Hydrodynamic forces acting on a microscopic emulsion drop growing at a capillary tip in relation to the process of membrane emulsification

Here, we calculate the hydrodynamic ejection force acting on a microscopic emulsion drop, which is continuously growing at a capillary tip. This force could cause drop detachment in the processes of membrane and microchannel emulsification, and affect the size of the released drops. The micrometer-sized drops are not deformed by gravity and their formation happens at small Reynolds numbers despite the fact that the typical period of drop generation is of the order of 0.1 s. Under such conditions, the flow of the disperse phase through the capillary, as it inflates the droplet, engenders a hydrodynamic force, which has a predominantly viscous (rather than inertial) origin. The hydrodynamic boundary problem is solved numerically, by using appropriate curvilinear coordinates. The spatial distributions of the stream function and the velocity components are computed. The hydrodynamic force acting on the drop is expressed in terms of three universal functions of the ratio of the pore and drop radii. These functions are computed numerically. Interpolation formulas are obtained for their easier calculation. It turns out that the increase in the viscosity of each of the two liquid phases increases the total ejection force. The results could find applications for the interpretation and prediction of the effect of hydrodynamic factors on the drop size in membrane emulsification.     

Role of surfactant type and concentration for the mean drop size during emulsification in turbulent flow

A systematic experimental study of the effect of several factors on the mean drop diameter, d32, during emulsification, is performed with soybean oil-in-water emulsions. These factors are (1) type of used emulsifier; (2) emulsifier concentration, CS; and (3) ionic strength of the aqueous solution. Three different types of emulsifier, anionic (sodium dodecyl sulfate, SDS), nonionic (polyoxyethylene-20 cetyl ether, Brij 58), and protein (whey protein concentrate), are studied. For all of the studied systems, two well-defined regions are observed in the dependence of d32 on CS: at low surfactant concentration, d32 increases significantly with the decrease of CS (region 1), whereas d32 does not depend on CS at high surfactant concentration (region 2). The model, proposed by Tcholakova et al. (Langmuir 2003, 19, 5640), is found to describe well the dependence of d32 on CS in region 1 for the nonionic surfactant and for the protein emulsifier at high electrolyte concentration, 150 mM NaCl. According to this model, a well defined minimal surfactant adsorption (close to that of the dense adsorption monolayer) is needed for obtaining an emulsion. On the other hand, this model is found inapplicable to emulsions stabilized by the ionic surfactant, SDS, and by the nonionic surfactant, Brij 58, at low electrolyte concentration. The performed theoretical analysis of drop-drop interactions, in the emulsification equipment, shows that a strong electrostatic repulsion between the colliding drops impedes the drop-drop coalescence in the latter systems, so that smaller emulsion drops are obtained in comparison with the theoretically predicted ones. The results for SDS-stabilized emulsions in region 1 are explained by a quantitative consideration of this electrostatic repulsion. The drop size in region 2 (surfactant-rich regime) is described very well by the Kolmogorov-Hinze theory of turbulent emulsification.     

Effect of membrane parameters on the size and uniformity in preparing agarose beads by premix membrane emulsification

Agarose microbeads were prepared by premix membrane emulsification with Shirasu-Porous Glass (SPG) membrane and Polyethylene (PE) membrane. The effects of membrane parameters, including pore size, pore size distribution, contact angle between membrane surface and the water phase, shape of pore opening and membrane thickness on size and uniformity of agarose beads were investigated in this study. The results showed that pore size distribution and shape of pore opening did not affect the emulsification results apparently within a wide range in premix membrane emulsification, not as the result in general emulsification. The contact angle between the water phase and the membrane surface must be large enough to obtain uniform-sized agarose beads in both direct membrane emulsification and premix membrane emulsification. The results also showed that the membrane pore size and thickness affected the size distribution of emulsion. Thicker membrane resulted in more uniform and smaller emulsion when the number of pass through membrane is controlled. There was a linear relationship between the number average diameter of agarose beads and membranes pores size in premix membrane emulsification. Agarose beads with diameters from 3.06 to 9.02 μm were prepared by controlling membranes pore size. The ratio of the number average diameter of agarose beads to membrane pore diameters was found to be 0.486.     

Nanoparticle-filled capillary electrophoresis for the separation of long DNA molecules in the presence of hydrodynamic and electrokinetic forces

We report the analysis of long DNA molecules by nanoparticle-filled capillary electrophoresis (NFCE) under the influences of hydrodynamic and electrokinetic forces. The gold nanoparticle (GNP)/polymer composites (GNPPs) prepared from GNPs and poly(ethylene oxide) were filled in a capillary to act as separation matrices for DNA separation. The separations of lambda-DNA (0.12-23.1 kbp) and high-molecular-weight DNA markers (8.27-48.5 kbp) by NFCE, under an electric field of -140 V/cm and a hydrodynamic flow velocity of 554 microm/s, were accomplished within 5 min. To further investigate the separation mechanism, the migration of lambda-DNA was monitored in real time using a charge-coupled device (CCD) imaging system. The GNPPs provide greater retardation than do conventional polymer media when they are encountered during the electrophoretic process. The presence of interactions between the GNPPs and the DNA molecules is further supported by the fluorescence quenching of prelabeled lambda-DNA, which occurs through an energy transfer mechanism. Based on the results presented in this study, we suggest that the electric field, hydrodynamic flow, and GNPP concentration are the three main determinants of DNA separation in NFCE.     

Multi-stage premix membrane emulsification for preparation of agarose microbeads with uniform size

Uniform-sized agarose beads with diameters less than 10 μm and agarose content as high as 14 wt% were prepared by premix membrane emulsification. Agarose aqueous solution was used as the water phase. A mixture of liquid paraffin and petroleum ether containing hexaglycerin penta ester (PO-500) was used as the oil phase. The water phase was mixed with the oil phase at 60 °C and a coarse W/O emulsion was produced in a homogenizer. Then, the coarse emulsion was extruded through a hydrophobic membrane under high pressure to form an emulsion, which was slowly cooled under gentle agitation to form gel beads. The effects of preparation conditions on emulsification results were investigated and it showed that the pressure, number of passes, petroleum ether/liquid paraffin (v/v) in the oil phase, the concentration of PO-500 and concentration of agarose in the water phase, all affected the size and uniformity; coarse emulsion did not affect the emulsification results. The coefficient variation (C.V.) of agarose beads under optimal preparation conditions was 9.8%. This method realized microbeads with both uniform sizes and high agarose contents that are difficult to be prepared by conventional emulsion methods.     

Thin film drainage: hydrodynamic and disjoining pressures determined from experimental measurements of the shape of a fluid drop approaching a solid wall

Accurate measurements of the shape of a mercury drop separated from a smooth flat solid surface by a thin aqueous film reported recently by Connor and Horn (Faraday Discuss. 2003, 123, 193-206) have been analyzed to calculate the excess pressure in the film. The analysis is based on calculating the local curvature of the mercury/aqueous interface, and relating it via the Young-Laplace equation to the pressure drop across the interface, which is the difference between the aqueous film pressure and the known internal pressure of the mercury drop. For drop shapes measured under quiescent conditions, the only contribution to film pressure is the disjoining pressure arising from double-layer forces acting between the mercury and mica surfaces. Under dynamic conditions, hydrodynamic pressure is also present, and this is calculated by subtracting the disjoining pressure from the total film pressure. The data, which were measured to investigate the thin film drainage during approach of a fluid drop to a solid wall, show a classical dimpling of the mercury drop when it approaches the mica surface. Four data sets are available, corresponding to different magnitudes and signs of disjoining pressure, obtained by controlling the surface potential of the mercury. The analysis shows that total film pressure does not vary greatly during the evolution of the dimple formed during the thin film drainage process, nor between the different data sets. The hydrodynamic pressure appears to adjust to the different disjoining pressures in such a way that the total film pressure is maintained approximately constant within the dimpled region.     

Adhesion hysteresis from interdependent capillary and electrostatic forces

Adhesion hysteresis commonly occurs at the nanoscale in humid atmospheres, yet mechanisms are not entirely understood. Here, the adhesion forces between silicon (111) oxide surfaces and tungsten oxide probes have been examined using interfacial force microscopy. The results show that the adhesion forces during surface approach and separation differ not only in magnitude but also in mechanism, arising mainly from capillary and electrostatic forces, respectively. Surface contact leads to a transient intersurface potential on dewetting. This mechanism of adhesion hysteresis differs in not relying singly on hysteretic wetting. Furthermore, by biasing the surfaces, nonadditivity is demonstrated between the capillary and electrostatic forces at the onset of condensation. These results hold important implications on the interpretation of force in nanoprobe geometries in humid atmospheres.     

The "Wimple": rippled deformation of a fluid drop caused by hydrodynamic and surface forces during thin film drainage

It is well-known that hydrodynamic pressures in a thin draining liquid film can cause inversion of the curvature of a drop or bubble surface as it approaches another surface, creating a so-called "dimple". Here it is shown that a more complicated rippled shape, dubbed a "wimple", can be formed if a fluid drop that is already close to a solid wall is abruptly pushed further toward it. The wimple includes a central region in which the film remains thin, surrounded by a ring of greater film thickness that is bounded at the outer edge by a barrier rim where the film is thin. This shape later evolves into a conventional dimple bounded by the barrier rim, which then drains in the normal way. During the evolution from wimple to dimple, some of the fluid in the thicker part of the film ring flows toward the central region before eventually draining in the opposite direction. Although the drop is pressed toward the wall, the central part of the drop moves away from the wall before approaching it again. This is observed even when the inward push is too small to create a wimple.     

The measurement of average hydrodynamic velocity in capillary zone electrophoresis

Summary Based on the linear relationship between large sample injection time during hydrodynamic injection and migration time in non-stacking runs, a new method is proposed to measure average hydrodynamic velocity in capillary zone electrophoresis (CZE). Only the migration times for large injections need to be measured in this new approach, so the method is simple. Additionally, a modified Poiseuille equation is proposed to eliminate the deviation involved in Poiseuille’s equation. The average hydrodynamic velocity values determined by our method generally compare favorably with those determined by the modified Poiseuille equation.     

Visualization and characterization of SPG membrane emulsification

Shirasu-porous-glass (SPG) membrane emulsification is highly attractive for various fields of foods, cosmetics, and pharmaceuticals because this technique produces monodispersed emulsions. However, there are few reports on the observation of membrane emulsification at the membrane surface. In the present work, we aimed to visualize the membrane emulsification using a microscope high-speed camera system. The direct observation made it possible to measure the mean rate of droplet formation and the percentage of active pores. The mean rate of droplet formation ranged 0.3–12 s⁻¹ and the percentage of active pores ranged 0.3–0.5% under the dispersed-phase flux of 0.58×10⁻⁶–5.8×10⁻⁶ m³/(m² s). We also observed that the droplets were formed without continuous-phase flow and the droplets were also formed by shear force at the continuous-phase flow under different experimental conditions. The balance among the dispersed-phase flux and the continuous-phase flow velocity influenced droplet formation.     

The mechanism of action and place of application of capillary forces

The question of the mechanism of action and the place of application of capillary forces has been discussed. It has been shown that the conventional notions of the character of capillary forces are often contradictory. A molecular-kinetic approach has been employed to determine the places of application of capillary forces and the mechanism of their action.     

Relaxation of microparticles exposed to hydrodynamic forces in microfluidic conduits

The behavior of microparticles exposed to gravitational and lift forces and to the velocity gradient in flow velocity profile formed in microfluidic conduits is studied from the viewpoint of the transient period (the relaxation) between the moment at which a particle starts to be transported by the hydrodynamic flow and the time at which it reaches an equilibrium position, characterized by a balance of all active forces. The theoretical model allowing the calculation of the relaxation time is proposed. The numerical calculus based on the proposed model is compared with the experimental data obtained under different experimental conditions, namely, for different lengths of microfluidic channels, different average linear velocities of the carrier liquid, and different sizes and densities of the particles used in the study. The results are important for the optimization of microfluidic separation units such as microthermal field-flow fractionation channels in which the separation or manipulation of the microparticles of various origin, synthetic, natural, biological, etc., is performed under similar experimental conditions but by applying an additional thermodynamic force.

Kinetics of liquid annulus formation and capillary forces

The dependence of the capillary adhesion force F(cap) between a silica microsphere and a flat silica surface versus a time period t of the samples' contact (i.e., dwell-in time) is experimentally investigated using atomic force microscopy (AFM). F(cap) was found to be dependent on t if the humidity was >30-35%. This dependence is exponential, with decay (characteristic) times of ～10 s. It is suggested that the kinetics of the adhesion process are related to the growth of the water annulus between surfaces. Furthermore, we propose that the growth kinetics has two components: (1) water vapor diffusion from the surrounding humid media into the gap between samples and (2) water drainage from the gap. The theory of diffusion through thin pores (i.e., gaps) is developed, and analytical formulas are obtained for the dependence of the meniscus radius r versus time t. However, the experimental dependence of F(cap) versus t and, consequently, r versus t obtained in this article disagrees with the theoretical prediction by several orders of magnitude. Similar results were obtained from the literature data for capillary forces between an AFM cantilever tip and a flat surface. Possible reasons for the deviation from diffusion theory are suggested: surface and Knudsen regimes of vapor diffusion, nonsteady state vapor flow, and tortuosity. Taking into account the viscous drainage of water from the multilayer gap can explain the experimental kinetics of bridge formation, but only if the viscosity of the adjacent multilayer of water is several orders of magnitude larger than the bulk viscosity.     

Influence of process parameters on the size distribution of PLA microcapsules prepared by combining membrane emulsification technique and double emulsion-solvent evaporation method

Relatively uniform-sized biodegradable poly(lactide) (PLA) microcapsules with various sizes were successfully prepared by combining a glass membrane emulsification technique and water-in-oil-in-water (w₁/o/w₂) double emulsion-solvent evaporation method. A water phase was used as the internal water phase, a mixture solvent of dichloromethane (DCM) and toluene dissolving PLA and Arlacel 83 was used as the oil phase (o). These two solutions were emulsified by a homogenizer to form a w₁/o primary emulsion. The primary emulsion was permeated through the uniform pores of a glass membrane into the external water phase by the pressure of nitrogen gas to form the uniform w₁/o/w₂ double emulsion droplets. Then, the solid polymer microcapsules were obtained by simply evaporating solvent. The influence of process parameters on the size distribution of PLA microcapsules was investigated, with an emphasis on the effect of oil-soluble emulsifier. A unique phenomenon was found that a large part of emulsifier could adsorb on the interface of internal water phase and oil phase, which suppressed its adsorption on the surface of glass membrane, and led to the successful preparation of uniform-sized double emulsion. Finally, by optimizing the process parameters, PLA microcapsules with various sizes having coefficient of variation (CV) value under 14.0% were obtained. Recombinant human insulin (rhI), as a model protein, was encapsulated into the microcapsules with difference sizes, and its encapsulation efficiency and cumulative release were investigated. The result suggested that the release behavior could be simply adjusted just by changing precisely the diameters of microcapsule, benefited from the membrane emulsification technique.     

The influence of environment on the drop size — contact angle relationship

Advancing contact angles are reported for the water-PTFE, water-copper, water-stainless steel, water-PMMA andn-decane-PTFE systems for a range of liquid drop sizes.The angles were determined at 25 °C in an air or nitrogen-saturated atmosphere and compared with those measured at the boiling point in an environment only of its vapor.For water-PTFE and water-PMMA systems, a decrease in contact angle with decreasing drop size was observed in an air-saturated environment at 25 ° confirming the data of Good and Koo. An increase in contact angle however occurred with decreasing drop size at the boiling point in the pure vapor atmosphere confirming the results of Boyes and Ponter. The introduction of nitrogen decreased the contact angle although the trend remained the same.     

Status of cross-flow membrane emulsification and outlook for industrial application

Cross-flow membrane emulsification has great potential to produce monodisperse emulsions and emulsions with shear sensitive components. However, until now, only low disperse phase fluxes were obtained. A low flux may be a limiting factor for emulsion production on a commercial scale. Therefore, the effects of membrane parameters on the disperse phase flux are estimated. Besides, the effects of these parameters on the droplet size and droplet size distribution are qualitatively described. Wetting properties, pore size and porosity mainly determine the droplet size (distribution). Membrane morphology largely determines the disperse phase flux. As an example, industrial-scale production of culinary cream was chosen to evaluate the required membrane area of different types of membranes: an SPG membrane, an -Al₂O₃ membrane and a microsieve. Due to the totally different morphologies of these membranes, the fraction of active pores is 1 for a microsieve and is very low for the other membranes. The choice of the optimal membrane did not depend on the production strategy: either to produce large quantities or to produce monodisperse emulsions, the best suitable was a microsieve with an area requirement of around 1 m². In general, the total membrane resistance should be low to obtain a large disperse phase flux. In contrast, the membrane resistance should be high to obtain monodisperse emulsions when using membranes with a high porosity.     

The effect of electroosmotic and hydrodynamic flow profile superposition on band broadening in capillary electrophoresis

The effect of the superposition of electroosmotic flow and pressureinduced hydrodynamic counterflow on efficiency has been investigated for different capillary electrophoretic systems. Results are shown for 50 and 75 μm internal diameter capillaries at several voltage and counterpressure levels. Hydrodynamic counterflows were successfully applied in electrokinetic chromatography in order to delay the entry of a UV-active pseudostationary phase, tetraphenyl porphyrintetrasulfonate, into the detection zone allowing the separation of neutral nitroaromatics. The separations are based on the weak charge-transfer interactions between the porphyrin and the analytes.     

Effect of long-range hydrodynamic and direct intermacromolecular forces on translational diffusion

Within the framework of recently formulated microscopic theories of macromolecular diffusion it is shown that hydrodynamic forces act always to diminish the influence of direct forces, but never to reverse the sign of the correction term due to direct forces alone. Although the correction term D(k) to the intrinsic diffusion coefficient may vary with scattering vector |k|, it is shown that a reversal in sigh of the correction term with increasing |k|, if it occurs, must be associated with an amplitude of less than 10% of the correction term at |k| = 0. At |k| = 0 direct repulsive forces are predicted to always increase the apparent diffusion constant, even after accounting for hydrodynamic interactions. Although experiments on polylysine (1 mg/ml) at salt concentrations above 0.01 M are in qualitative accord with the theory, below 10^?3 M salt the apparent diffusion coefficient is reduced by a factor of about 20, concomitant with a much reduced intensity of scattered light. The strong contradiction of the theory implied by this observation is attributed to a dramatic rise in Stokes friction arising from long-range interionic forces in the low-salt solutions.     

Using the Surface Evolver to model droplet formation processes in membrane emulsification

A model was developed to describe the droplet formation mechanism in membrane emulsification from the point of view of Gibbs free energy with the help of the Surface Evolver, which is an interactive finite element program for the study of interfaces shaped by surface tension. A program to test the model was written and run which allows the user to track the droplet shape as it grows, to identify the point of instability due to free energy, and thus predict droplet size. The inputs of the program are pore geometry, oil-aqueous phase interfacial tension, and contact angle. The model reasonably predicted droplet sizes for oblong-shaped pores under quiescent conditions where the force balance approach is not applicable. The model was validated against experimental conditions from the literature where the average error of the predictions compared to the mean droplet sizes was 8%.     

The role of capillary and surface forces in the crossover behavior of solid nanoparticles at liquid interfaces

We investigate the interaction between a nanoparticle and an oil-water interface with particular emphasis on the particle crossing through the interface. The formation of a three-phase contact line is investigated in two cases, namely in the presence and in the absence of surface forces. We carefully examine the interplay between capillary and surface forces in such systems. Two instabilities of the interface (snap-in/snap-out) as the particle is moved through the interface are identified and quantitatively described. While the snap-in instability was observed in some AFM studies, the precise interface position and configuration relative to the particle at the instability depends on the nature of the surface forces present in the system. After the snap-in, the particle is adsorbed and must overcome an energy barrier due to the interface deformation in order to cross-over to the other liquid. We make quantitative predictions on the interface configuration at the instabilities and the free energy barrier height. The roles of particle size and different interaction parameters characterizing the system in determining the magnitude of the energy barrier for crossing and in the formation of a three-phase contact line are discussed. Ultimately, this study will enable us to make quantitative predictions on capillary effects in nanoparticle-microemulsions mixtures and other colloidal systems. For particles in the micrometer range and larger the capillary forces dominate over the surface forces and dictate how the snap-in occurs. However, the situation becomes different for particle sizes smaller than about 100 nm. The presence of surface forces modifies the interface configuration and the free energy jump at the snap-in instability.