Drop in a metastable vapor: Laplace equation,surface tension,and minimum drop size

A van der Waals mean field theory is applied to a Lennard–Jones fluid for studying drop formation in a supersaturated vapor. A spherical surface separates the fluid particles in two homogeneous regions. The model provides densities, radii, minimum radii and excess pressure. By comparing the excess pressure with that given by the Laplace equation, surface tension is worked out. Its dependence on drop size, densities, and temperature, and its asymptotic values to planar interface are found. The model reveals the existence of an absolute minimum drop and drops with densities close to the supersaturated vapor.     

The permeation of binary gas mixtures through support structures of composite membranes

The dusty gas model (DGM) is used to describe transport of binary gas mixtures through porous membrane supports to quantify the resistance towards permeation. The model equations account for three different transport mechanisms for the permeating components: conventional viscous pore flow, Knudsen diffusion, and binary diffusion. Experimental data obtained with the uncoated membrane supports are used to determine the morphological parameters needed in the DGM equations. Flat sheet and hollow fiber membrane supports are characterized by the permeation of a TCE/nitrogen vapor. The DGM shows an excellent fit to experimental data when the asymmetric structure of the membrane supports is taken into account, but the morphological parameters cannot necessarily be related to precise physical structure parameters such as pore size, porosity, and tortuosity. The DGM works well even when the membrane supports are modeled as a single homogenous structure. The membrane supports exhibit different resistances towards the various transport mechanisms that occur within the porous support and the resistances vary with process conditions so that support optimization is not straightforward. With the analysis presented in this paper and transport equations specific to the dense coating and module geometries, the influence of the support layer on gas or vapor separation can be quantified.     

Equations for describing liquid-vapor phase equilibria in binary mixtures

Three forms of equations for describing experimental data on liquid and vapor pressures, depending on temperature and composition at phase equilibria in binary mixtures, are proposed and evaluated. It is determined that the form of equation depends on the relationship between the temperature of a mixture and the critical temperatures of the components of the mixture. Exact data on the phase equilibria in nitrogenoxygen, nitrogen-argon, and oxygen-argon mixtures [1] are approximated to assess the effectiveness of the equations’ forms. It is found that the equations also allow us to determine the phase composition at a given temperature and pressure and temperatures of phases at a given pressure and composition.     

A Helmholtz energy equation of state for calculating the thermodynamic properties of fluid mixtures

A new approach has been developed for calculating the properties of mixtures based on an equation of state explicit in reduced Helmholtz energy. This approach allows for the representation of the thermodynamic properties over a wide range of fluid states and is based on highly accurate equations of state for the pure components combined at the reduced temperature and density of the mixture. The reducing parameters used for temperature and density depend on composition. For simple mixtures (those that closely follow Raoult's law), a very accurate representation of all thermodynamic properties has been achieved with relatively simple functions. For nonideal mixtures, the reducing functions for density and temperature were modified, and a departure function was added to the equation of state. Generally, the model is able to represent liquid and vapor states with uncertainties of 0.1% in density, 1% in heat capacities and 1% in bubble point pressures if experimental data of comparable uncertainties exist. Two applications of the mixture model concepts were developed independently by the authors in the United States and Germany over the same time period. These applications include the development of individual equations for each binary system and a generalization of the model which is valid for a wide variety of mixtures. The individual approaches are presented with an explanation of the similarities and differences. Although the paper focuses mainly on binary systems, some results for ternary mixtures are also presented.     

Study on volatility and flash point of the pseudo binary mixtures of sunflower-based biodiesel + methylcyclohexane

The transesterification of sunflower seed oil was carried out in supercritical ethanol without using any catalyst to produce biodiesel. In the present work, methylcyclohexane was added to enhance the vapor pressure of biodiesel. The vapor pressures of mixtures of biodiesel + methylcyclohexane as a function of temperature were measured by comparative ebulliometry with an inclined ebulliometer. The vapor pressures versus composition at different temperatures were obtained. Experimental data of vapor pressures and equilibrium temperatures were correlated by the Antoine equation. A mathematical model was used to predict the flash point of the pseudo binary mixtures. With the regular solution theory, the predictive flash point displays agreement with the experimental data obtained by closed cup test.     

Vapor permeation of ethanol-water mixtures using sodium alginate membranes with crosslinking gradient structure

For the vapor permeation of ethanol-water mixtures, two types of dense sodium alginate (SA) membranes have been prepared: a nascent SA membrane and crosslinked SA membranes with glutaraldehyde (GA). In the vapor permeation of the concentrated ethanol-water mixtures through the SA membranes, the effects of feed temperature, cell temperature and crosslinking density in the membrane were investigated on the membrane performance, and a comparison of vapor permeation process was made with pervaporation. SA membranes having different crosslinking gradients have been fabricated by exposing the nascent membrane to different GA content of reaction solutions. The extent of the gradient was controlled by the exposing time. The permeation performance of the membranes will be discussed with the extent of the gradient. An optimal crosslinking gradient was determined in terms of flux and membrane stability. The separation of ethanol-water mixtures through the membrane with the optimal crosslinking gradient was carried out by vapor permeation and the permeation performance will be discussed, and compared with pervaporation.     

Analyzing the density fluctuation effect on molecular distributions in small drops

The characteristics of a vapor-liquid interface are calculated using the lattice gas model applied to the analysis of the states of metastable supersaturated vapor, depending on the size of a liquid drop and the system temperature. The interaction of molecules is considered in a quasi-chemical approximation describing the effects of direct correlations of nearby molecules. It is found that considering the density fluctuation increases the drop radius, corresponding to the condition of the generation of a new phase.     

Effect of anionic surfactant and short-chain alcohol mixtures on adsorption at quartz/water and water/air interfaces and the wettability of quartz

Measurements of the advancing contact angles for aqueous solutions of sodium dodecyl sulfate (SDDS) or sodium hexadecyl sulfonate (SHS) in mixtures with methanol, ethanol, or propanol on a quartz surface were carried out. On the basis of the obtained results and Young and Gibbs equations the critical surface tension of quartz wetting, the composition of the surface layer at the quartz-water interface, and the activity coefficients of the anionic surfactants and alcohols in this layer as well as the work of adhesion of aqueous solutions of anionic surfactant and alcohol mixtures to the quartz surface were determined. The analysis of the contact angle data showed that the wettability of quartz changed visibly only in the range of alcohol and anionic surfactant concentration at which these surface-active agents were present in the solution in the monomeric form. The analysis also showed that there was a linear dependence between the adhesion and the surface tension of aqueous solutions of anionic surfactant and alcohol mixtures. This dependence can be described by linear equations for which the constants depend on the anionic surfactant and alcohol concentrations. The slope of all linear dependence between adhesion and surface tension was positive. The critical surface tension of quartz wetting determined from this dependence by extrapolating the adhesion tension to the value equal to the surface tension (for contact angle equal zero) depends on the assumption whether the concentration of anionic surfactant or alcohol was constant. Its average value is equal to 29.95mN/m and it is considerably lower than the quartz surface tension. The positive slope of the adhesion-surface tension curves was explained by the possibility of the presence of liquid vapor film beyond the solution drop which settled on the quartz surface and the adsorption of surface-active agents at the quartz/monolayer water film-water interface. This conclusion was confirmed by the work of adhesion of aqueous solutions of anionic surfactants and short-chain alcohol mixtures to the quartz surface determined on the basis of the contact angle data and molar fraction of anionic surfactants and alcohols and their activity coefficient in the surface layer.     

Analysis of phase change during pervaporation with single component permeation

Individual (single) component pervaporation study helped to address some of the basic curiosities for the process of pervaporation. Investigations were carried out to focus on the location of vaporization during single component pervaporation. A mathematical model was developed for single component permeation during pervaporation, assuming two zones inside the membrane; namely, liquid permeation and vapour permeation zones. Considering a pressure distribution across the thickness of the membrane, Kelvin equation (saturation vapour pressure gets modified inside the membrane due to permeant membrane interactions) proved to be useful in developing the model. According to the model assumptions, the sorbed liquid first transports as liquid; and as soon as it finds the region, where pressure is Kelvin pressure, it evaporates and continues to transport as vapor. Further, the developed model was found to be useful in describing the flux in terms of downstream pressure variations. Accordingly, location of vaporization was determined. It was observed that vapor phase transport dominates in the membrane at low downstream pressures. Importance of consideration for both the phases, during modeling, is discussed. Activity profile, determined across the membrane, was observed to be in agreement with the experimental observations (as per literature). The study may help to establish a fundamental framework in turn to model for binary and/or multi-component mixtures.     

氯仿,乙醇,苯有关二元体系加压相平衡研究

氯仿、乙醇、苯有关二元体系加压相平衡研究马忠明，陈庚华，王琦，严新焕，韩世钧，余淑娴（浙江大学化学系，杭州，３１００２７）（江西大学化学系）关键词加压汽液平衡，醇烃体系，氯仿，乙醇，苯醇是极性分子，烃是非极性或弱极性分子，醇与醇、烃与烃分子及醇与烃分...     

Interfacial transport of evaporating water confined in nanopores

A semianalytical, continuum analysis of evaporation of water confined in a cylindrical nanopore is presented, wherein the combined effect of electrostatic interaction and van der Waals forces is taken into account. The equations governing fluid flow and heat transfer between liquid and vapor phases are partially integrated analytically, to yield a set of ordinary differential equations, which are solved numerically to determine the flow characteristics and effect on the resulting shape and rate of evaporation from the liquid-vapor interface. The analysis identifies three important parameters that significantly affect the overall performance of the system, namely, the capillary radius, pore-wall temperature, and the degree of saturation of vapor phase. The extension of meniscus is found to be prominent for smaller nanoscale capillaries, in turn yielding a greater net rate of evaporation per unit pore area. The effects of temperature and ambient vapor pressure on net rate of evaporation are shown to be analogous. An increase in pore-wall temperature, which enhances saturation pressure, or a decrease in the ambient vapor pressure result in enhancing the net potential for evaporation and increasing the curvature of the interface.     

Theoretical modeling and experimental analysis of direct contact membrane distillation

A two-dimensional mathematical model was theoretically developed to predict the temperature polarization profile of direct contact membrane distillation (DCMD) processes. A concurrent flat-plate device was designed to verify the theoretical prediction of pure water productivity on saline water desalination. The numerical results from the temperature polarization profile were obtained using the finite difference technique to reduce the two-dimensional partial differential equations into an ordinary differential equations system. The resultant simultaneous linear equations system was solved with the fourth-order Runge-Kutta method. The results show theoretical prediction agreement with the measured values from the experimental runs. A combination of the Knudsen flow and Poiseuille flow models in the present mathematical formulation for membrane coefficient estimation was used to establish theoretical agreement. The influence of the inlet saline water temperature and volumetric flow rate on the pure water productivity as well as the hydraulic dissipated energy are also delineated.     

Theoretical analysis of the influence of the axial variation of the transmembrane pressure in cross-flow filtration of rigid spheres

A model of the axial and the radial transmembrane pressure drop in a cylindrical cross-flow filtration module was developed by performing a hydrodynamic analysis of the fluid flow based on the momentum and the continuity equations. Use of this expression for the transmembrane pressure drop together with the resistance model and the concept of shear induced diffusion of the particles at the membrane surface resulted in an expression of the permeate flux. The predictions of the transmembrane pressure drop, the permeate flux and the particles near the membrane surface are discussed for cases with and without the formation of a stagnant layer. The importance of the cylindrical membrane fiber dimensions on the permeate flux is also discussed.     

Stability of thin polymer films: influence of solvents

The interface and surface properties and the wetting behavior of polymer-solvent mixtures are investigated using Monte Carlo simulations and self-consistent field calculations. We carry out Monte Carlo simulations in the framework of a coarse-grained bead-spring model using short chains (oligomers) of N(P)=5 beads and a monomeric solvent, N(S)=1. The self-consistent field calculations are based on a simple phenomenological equation of state for compressible binary mixtures and we employ Gaussian chain model. The bulk behavior of the polymer-solvent mixture belongs to type III in the classification of van Konynenburg and Scott [Phil. Trans. R. Soc. London, Ser. A 298, 495 (1980)]. It is characterized by a triple line on which the polymer-liquid coexists with solvent-vapor and a solvent-rich liquid. The solvent is not homogeneously distributed across the dense polymer film but tends to accumulate at the surface and the polymer-vapor interface. This solvent enrichment at the interface and surface becomes more pronounced upon increasing the vapor pressure and alters the surface and interface tensions. This effect gives rise to a nonmonotonic dependence of the contact angle on the vapor pressure and one might observe reentrant wetting. The results of the Monte Carlo simulations and the self-consistent field calculations qualitatively agree. The profiles of drops are investigated by Monte Carlo simulations and a pronounced solvent enrichment is observed at the wedge formed by the substrate and the liquid-vapor interface at the three-phase contact line.     

A new cubic equation of state for simple fluids: pure and mixture

A two-parameter cubic equation of state is developed. Both parameters are taken temperature dependent. Methods are also suggested to calculate the attraction parameter and the co-volume parameter of this new equation of state. For calculating the thermodynamic properties of a pure compound, this equation of state requires the critical temperature, the critical pressure and the Pitzer’s acentric factor of the component. Using this equation of state, the vapor pressure of pure compounds, especially near the critical point, and the bubble point pressure of binary mixtures are calculated accurately. The saturated liquid density of pure compounds and binary mixtures are also calculated quite accurately. The average of absolute deviations of the predicted vapor pressure, vapor volume and saturated liquid density of pure compounds are 1.18, 1.77 and 2.42%, respectively. Comparisons with other cubic equations of state for predicting some thermodynamic properties including second virial coefficients and thermal properties are given. Moreover, the capability of this equation of state for predicting the molar heat capacity of gases at constant pressure and the sound velocity in gases are also illustrated.     

Vapor–liquid equilibria in the binary system (−)-beta-pinene + (+)-fenchone: Analysis in terms of group contributions models of some binary systems containing terpenoids

Isobaric vapor–liquid equilibrium measurements are reported for the binary system (−)-beta-pinene + (+)-fenchone at the constant pressure of 13.33 kPa in the temperature range from 341.60 K to 393.25 K. The boiling temperatures of the mixtures were also measured at seven constant compositions in the pressure range from 2.56 kPa to 20.80 kPa. The experimental data were found to be thermodynamically consistent. Reduction of the vapor–liquid equilibrium data was carried out by means of the Wilson, NRTL and UNIQUAC equations. Our data on vapor–liquid equilibria for mixtures containing terpenoids are examined in terms of the DISQUAC and modified UNIFAC (Dortmund) group contributions models. Interaction parameters of the DISQUAC model are reported.     

Transport of binary water–ethanol mixtures through a multilayer hydrophobic zeolite membrane

Transport of water–ethanol mixtures through a hydrophobic tubular ZSM-5 (Si/Al = 300) zeolite membrane during pervaporation was studied experimentally and theoretically. The zeolite membrane was deposited on a support made of pure titania coated with three intermediate ceramic titania layers. The influence of feed concentration, feed temperature and permeate pressure on permeate fluxes and permeate concentrations was investigated in a wide range. Dusty gas model parameters of the support and all ceramic intermediate layers were calculated on the basis of gas permeation data. Mass transfer resistances and pressure drops in the different membrane layers during pervaporation were calculated for several process conditions. In particular the influence of the undesired but unavoidable pressure drop in the support and the intermediate layers on the effective driving force for pervaporation was evaluated and found to be relevant for predicting the overall process performance. The membrane prepared was found to be suitable for the recovery of highly concentrated ethanol from feed mixtures of relatively low ethanol concentrations at relatively low feed temperatures.     

Dehydration of water-alcohol mixtures by pervaporation and vapor permeation through surface resintering expanded poly(tetrafluoroethylene) membranes

For the purpose of separating aqueous alcohol mixtures by the use of the pervaporation and vapor permeation techniques, a surface resintering expanded poly(tetrafluoroethylene) (e-PTFE), membrane was investigated. The surface properties of the modified e-PTFE membranes were characterized by atomic force microscopy, scanning electron microscopy, and contact angle meter. The X-ray diffraction measurements show that the crystallinity of the e-PTFE membrane decreases with increasing the surface resintering temperature. The surface roughness decreases with the surface resintering temperature increases. The membrane exhibited water selectivity during all process runs. The effects of feed composition, surface resintering temperature, and molar volume of the alcohols on pervaporation and vapor permeation were investigated. Compared with the e-PTFE membrane without surface modified, the e-PTFE membrane with surface resintering treatment effectively improve the separation factor for pervaporation of aqueous alcohol mixtures. The separation performances of e-PTFE membranes in vapor permeation are higher than that in pervaporation.     

Calculations of the thermodynamic properties of dimethylsulfoxide-water solutions on the basis of the cluster solvation model

The thermodynamic functions of dimethylsulfoxide mixtures with water were analyzed over the whole composition range using the cluster solvation model taking into account the distribution of clusters over solvation numbers. The equations of the model were shown to correctly describe the concentration dependences of saturated vapor pressure and excess enthalpy and volume on the assumption of dimethylsulfoxide hydration. The hydration numbers of dimethylsulfoxide and the variance of the distribution of hydrates over stoichiometric numbers were shown to increase as the temperature decreased.     

Modelling of Amperometric Biosensors with Rough Surface of the Enzyme Membrane

A two-dimensional-in-space mathematical model of amperometric biosensors has been developed. The model is based on the diffusion equations containing a nonlinear term related to the Michaelis–Menten kinetic of the enzymatic reaction. The model takes into consideration two types of roughness of the upper surface (bulk solution/membrane interface) of the enzyme membrane, immobilised onto an electrode. Using digital simulation, the influence of the geometry of the roughness on the biosensor response was investigated. Digital simulation was carried out using the finite-difference technique.