new interfacial structure, in turn, attracts further surfactant molecules to adsorb. Improving the theoretical description of experimental data was finally achieved by applying suitable adsorption models for the two adsorbing compounds, i.e. a Frumkin adsorption model for the oil molecules and a Langmuir, Frumkin, or reorientation model for the adsorbing surfactant molecules. Here, the progress in modelling surfactant adsorption at water/oil interfaces is discussed mainly for the homologous series of the cationic surfactants C n TAB, of the anionic surfactant SDS, and members of the homologous series of the non-ionic surfactants C n DMPO at water/alkane interfaces., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2020 Elsevier B.V. All rights reserved.)

The sedimentation of a two-dimensional suspension containing rods was studied by means of Monte Carlo (MC) simulations. An off-lattice model with continuous positional and orientational degrees of freedom was considered. The initial state before sedimentation was produced using a model of random sequential adsorption. During such sedimentation, the rods undergo translational and rotational Brownian motions. The MC simulations were run at different initial number densities (the numbers of rods per unit area), ρ_{i}, and sedimentation rates, u. For sediment films, the spatial distributions of the rods, the order parameters, and the electrical conductivities were examined. Different types of sedimentation-driven self-assembly and anisotropy of the electrical conductivity were revealed inside the sediment films. This anisotropy can be finely regulated by changes in the values of ρ_{i} and u.

The dilational visco-elasticity of surfactant adsorption layers was measured at low frequencies by the drop profile analysis tensiometry using oscillating drops. As the studied non-ionic surfactant C 13 DMPO (tridecyl dimethyl phosphine oxide) is soluble in water and in hexane, the partitioning of the surfactant between the two solvents had to be taken into consideration. The diffusion controlled exchange of matter theory was generalized in order to take into consideration the curvature of the interface, the diffusional transport in both adjacent bulk phases as well as the transfer across the liquid interface. Using two configurations, i.e. water drop in hexane and hexane drop in water, it is shown that the frequency dependence of the visco-elasticity modulus and the phase angle can be well described when the correct partition coefficient is applied. The surface activity of the selected surfactant C 13 DMPO is optimum to demonstrate the impact of matter transfer across the interface on the dilational visco-elasticity of interfacial adsorption layers of non-ionic surfactants., (Copyright © 2018 Elsevier Inc. All rights reserved.)

Drop profile analysis tensiometry used in the oscillating drop mode provides the dilational viscoelasticity of adsorption layers at liquid interfaces. Applied during the progress of adsorption the dynamic surface rheology can be monitored. For β-casein solutions at the same surface pressure values, the larger the dynamic dilational viscoelasticity the longer the adsorption time, i.e., the smaller the studied protein concentration is. For β-lactoglobulin and human serum albumin, the differences in the viscoelasticity values are less or not dependent on the adsorption time at identical surface pressures. The observed effects are caused by the flexibility of BCS, while the globular proteins BLG and HSA do not change their conformation significantly within the adsorption layer.

The dynamic and equilibrium surface tension for drops of aqueous C 14 EO 8 solutions at the interface to pure air or pentane, hexane, heptane and toluene saturated air, and the dynamic surface tension of pure water at these interfaces are presented. Two theoretical models were employed: both assuming a diffusion controlled adsorption of the surfactant, and either a diffusion or kinetic barrier governed adsorption of the alkanes. The experimental results are best described by the model which implies a diffusion control for the C 14 EO 8 molecules and the existence of a kinetic barrier for the alkane molecules. The desorption of alkanes from the surface layer after equilibration and their subsequent removal from the measuring cell was studied as well. The desorption process was shown to be slow for heptane and hexane. However, for the pentane vapor the desorption is quite rapid, and after the desorption commences the surface tension becomes equal to that at the interface with pure air.

The dilational viscoelasticity of adsorption layer was measured at different frequencies of drop and bubble surface area oscillations for aqueous C12EO5 solutions. The modulus values obtained by the two experimental protocols are the same for Π < 15 mN/m, while for higher surface pressures the values from drop experiments exceed those from bubble profile analysis. The nature of this phenomenon was studied using stress deformation experiments. At high surfactant concentrations the magnitude of surface tension variations is essentially higher for drops as compared with bubbles, leading to an increased viscoelasticity modulus for oscillating drops. The observed effects are analyzed quantitatively using a diffusion controlled exchange of matter model. The viscoelasticity moduli for a number of surfactants (different CnEOm and Tritons, C13DMPO, and SDS) are reported, and it is shown that the discrepancies between the data obtained by the two methods for many surfactants agree well with the predictions made here.

On the surface of bubbles rising in a surfactant solution the adsorption process proceeds and leads to the formation of a so called Rear Stagnant Cap (RSC). The larger this RSC is the stronger is the retardation of the rising velocity. The theory of a steady RSC and steady retarded rising velocity, which sets in after a transient stage, has been generally accepted. However, a non-steady process of bubble rising starting from the initial zero velocity represents an important portion of the trajectory of rising, characterized by a local velocity profile (LVP). As there is no theory of RSC growth for large Reynolds numbers Re » 1 so far, the interpretation of LVPs measured in this regime was impossible. It turned out, that an analytical theory for a quasi-steady growth of RSC is possible for small Marangoni numbers Ma « 1, i.e. when the RSC is almost completely compressed, which means a uniform surface concentration Γ(θ)=Γ(∞) within the RSC. Hence, the RSC angle ψ(t) is obtained as a function of the adsorption isotherm parameters and time t. From the steady velocity v(st)(ψ), the dependence of non-steady velocity on time is obtained by employing v(st)[ψ(t)] via a quasi-steady approximation. The measurement of LVP creates a promising new opportunity for investigation of the RSC dynamics and adsorption kinetics. While adsorption and desorption happen at the same localization in the classical methods, in rising bubble experiments desorption occurs mainly within RSC while adsorption on the mobile part of the bubble surface. The desorption flux from RSC is proportional to αΓ(∞), while it is usually αΓ. The adsorption flux at the mobile surface above RSC can be assumed proportional to βC0, while it is usually βC0(1-Γ/Γ(∞)). These simplifications may become favorable in investigations of the adsorption kinetics for larger molecules, in particular for globular proteins, which essentially stay at an interface once adsorbed., (Copyright © 2014 Elsevier B.V. All rights reserved.)

The paper contains an extended historical overview of research activities focused on determining interfacial potential and charge of dispersed particles from electrophoretic and coagulation dynamic measurements. Particular attention is paid to nano-suspensions for which application of Standard Electrokinetic Model (SEM) to analysis of experimental data encounters difficulties, especially, when the solutions contain more than two ions, the particle charge depends on the solution composition and zeta-potentials are high. Detailed statements of Standard Electrokinetic and DLVO Models are given in the forms that are capable of addressing electrophoresis and interaction of particles for arbitrary ratios of the particle to Debye radius, interfacial potentials and electrolyte compositions. The experimental part of the study consists of two groups of measurements conducted for Pt/C nano-suspensions, namely, the electrophoretic and coagulation dynamic studies, with various electrolyte compositions. The obtained experimental data are processed by using numerical algorithms based on the formulated models for obtaining interfacial potential and charge. While analyzing the dependencies of interfacial potential and charge on the electrolyte compositions, conclusions are made regarding the mechanisms of charge formation. It is established that the behavior of system stability is in a qualitative agreement with the results computed from the electrophoretic data. The verification of quantitative applicability of the employed models is conducted by calculating the Hamaker constant from experimental data. It is proposed how to explain the observed variations of predicted Hamaker constant and its unusually high value., (Copyright © 2014 Elsevier B.V. All rights reserved.)

The complementary drop and bubble profile analysis and maximum bubble pressure tensiometry are used to measure the dynamic surface tension of aqueous SDS solutions in the presence of hardness salts (CaCl(2) and MgCl(2) in the ratio of 2:1 at concentrations of 6 and 40FH). The presence of hardness salts results in an essential increase of the SDS adsorption activity, which indicates the formation of Ca(DS)(2) and Mg(DS)(2) in the SDS solutions. The surface tension isotherms of SDS in presence of Ca(DS)(2) and Mg(DS)(2) are described using the generalised Frumkin model. The presence of hardness salts accelerates the ageing of SDS solutions as compared with the addition of 0.01 M NaCl due to a faster hydrolysis and hence formation of dodecanol. These results are used to estimate the possible concentration of dodecanol in the studied SDS solutions. The buoyant bubble profile method with harmonic surface oscillations is used to measure the dilational rheology of SDS solutions in presence of hardness salts in the frequency range between 0.005 Hz and 0.2 Hz. The visco-elasticity modulus in the presence of hardness salts is higher as compared with its values in the presence of 0.01 M NaCl additions. The ageing of SDS solutions leads to an essential increase of the visco-elastic modulus., (Copyright © 2012 Elsevier Inc. All rights reserved.)

The review summarizes the results of the recent studies of the electrokinetic relaxation process within the meniscus region during the deposition of charged Langmuir monolayers. Such electrokinetic relaxation is the consequence of the initial misbalance of partial ion fluxes within a small region near the contact line, where the diffuse parts of electric double layers, formed at the monolayer and the substrate surface, overlap. The concentration polarization within the solution near the three-phase contact line should lead to long-term relaxations of the meniscus after beginning and stopping the deposition process, to changes of the ionic composition within the deposited films, to change of the interaction of the monolayer with the substrate, and to dependence of the maximum deposition rate on the subphase composition.

Nonstationary kinetics of the ion redistribution within the meniscus region during deposition of a charged Langmuir monolayer after beginning or stopping of the substrate motion is analyzed on the basis of the results of numerical simulations. The time evolution of the ions concentration profiles forming at the contact line and propagating toward the bulk solution is considered. It is shown that the diffusion front propagates much slower within the region of overlapping diffuse layers than outside of this region. At the beginning of the deposition process a region characterized by quasi-stationary behavior of the ion concentration and electric potential distributions is formed in close vicinity to the contact line. A stationary deposition regime is established when the region of quasi-stationary distributions reaches the external boundary of the Nernst layer provided that the substrate motion is not very fast. For the substrate velocities higher than the critical one the concentration near the contact line can decrease to such small values which do not allow a stable deposition process. The developed mathematical model allows addressing to transient regimes of the monolayer deposition which are very important for understanding the mechanisms leading to meniscus instability., (© 2011 American Chemical Society)

For the understanding of short-time adsorption phenomena and high-frequency relaxations at liquid interfaces particular experimental techniques are needed. The most suitable method for respective studies is the capillary pressure tensiometry. However, under gravity conditions there are rather strong limitations, in particular due to convections and interfacial deformations. This manuscript provides an overview of the state of the art of experimental tools developed for short-time and high-frequency investigations of liquid drops and bubbles under microgravity. Besides the brief description of instruments, the underlying theoretical basis will be presented and limits of the applied methods under ground and microgravity conditions will be discussed. The results on the role of surfactants under highly dynamic conditions will be demonstrated by some selected examples studied in two space shuttle missions on Discovery in 1998 and Columbia in 2003., (Copyright © 2010 Elsevier B.V. All rights reserved.)

Depending on the bulk composition, adsorption layers formed from mixed protein/surfactant solutions contain different amounts of protein. Clearly, increasing amounts of surfactant should decrease the amount of adsorbed proteins successively. However, due to the much larger adsorption energy, proteins are rather strongly bound to the interface and via competitive adsorption surfactants cannot easily displace proteins. A thermodynamic theory was developed recently which describes the composition of mixed protein/surfactant adsorption layers. This theory is based on models for the single compounds and allows a prognosis of the resulting mixed layers by using the characteristic parameters of the involved components. This thermodynamic theory serves also as the respective boundary condition for the dynamics of adsorption layers formed from mixed solutions and their dilational rheological behaviour. Based on experimental studies with milk proteins (beta-casein and beta-lactoglobulin) mixed with non-ionic (decyl and dodecyl dimethyl phosphine oxide) and ionic (sodium dodecyl sulphate and dodecyl trimethyl ammonium bromide) surfactants at the water/air and water/hexane interfaces, the potential of the theoretical tools is demonstrated. The displacement of pre-adsorbed proteins by subsequently added surfactant can be successfully studied by a special experimental technique based on a drop volume exchange. In this way the drop profile analysis can provide tensiometry and dilational rheology data (via drop oscillation experiments) for two adsorption routes--sequential adsorption of the single compounds in addition to the traditional simultaneous adsorption from a mixed solution. Complementary measurements of the surface shear rheology and the adsorption layer thickness via ellipsometry are added in order to support the proposed mechanisms drawn from tensiometry and dilational rheology, i.e. to show that the formation of mixed adsorption layer is based on a modification of the protein molecules via electrostatic (ionic) and/or hydrophobic interactions by the surfactant molecules and a competitive adsorption of the resulting complexes with the free, unbound surfactant. Under certain conditions, the properties of the sequentially formed layers differ from those formed simultaneously, which can be explained by the different locations of complex formation.

The present study deals with dilational and shear rheological properties of adsorption layers of the milk protein beta-casein (BCS) mixed with the nonionic dodecyl dimethyl phosphine oxide (C12DMPO) and the positively charged dodecyl trimethyl ammonium bromide (DoTAB), respectively. The drop profile analysis tensiometer PAT-1 was applied for the dilational rheological studies at low frequency harmonic relaxations. A special modification of the setup, consisting of a coaxial capillary combined with a double dosing system, provides exchange of the drop volume during experiments. This arrangement offers a unique protocol for studies of mixed surface layers, formed by sequential adsorption of the individual compounds. The dilational viscoelastic modulus and the dilational viscosity of the mixed layers, built-up in the two different ways, were investigated and compared. The features of the mixed surface layers drawn from the dilational rheology are qualitatively confirmed by the shear rheological parameters measured by torsion shear rheometry ISR-1. Recently derived theoretical models were used for a quantitative description of the equilibrium state and dilational rheology of the surface layers formed by the single components and their mixtures.

The effect of ion transfer kinetics on the ionic composition of Langmuir-Blodgett (LB) films formed by charged monolayers is analyzed. The dynamic regimes of the LB deposition are considered by taking into account the competitive adsorption of several counterions having different diffusivities, valences, binding constants, and bulk concentrations. It is shown that the composition of deposited films should change with the deposition rate. At lower deposition rates, the ion with higher binding constant is more represented within the deposited monolayer in comparison to the higher deposition rates. At low deposition rates, the ratio of counterion amounts within the LB films is the same as that within the floating monolayer excluding the ions within the diffuse layer. At high deposition rates, the ratio of the counterion amounts is the same as that within the floating monolayer when the potential-determining counterions within the diffuse layer are taken into account.

The analysis of processes taking place in a steady pneumatic (dynamic) foam shows the possibility of different modes of surfactant accumulation within the top layers of bubbles due to rupture of external foam films. An increasing surfactant concentration within the top layers promotes the stabilisation of bubbles and the foam as a whole. Considering the balance of surfactant and water during the bursting of films it is possible to estimate the accumulated surfactant loss caused by a downwards flow through the Plateau borders of the subsurface bubble layer. This effect depends on the particular conditions, especially on the surfactant activity and concentration of the surfactant, water volume fraction in the foam and size of foam bubbles. The process of surfactant accumulation in the top foam bubble layer can be complicated due to the removal of part of the accumulated surfactant through transport with droplets spread out during bubble bursting.

Under dynamic conditions of the charged Langmuir monolayer deposition onto a substrate surface, ion concentration and electric potential profiles are induced in the subphase around the three-phase contact line. Such local changes in the subphase influence the deposition process, particularly the monolayer adhesion work and the maximum deposition rate. If indifferent electrolytes (not interacting chemically with interfacial groups) are present in the solutions, they can affect electric potential distributions and therefore the monolayer charge and the deposition process as a whole. With increasing deposition rate, the indifferent electrolyte counterions replace gradually the potential-determining counterions in a close vicinity to the contact line. This leads to increasing monolayer ionization and increasing electrostatic repulsion between the monolayer and substrate. When the deposition rate approaches the critical one, the charge of the monolayer increases dramatically and the stationary monolayer deposition becomes impossible. Such a significant increase of the monolayer charge is not observed in the absence of indifferent electrolytes.

Surface layers of micro- and nanoparticles at fluid/liquid interfaces in absence and presence of surfactants are of large importance in the process of re-discovering Pickering systems, i.e. emulsions and foams stabilized by particles. The surface pressure/area isotherms of such layers can provide information about the properties of the used particles (dimensions, interfacial contact angles), the structure of interfacial layers, the interactions between the particles as well as about relaxation processes within the layers. For a correct description of Pi-A isotherms of composite surface layers containing particles the significant difference in size of these particles to that of solvent and surfactant molecules should be taken into account. Corresponding equations can be derived on the basis of the two-dimensional solution theory. The gained equations provide satisfactory agreement with experimental data and predict realistic values for the area of particles at the interface. Also equations of state and of the dilational elasticity for composite surface layers containing particles can be obtained in the framework of the presented methodology.

The dilational rheology for mixed solutions of surface active compounds is easy to measure with existing methods, however, there are very few attempts only to analyse the resulting data on the basis of a theoretical model. Models by Jiang et al., Joos, and by Lucassen and van den Tempel (for single compounds) are compared here and applied to experimental data. The mentioned models converge to each other after some small modifications and represent a very good scientific background for studies of the mechanical behaviour of mixed adsorption layers. As example, the experimental results for mixed solutions containing a globular protein (beta-lactoglobulin) and a non-ionic surfactant (alkyl dimethyl phosphine oxide) are analysed by the obtained dependencies, using some new proposed numerical procedures.

The thermodynamic model of a 2D solution developed earlier for protein monolayers at liquid interfaces is generalized for monolayers composed of micro- and nanoparticles. Surface pressure isotherms of particle monolayers published in the literature for a wide range of particles sizes (between 75 microm and 7.5 nm) are described by the theoretical model with one modification. The calculations of surface pressure pi on area A provide satisfactory agreement with the experimental data. The theory also yields reasonable cross-sectional area values of the solvent molecule water in the range between 0.12 and 0.18 nm2, which is almost independent of particle size. Also, the area per particle in a closely packed monolayer obtained from the theory is quite realistic.

A mathematical problem is formulated and numerically solved for addressing the electric field and ionic concentration distributions developing around the three-phase contact line during the Langmuir-Blodgett deposition of charged monolayers. Compared to a previous paper dealing with the same effect (J. Phys. Chem. B 2004, 108, 13449), the present analysis is not restricted to the case of low deposition rates and small concentration changes. The obtained results show that, for sufficiently high deposition rates, the subphase composition substantially changes in the immediate vicinity of the three-phase contact line. It is shown that the predicted changes in the subphase composition can drastically affect the adhesion work and the dynamic contact angle. On this basis, the influence of the concentration polarization effect on meniscus behavior is discussed.

A comparative investigation of the adsorption of (13)C(18)O + (12)C(16)O and (13)C(16)O + (12)C(16)O mixtures on silica-supported Pt has been conducted. It is advantageous to use (13)C(18)O + (12)C(16)O mixtures rather than (13)C(16)O + (12)C(16)O to probe the adsorption sites and electronic state of supported Group VIII metals because the vibrational bands of the adsorbed (13)C(18)O and (12)C(16)O isotopic molecules do not overlap. In addition, while an intensity redistribution suppresses the lower-frequency band with adsorbed (13)C(16)O and (12)C(16)O with vibrational frequencies differing by 50 cm(-1), the intensity redistribution is less pronounced with the adsorbed (13)C(18)O and (12)C(16)O in which the frequency difference is 100 cm(-1). Moreover, the small intensity redistribution that does occur between the bands of adsorbed (13)C(18)O and (12)C(16)O still allows the detection of the vibrational band of adsorbed (13)C(18)O at (13)C(18)O gas-phase concentrations as low as 3%. At such low concentrations, the dipole-dipole interaction between adsorbed (13)C(18)O molecules is negligible, and, hence, both the singleton frequency and the dipole-dipole shift for adsorbed CO may be obtained in a single experiment. Two types of strongly bound and one type of weakly bound linear CO-Pt adsorption complexes have been identified and characterized by their singleton frequencies and dipole-dipole coupling shifts. The origin of these CO adsorption modes is discussed.

Considering the deposition of charged Langmuir monolayers, it is necessary to take into account electrostatic interactions between the monolayer and the substrate surface. These interactions depend on the nature of ionizable surface groups and on the ionic composition of the subphase (e.g. pH, multivalent counterions, indifferent electrolytes). The non-uniformity of electric, concentration and hydrodynamic velocity fields leads to the formation of ion concentration profiles near the three-phase contact line during the deposition. This effect is similar to the effect of concentration polarization in membranes and electrode systems. The ions redistribution results in change of the monolayer ionization, adhesion work, dynamic contact angle, and, therefore, in the change of morphology, composition and structure of the deposited monolayer. With increasing withdrawal velocity the meniscus can become unstable because of concentration polarization in the solution.

The frequency and concentration dependencies of the dilational elasticity and viscosity of adsorbed surfactant layers is yet not quantitatively understood. Especially at a surface coverage above 50% the measured high frequency limits of the elasticity pass typically a maximum or reach a plateau while classical models expect an exponential increase to very high values. The consideration of an intrinsic two-dimensional compressibility allows a much better description of experimental data. There are various surfactant systems discussed in literature following this new model. Although the impact of these interfacial characteristics on the dilational rheology is significant, the adsorption isotherm and equation of state change only slightly.

The experimental data on the surface rheological characteristics of dodecyl dimethyl phosphine oxide solutions obtained in a fully automatic oscillating bubble device under microgravity conditions in the frequency range 0.01-100 Hz are presented. The complex surface elasticity modulus is obtained form the amplitude- and phase-frequency characteristics of established pressure oscillations in a closed cell without calibration experiments by direct calculation of the necessary coefficients. The characteristics of the adsorption layers obtained from the elasticity modulus are in good agreement with adsorption isotherms and equations of state accounting for the intrinsic (2D) monolayer compressibility.

The present analysis shows that the introduction of intrinsic two-dimensional compressibility of a surfactant adsorption layer allows a much better interpretation of experimental data on the limiting (high-frequency) elasticity and characteristic frequency of diffusional relaxation than models using Frumkin's or other adsorption isotherms. The proposed model describes experimental data on surface dilational elasticity, as well as on surface pressure, sufficiently well at low and high surfactant concentrations, assuming the Lucassen and van den Tempel model of surface dilational elasticity is realized.

The amplitude- and phase-frequency characteristics of oscillating bubble systems with a closed measuring cell are analyzed. The shape of the frequency characteristics is qualitatively different for bubbles smaller or larger than a hemisphere, respectively, and also for diluted and concentrated surfactant solutions. Moreover, the presence of a surfactant in the solution strongly influences the characteristic frequencies of the system. The experiments performed under ground and microgravity conditions show a good qualitative agreement with theoretically predicted amplitude- and phase-frequency characteristics and confirm the adequacy of the proposed theory. The comparison of high-frequency limits of the surface dilatational elasticity with the theoretical Gibbs elasticities calculated according to the respective adsorption isotherm shows good agreement for small surfactant concentrations. At higher concentrations large discrepancies are observed which can possibly be explained by the violation of the linearity condition for the surface layer.

Theoretical studies are performed to explain the mechanism of surface tension auto-oscillations recently found. The Marangoni instability in a system containing a surfactant droplet under the air-water interface is investigated numerically. The simulations, based on the equations of fluid mechanics, take into account convective diffusion and adsorption of the surfactant. The behavior of the system is determined by nonstationary concentration gradients that are nonuniform on the surface as well as in the normal to the surface direction. Initially a slow diffusion dissolution of the drop material takes place. The convective transfer of the surfactant is negligible, the surface tension remains nearly constant and the system parameters change rather slowly during the induction period. With the increase of the concentration gradients the system becomes unstable, resulting in a jump in the convection velocity, surface tension, and adsorption on the surface. The concentration and velocity distributions in the bulk and on the surface are obtained from the numerical solution of the problem. The contributions of different mechanisms of the mass transfer are compared in different stages of the process.

The dynamic behavior of a bubble or drop oscillating at the tip of a capillary immersed in a surfactant solution is considered. The pressure variation in the cell and the nonstationary flow in the capillary are taken into account. The amplitude- and phase-frequency characteristics of the system are obtained, which contain information about the relaxation processes at the interface and in the bulk phases. Their dependency on the system geometry, the bulk properties of contacting media, and the viscoelastic properties of the interface is analyzed. Copyright 2000 Academic Press.

Human biological liquids comprise various surfactants, which adsorb at liquid interfaces and lead to a variation in surface tension. The adsorption processes involving low molecular weight surfactants, proteins and phospholipids play a vital role in the physiological functions of the human organism, especially if large surfaces are involved (e.g., gas exchange in lungs, metabolism of kidneys, liver and brain). Dynamic surface tensiometric studies of biological liquids like serum and cerebrospinal fluid provide surrogate parameters that reflect surface tension phenomena. We provide dynamic surface tension data of serum and cerebrospinal fluid that were collected from healthy volunteers and patients with rheumatic, neurological or oncological diseases. Our studies indicate that dynamic surface tension data are helpful for diagnostic purposes and for monitoring of therapeutic interventions.

A theoretical analysis is given to describe the behavior of an oscillating bubble in a closed measuring cell taking into account the finite liquid compressibility and the cell deformation. The results show that the behavior of a closed liquid cell can differ significantly from that of open cells. For example, under the same conditions two stable meniscus positions can be obtained in a closed cell. In a closed cell a meniscus larger than a hemisphere can be stable even when the gas compartment is open, while in an open cell such a meniscus is always unstable. For closed cells the meniscus can jump between the two equilibrium positions either randomly or under the influence of regular factors, such as external pressure, temperature, and surface tension changes. Relationships are obtained for the description of the pressure response on external harmonic perturbations which make it possible to determine the complex dilatational elasticity as a function of frequency. It is shown that the measured signal can depend on the cell properties, which should be taken into account in the interpretation of experimental data. Copyright 2000 Academic Press.

A convolution-type equation has been derived to describe the behavior of a bubble under periodical pressure oscillations. This equation holds for a diffusion-controlled adsorption mechanism and small disturbances of the equilibrium state, and it describes both the established and transition regimes of bubble oscillation. Systems free of any surfactant and in the presence of a surfactant are considered. The results obtained allow all aspects of surfactant influence on the bubble oscillation resonance to be analyzed. The sharp increase in the bubble oscillation amplitude may result in bubble detachments, even at rather low harmonic pressure oscillations. The presence of surfactant can result in a depression of the resonance amplitudes. Copyright 2000 Academic Press.

Long-time auto-oscillation of the surface tension can evolve when in an aqueous system a diethyl phthalate droplet is placed under the free water surface. The experimental conditions for development of surface tension auto-oscillations are described. Based on a theoretical analysis the mechanism of these auto-oscillations is proposed. The mechanism of the auto-oscillations results from a switching between diffusion and convection transfer of diethyl phthalate in the solution. A periodic Marangoni flow on the water surface resulting from a surface layer instability is discussed. The solubility of the amphiphile in the water and its surface activity are the main characteristics that determine the system behavior.