MASS TRANSPORT EFFECTS ON THE STABILITY OF EMULSION: EMULSION FILMS WITH ACETIC ACID AND ACETONE DIFFUSING ACROSS THE INTERFACE

The stability of emulsions is studied using, as a model of two interacting drops, an aqueous film of a surfactant immersed in an oil phase. It is shown that the mass transfer of a solute across the film changes its life-time. This change depends on several parameters as the nature and concentration of the solute. the direction of mass transfer, the time elapsed after the formation of the film. The destabilizing effect, of the transfer is found to be much less pronounced when the solute is in the continuous water phase. The instability is ascribed to the Marangoni effect and/or to liquid flow from the film drawn by diffusion of the solute.     

A perturbation solution for batch extraction with double emulsions: role of continuous phase mass transfer resistance

The effect of the continuous phase mass transfer resistance on solute extraction with double emulsions in a batch reactor is investigated. A model presented by Ho et al. (1982) for diffusion controlled mass transfer into the double emulsions is solved by perturbation analysis. In the case of a significant continuous phase mass transfer resistance, the extraction of solute is a function of the inverse Biot modulus, m. For values of m greater than 0.01 the external phase resistance must be taken into account in order to accurately predict extraction rates. Such conditions will exist when double emulsion drops are relatively small or when stirring rates in the batch extractor are low.     

Film drainage between two surfactant-coated drops colliding at constant approach velocity

The drainage of the intervening continuous phase film between two drops approaching each other at constant velocity under the influence of insoluble surfactant is investigated. The mathematical model to be solved is a coupled pair of fourth-order nonlinear partial differential equations which arise from the relationships governing the evolution of the film thickness and the surfactant interfacial concentration in the lubrication approximation. We adopt a simplified approach which uses lubrication theory to describe the flow within the drop, marking a departure from the conventional framework in which Stokes flow is assumed. When the model is solved numerically together with the relevant initial and boundary conditions, the results obtained are compared with those found in the literature using the "boundary integral" method to solve for the flow in the drop phase. The close agreement between the results inspires confidence in the predictions of the simplified approach adopted. The analysis on the effect of insoluble surfactant indicates that its presence retards the drainage of the film: The fully immobile interface limit is recovered even in the presence of a small amount of surfactant above a critical concentration; film rupture is either prolonged or prevented. The retardation of the film was attributed to gradients of interfacial tension which gave rise to the Marangoni effect. A study of the influence of various system parameters on the drainage dynamics was conducted and three regimes of drainage and possible rupture were identified depending on the relative magnitudes of the drop approach velocity and the van der Waals interaction force: Nose rupture, rim rupture, and film immobilization and flattening. Finally, the possibility of forming secondary droplets by encapsulating the continuous phase film into the coalesced drop at rupture was examined and quantified in light of these regimes.     

Mass transfer across liquid—liquid interfaces : Part 2. Calculation of Mass-transfer Coefficients from Experiments with an Automated Falling-drop Apparatus

The mass transfer of 4-methoxy-N,N-dimethylbenzylamine from aqueous drops to cyclohexane was studied by the falling-drop method with computer-controlled equipment. Different contact times were achieved by letting the drop-forming device ascend or descend to previously defined levels in the column containing the continuous phase. The overall mass-transfer coefficient was evaluated from the relationship between contact time and solute concentration in the donating phase. Whether or not the continuous phase must be replaced between the measurements needed to calculate the overall mass-transfer coefficient is discussed in detail. Corrections for the gradually increasing concentration of the transported solute in the receiving phase are proposed and tested. The order of contact times (decreasing or increasing) is shown to be of great importance for these corrections.     

The Dynamics of Marangoni-Driven Local Film Drainage between Two Drops

A study of Marangoni-driven local continuous film drainage between two drops induced by an initially nonuniform interfacial distribution of insoluble surfactant is reported. Using the lubrication approximation, a coupled system of fourth-order nonlinear partial differential equations was derived to describe the spatio-temporal evolution of the continuous film thickness and surfactant interfacial concentration. Numerical solutions of these governing equations were obtained using the Numerical Method of Lines with appropriate initial and boundary conditions. A full parametric study was undertaken to explore the effect of the viscosity ratio, background surfactant concentration, the surface Péclet number, and van der Waals interaction forces on the dynamics of the draining film for the case where surfactant is present in trace amounts. Marangoni stresses were found to cause large deformations in the liquid film: Thickening of the film at the surfactant leading edge was accompanied by rapid and severe thinning far upstream. Under certain conditions, this severe thinning leads directly to film rupture due to the influence of van der Waals forces. Time scales for rupture, promoted by Marangoni-driven local film drainage were compared with those associated with the dimpling effect, which accompanies the approach of two drops, and implications of the results of this study on drop coalescence are discussed. Copyright 2001 Academic Press.     

Continuous-phase mass transfer in a laminar suspended slug for a liquid-liquid system

A very simple slug apparatus capable of forming a slug long enough to make the inherent end effect for mass transfer negligible, has been developed. Continuous phase mass transfer in a stable laminar liquid-liquid flow was studied for the dissolution of an MIBK slug into water flowing as a continuous phase. The observed mass transfer coefficients were shown to be in good agreement, over a wide range of contact time between the two phases, with the penetration theory or the Hatta theory, which allows for the effect of a finite thickness and velocity distribution in the relevant phase.     

Computer simulations of solute exchange using micelles by a collision-driven fusion process

In this work, the kinetic process of collision-driven solute exchange in an aqueous phase in which micelles are used as solute carriers is investigated by dissipative particle dynamics simulations. Here, we try to answer two questions about the exchange process of hydrophobic solute molecules: How the solute molecules are exchanged and what factors affect the process. For the first question, the simulation results indicate that, after a stage of intermittent collision between two neighboring aggregates, there are roughly three sequential events in a coalescence stage: (1) molecular contact, (2) neck formation, and (3) neck growth. The coalescence stage is followed by a stage of solute transfer and diffusion. It is found that there are two rate-limiting steps in the whole process of solute exchange, i.e., the break of the water film between two neighboring aggregates and the nucleation of a pore between two surfactant films. For the second question, the effects of the collision velocity, the surface tension, the repulsive interaction between the surfactant films of the colliding aggregates, as well as the steric repulsion are examined. For example, the simulation results show that the depletion force plays an important role during the coalescence stage, while the initial collision velocity basically does not change the fusion ratio. The results also demonstrate that the surface tension and interaction show different effects on the different stages of a solute exchange process.     

A theoretical plate model accounting for slow kinetics in chromatographic elution

The chromatographic elution has been studied from different perspectives. However, in spite of the simplicity and evident deficiencies of the plate model proposed by Martin and Synge, it has served as a basis for the characterization of columns up-to-date. This approach envisions the chromatographic column as an arbitrary number of theoretical plates, each of them consisting of identical repeating portions of mobile phase and stationary phase. Solutes partition between both phases, reaching the equilibrium. Mobile phase transference between the theoretical plates is assumed to be infinitesimally stepwise (or continuous), giving rise to the mixing of the solutions in adjacent plates. This yields an additional peak broadening, which is added to the dispersion associated to the equilibrium conditions. It is commonly assumed that when the solute concentration is sufficiently small, chromatographic elution is carried out under linear conditions, which is the case in almost all analytical applications. When the solute concentration increases above a value where the stationary phase approximates saturation (i.e. becomes overloaded), non-linear elution is obtained. In addition to overloading, another source of non-linearity can be a slow mass transfer. An extended Martin and Synge model is here proposed to include slow mass-transfer kinetics (with respect to flow rate) between the mobile phase and stationary phase. We show that there is a linear relationship between the variance and the ratio of the kinetic constants for the mass transfer in the flow direction (τ) and the mass transfer between the mobile phase and stationary phase (ν), which has been called the kinetic ratio (κ=τ/ν). The proposed model was validated with data obtained according to an approach that simulates the solute migration through the theoretical plates. An experimental approach to measure the deviation from the equilibrium conditions using the experimental peak variances and retention times at several flow rates is also proposed.     

Hydrodynamics and mass exchange in gas-liquid slug flow in microchannels

The present state of hydrodynamics and mass transfer studies in segmented gas-liquid flow in microchannels has been analyzed. It has been shown that such parameters as gas bubble velocity, gas hold-up, relative gas bubble length, pressure drop, mass transfer coefficients from gas bubbles to liquid slugs and to liquid film, as well as mass transfer coefficient from liquid to channel wall can be satisfactorily predicted. Nevertheless, some correlations were obtained under definite conditions and should be summarized. The purpose of further research is to develop reliable methods for calculation of mass transfer coefficients as functions of channel geometry, phase properties, and phase velocities in mini- and microchannels.     

Film drainage between two captive drops: PEO-water in silicon oil

An experimental study of the deformation and drainage of a Newtonian liquid film trapped between two drops is performed for the cases of a constant and slightly rising interaction force. Series of polyethylene oxide (PEO) water solutions are used for the dispersed and polydimethylsiloxane (PDMS) for the continuous phase. The film evolution is observed by an interferometric technique. Experimental data for the film thinning rate and for the film profile allow quantitative comparison with the available drainage models.     

Experimental investigation of bubble and drop formation at submerged orifices

The aim of this study was to investigate bubble/drop formation at a single submerged orifice in stagnant Newtonian fluids and to gain qualitative understanding of the formation mechanism. The effects of various governing parameters were studied. Formation behavior of bubbles and drops in Newtonian aqueous solutions were investigated experimentally under different operating conditions with various orifices. The results show that the volume of the detached dispersed phase (bubble or drop) increases with the viscosity of the continuous phase (or dispersion medium), surface tension, orifice diameter, and dispersed phase flow rate. A PIV system was employed to measure the velocity flow field quantitatively during the bubble/drop formation, giving interesting information useful for the elucidation of the fundamental formation process at the orifice. It was revealed that the orifice shape strongly influences the size of the bubble formed. Furthermore, based on a simple mass balance, a general correlation successfully predicting both bubble and drop sizes has been proposed.     

Control and measurement of the phase behavior of aqueous solutions using microfluidics

A microfluidic device denoted the Phase Chip has been designed to measure and manipulate the phase diagram of multicomponent fluid mixtures. The Phase Chip exploits the permeation of water through poly(dimethylsiloxane) (PDMS) in order to controllably vary the concentration of solutes in aqueous nanoliter volume microdrops stored in wells. The permeation of water in the Phase Chip is modeled using the diffusion equation, and good agreement between experiment and theory is obtained. The Phase Chip operates by first creating drops of the water/solute mixture whose composition varies sequentially. Next, drops are transported down channels and guided into storage wells using surface tension forces. Finally, the solute concentration of each stored drop is simultaneously varied and measured. Two applications of the Phase Chip are presented. First, the phase diagram of a polymer/salt mixture is measured on-chip and validated off-chip, and second, protein crystallization rates are enhanced through the manipulation of the kinetics of nucleation and growth.     

两个液滴之间的聚并

对于系统中不含杂质时两个液滴在不互溶液体中的聚并过程进行理论分析，得到聚并所需时间与两相物理性质一范德华力的关系，该结果也适用于气泡在液体中的聚并，只要知道系统的物性数据和液滴半径，就可以计算聚并时间，理论预测与实验结果符合较好。     

Measurement of the Mass Transfer into Single Drops in the System of Water/Supercritical Carbon Dioxide

This paper presents a new method for the measurement of mass transfer in isolated water drops. The transport of a component in the water drop can be detected by a change in electrical conductivity. Measurements were performed using a new type of sensor design. In particular the transfer of CO(2) from a continuous fluid phase into the water drop was investigated. CO(2) leads to an increased conductivity in water because of the carbonic acid equilibrium. Experimental conditions ranged from 298 to 323 K in temperature and from 2.5 up to 30.7 MPa in pressure. The mass transfer coefficients obtained give insight into the transfer process and its physical mechanisms. Increasing temperature and density of the surrounding carbon dioxide lead to faster mass transfer processes. The effects of drop geometry and internal turbulences on the mass transfer velocity are discussed. Copyright 2000 Academic Press.     

Linear stability of a draining film squeezed between two approaching droplets

In the present paper we analyze the effect of infinitesimal non-axisymmetric perturbations in determining the critical gap thickness at which a draining, finite radius thin-film becomes unstable. The film is part of the suspending fluid trapped between two approaching deformable drops under the action of a flow field. We carry out a linear stability analysis in the context of a quasi-static approximation where the rate of growth of the disturbances is assumed to be much faster than the rate of film drainage. An analytical solution is derived for the model in the special case of a uniformly thick film, for two types of perturbation: fixed-end and free-end. It is shown, for this special case, when the hydrodynamic force pushing the drops together from the external flow is constant, that the four most unstable disturbances are of the free-end kind, associated with the lowest frequency modes of azimuthal variation in the film thickness. Higher modes are stabilized by surface tension. Our analysis also shows that adopting the unretarded form of the van der Waals disjoining pressure yields results similar to the analysis when electromagnetic retardation effects are included in the calculation. A second case is analyzed where the film is also of uniform thickness but its lateral extent and the gap thickness are both time-dependent. This case was included to extend the predictions to glancing drop-collisions where the external hydrodynamic force is time-dependent. We find that there is a maximum capillary number below which the film becomes unstable, and that there is range of angles in the trajectory where the film becomes unstable, but that outside this range the film is stable.     

Method to predict the bandwidth of elution profile under the linear gradient elution in reversed‐phase HPLC

Solute migration in a chromatographic column is an important consideration when designing batch or continuous chromatographic separation processes. Most design methods for the chromatographic processes are based on the equilibrium theory which concerns only the migration velocity of the solute. However, in real cases, it is important to predict the zone spreading which occurs by axial dispersion and mass transfer resistance. To predict the actual solute profiles in the column or effluent stream, numerical methods to solve nonlinear partial differential equations have been used. However, these methods involve much time and expense. In this work, two different rate factors are considered to predict the characteristics of the solute profiles. The first is solute migration velocity and the second is the zone spreading rate. The zone spreading rate can be estimated by the apparent axial dispersion coefficient which is obtained from the height of the equivalent theoretical plate in particular. Four benzene derivatives (benzene, toluene, p‐xylene, and acetophenone) were used as model solutes, and two mobile phase systems, water/methanol and water/ACN, were used in RP‐HPLC. The bandwidths and retention times of the solutes were predicted under several linear gradient conditions. The predicted and experimental bandwidths and retention times showed good agreement.     

High Performance Size Exclusion Chromatography with Microparticulate Porous Silica Spheres. Influence of Flow Rate,Salute Mass Transfer and Polydispersity of Samples

Abstract

The contributions to peak broadening in Size Exclusion Chromatography with microparticles of porous silica spheres having narrow size distributions have been determined by measuring the plate height dependence on flow rate for toluene and for polystyrene standards covering a wide range of molecular weights. From these contributions, the diffusion coefficients of the macromolecules in the pore matrix and the polydispersities of the samples could be evaluated. It is shown that for permeating polymers the band broadening is determined by the eddy diffusion in the mobile phase, by the slow mass transfer of the solute in the stationary phase and by the polydispersity of the standards. In properly packed columns the eddy diffusion term is of minor importance compared to the other effects, whereas the solute mass transfer, which is a velocity dependent process, can be minimized only at extremely low flow rates.     

Expressions for the C-term in the presence of pore flow

In the course of our work on capillary electrochromatography (CEC) we, as others, have found strong evidence that flow in pores of particles can be significant. Its magnitude relative to the interstitial flow is characterized by the flow reduction factor, omega. Indirect evidence for pore flow was obtained much earlier by others, when it was noted that plate height, especially the C-term part, was significantly smaller in electrically driven (ED) than in pressure drive (PD) systems. This was interpreted as enhanced mass transfer, for which the intra-particle flow was held responsible. More direct evidence was produced by us when the size-exclusion (SEC) behaviour of polymers was studied in ED systems. It was found that the effect of exclusion on migration velocity could vanish entirely, and large and small molecules were co-eluted. This can only be explained if omega approaches 1; flow within the pores being as large as the interstitial flow. Indeed, consideration of double layer overlap indicated that omega-values close to 1 can often be expected in CEC. These large values omega inspired us to reconsider the effect of pore flow on the mass transfer term. We have arrived at the conclusion that enhanced mass transfer cannot explain in itself the extremely small values for the reduced plate height, h, (<1) observed especially for weakly retained solutes. In fact, when the pore flow is equal in magnitude to the interstitial flow, an unretained solute moves as fast within the particle as in the interstices; there is no non-equilibrium generated and a mass transfer term in h is not expected. For the migration of the solute the system is essentially uniform. Thus, apart from the mass transfer enhancement, another factor plays a role in the decrease of the h-values. We have attempted to derive a suitable expression for this effect. Some results are presented here. In one approach the situation is compared to that of an open tubular column with moving pseudo-stationary phase on the wall, an experiment that has actually been carried out by Krejci et al., or with micellar electrokinetic chromatography. In that case the plate height is easily derived. The result says that the plate height is proportional to the square of velocity difference between the two zones. However, the analogy is not perfect, and another approach suggests a direct proportionality rather than a square law one. Finally, a more refined treatment could be made only for a slab, not for a sphere. Extrapolation of this result to a sphere is put forward as a tentative expression for this effect.     

On the Earnshaw and the Van den Tempel-Lucassen Compositional Viscoelastic Theories

We consider a diffusion-controlled solute transfer and discuss the reasons to study the complete convective-diffusive equation to determine the coupling resonant domain between capillary and longitudinal waves in terms of viscoelastic compositional behavior. A perturbation of the surface tension due to solute transfer has two contributions. One is proportional to the surface area change while the other, not considered in the Van den Tempel-Lucassen theory, is due to the surface velocity. Copyright 2000 Academic Press.     

Film drainage and interfacial instabilities in polymeric systems with diffuse interfaces

We report an experimental investigation on the effect of mutual diffusion in polymeric systems on film drainage between two captive drops. The main objective is to study the influence of diffuse interfaces on film drainage. This is done by using material combinations with different interfacial properties and interferometric visualization of the film between two interacting drops. For highly diffusive systems film drainage is observed to be, in contrast to immiscible systems, non-axisymmetric and unstable immediately after the film formation (at a few micrometers film thickness). Depending on whether the total thickness of the diffusion layers in the film is smaller or larger than the thickness of the film, Marangoni convection is found to enhance or delay film drainage. Enhanced film drainage is determined to be in order of 100 times faster than predicted by the current models, while delayed film drainage is observed after a drainage period where experimental and predicted results (assuming, a partially mobile interface) are in close agreement.