Krassimir D. Danov

Flocculation and coalescence of micron-size emulsion droplets

Abstract We analyze the relative importance of droplet deformation, surfactant transfer and interfacial rheology for the properties and stability of emulsions. The appearance of deformation (flattening or film) in the zone of contact of two interacting droplets has the following consequences. It enhances the importance of the surface forces of intermolecular origin and gives rise to contributions from the interfacial dilatation and the bending energy. The flattening increases the viscous dissipation in the gap between two colliding drops and thus prolongs the lifetime of the doublet of two such drops. The critical thickness of the gap also depends on whether the drops are deformed or non-deformed. The factors which facilitate the flattening in the zone of contact between two emulsion drops are the increase in droplet size, the decrease in interfacial tension, the bending energy for water-in-oil emulsions, the increase in droplet–droplet attraction and the suppression of droplet–droplet repulsion. The presence of surfactant strongly affects the interfacial tension, the bending moment, and influences all kinds of DLVO and non-DLVO surface forces operative in the gap between two droplets. The rheological and dynamic properties of the surfactant adsorption monolayers (Gibbs elasticity, surface diffusivity, surface viscosity, and adsorption relaxation time) are major factors for the stability of emulsions under dynamic conditions. The solubility of the surfactant in one of the two phases can determine whether oil-in-water or water-in-oil emulsion will be formed. A criterion for emulsion stability accounting for the interplay of all thermodynamic and hydrodynamic factors mentioned above is obtained. It provides an interpretation and generalization of the Bancroft rule.

Capillary mechanisms in membrane emulsification: oil-in-water emulsions stabilized by Tween 20 and milk proteins

We investigate the process of membrane emulsification in the presence of the nonionic surfactant Tween 20, and the milk proteins Na-caseinate and beta-lactoglobulin (BLG). Our goal is to examine the factors which control the drop-size distribution in the formed emulsions. The drops are produced at the outer surface of a cylindrical microporous glass membrane, so that the process of their formation and detachment can be directly observed by an optical microscope. In the case of 2 wt.% aqueous solution of Tween 20 we obtain a relatively fine and monodisperse oil-in-water emulsion with a mean drop diameter about three times that of the pore. The microscopic observations show that in this case the oil drops intensively pop out of separate pores. In contrast, for the lower concentrations of Tween 20, as well as for the investigated solutions of Na-caseinate and BLG, we observe that the membrane is covered by a layer of growing attached emulsion drops, which are polydisperse, with a relatively large mean drop size. This fact can be explained with a greater dynamic contact angle solid-water-oil. In such a case, after a drop protrudes from an opening, it does not immediately detach, but instead, the contact area drop/membrane expands over several pore openings. The smaller drop size in the emulsions stabilized by BLG, in comparison with those stabilized by Na-caseinate, is related to the circumstance that BLG adsorbs faster at the oil-water interface than Na-caseinate. In the investigated emulsions we did not observe any pronounced coalescence of oil drops. Hence, the generation of larger and polydisperse oil drops in some of the studied solutions is attributed mostly to the effect of expansion of the drop contact line and formation of hydrophobized domains on the membrane surface. Therefore, any factor, which leads to decrease of the dynamic three-phase contact angle, and thus prevents the contact-line expansion, facilitates the production of fine and monodisperse emulsions.

Capillary forces between particles at a liquid interface: General theoretical approach and interactions between capillary multipoles

The liquid interface around an adsorbed colloidal particle can be undulated because of roughness or heterogeneity of the particle surface, or due to the fact that the particle has non-spherical (e.g. ellipsoidal or polyhedral) shape. In such case, the meniscus around the particle can be expanded in Fourier series, which is equivalent to a superposition of capillary multipoles, viz. capillary charges, dipoles, quadrupoles, etc. The capillary multipoles attract a growing interest because their interactions have been found to influence the self-assembly of particles at liquid interfaces, as well as the interfacial rheology and the properties of particle-stabilized emulsions and foams. As a rule, the interfacial deformation in the middle between two adsorbed colloidal particles is small. This fact is utilized for derivation of accurate asymptotic expressions for calculating the capillary forces by integration in the midplane, where the Young-Laplace equation can be linearized and the superposition approximation can be applied. Thus, we derived a general integral expression for the capillary force, which was further applied to obtain convenient asymptotic formulas for the force and energy of interaction between capillary multipoles of arbitrary orders. The new analytical expressions have a wider range of validity in comparison with the previously published ones. They are applicable not only for interparticle distances that are much smaller than the capillary length, but also for distances that are comparable or greater than the capillary length.

The formation of satellite droplets by unstable binary drop collisions

Experimental investigations on the process of satellite droplet formation by unstable binary drop collisions are presented. The experiments are carried out using two monodisperse streams of drops of equal size. A systematic variation of the parameters influencing the collisions leads to an extended version of the stability nomogram which involves the numbers of satellite droplets formed by stretching separation after off-center collisions. The time scales for the formation of liquid filaments and their breakup into the satellites are measured and, in the case that a single satellite is formed, the satellite size is measured by means of a phase-Doppler anemometer. Furthermore, a theoretical model for the breakup of cylindrical liquid filaments in head-on and off-center collisions is presented. The model is based on a linear stability analysis of the filament formed after the collision. The critical wavelength associated with the largest deformation energy is calculated and identified with the disturbance w...

Unique Properties of Bubbles and Foam Films Stabilized by HFBII Hydrophobin

The HFBII hydrophobin is an amphiphilic protein that can irreversibly adsorb at the air/water interface. The formed protein monolayers can reach a state of two-dimensional elastic solid that exhibits a high mechanical strength as compared to adsorption layers of typical amphiphilic proteins. Bubbles formed in HFBII solutions preserve the nonspherical shape they had at the moment of solidification of their surfaces. The stirring of HFBII solutions leads to the formation of many bubbles of micrometer size. Measuring the electrophoretic mobility of such bubbles, the ζ-potential was determined. Upon compression, the HFBII monolayers form periodic wrinkles of wavelength 11.5 μm, which corresponds to bending elasticity k(c) = 1.1 × 10(-19) J. The wrinkled hydrophobin monolayers are close to a tension-free state, which prevents the Ostwald ripening and provides bubble longevity in HFBII stabilized foams. Films formed between two bubbles are studied by experiments in a capillary cell. In the absence of added electrolyte, the films are electrostatically stabilized. The appearance of protein aggregates is enhanced with the increase of the HFBII and electrolyte concentrations and at pH close to the isoelectric point. When the aggregate concentration is not too high (to block the film thinning), the films reach a state with 12 nm uniform thickness, which corresponds to two surface monolayers plus HFBII tetramers sandwiched between them. In water, the HFBII molecules can stick to each other not only by their hydrophobic moieties but also by their hydrophilic parts. The latter leads to the attachment of HFBII aggregates such as dimers, tetramers, and bigger ones to the interfacial adsorption monolayers, which provides additional stabilization of the liquid films.

Stability of draining plane-parallel films containing surfactants

The stability of partially mobile draining thin liquid films with respect to axisymmetric fluctuations was studied. The material properties of the interfaces (Gibbs elasticity, surface and bulk diffusions) were taken into account. When studying the long wave stability of films, the coupling between the drainage and perturbation flows was considered and the lubrication approximation was applied. Two types of wave modes were examined: radially-bounded and unbounded waves. The difference between the thickness of loss of stability, h(st), the transitional thickness, h(tr), at which the critical wave causing rupture becomes unstable, and the critical thickness, h(cr), when the film ruptures, is demonstrated. Both the linear and the non-linear theories give h(st) > h(tr) > h(cr). The numerical results show that the interfacial mobility does not significantly influence the thickness of the draining film rupture. The interfacial tension and the disjoining pressure are the major factors controlling the critical thickness. The available experimental data for critical thicknesses of foam and emulsion films show excellent agreement with the theoretical predictions. The important role of the electromagnetic retardation term in the van der Waals interaction is demonstrated. Other published theories of the film stability are discussed.

Pair interaction energy between deformable drops and bubbles

The potential energy of interaction between two deformed particles, having the shape of spherical segments and separated by a planar film, is considered. An exact explicit expression for the van der Waals interaction energy between such deformed particles of arbitrary size and deformation is derived by using the microscopic approach of Hamaker [Physica 4, 1058 (1937)]. By means of Derjaguin’s approximation [Kolloid Z. 69, 155 (1934)] explicit expressions for the electrostatic, steric, depletion, and other types of interaction are derived. The relative contributions of the interaction across the planar film and between the spherical surfaces surrounding the film, are analyzed for different cases. The surface deformation energy caused by an increase of the interfacial area during the particle deformation is also considered. The implication of the obtained formulas for treatment of the particle interactions in some particular systems like emulsions, microemulsions, and vesicles, as well as for the adhesion o...

Determination of the aggregation number and charge of ionic surfactant micelles from the stepwise thinning of foam films

The stepwise thinning (stratification) of liquid films, which contain micelles of an ionic surfactant, depends on the micelle aggregation number, N(agg), and charge, Z. Vice versa, from the height of the step and the final film thickness one can determine N(agg), Z, and the degree of micelle ionization. The determination of N(agg) is based on the experimental fact that the step height is equal to the inverse cubic root of the micelle concentration. In addition, Z is determined from the final thickness of the film, which depends on the concentration of counterions dissociated from the micelles in the bulk. The method is applied to micellar solutions of six surfactants, both anionic and cationic: sodium dodecylsulfate (SDS), cetyl trimethylammonium bromide (CTAB), cetylpyridinium chloride (CPC), sodium laurylethersulfates with 1 and 3 ethylene oxide groups (SLES-1EO and SLES-3EO), and potassium myristate. The method has the following advantages: (i) N(agg) and Z are determined simultaneously, from the same set of experimental data; (ii) N(agg) and Z are determined for each given surfactant concentration (i.e. their concentration dependence is obtained), and (iii) N(agg) and Z can be determined even for turbid solutions, like those of carboxylates, where the micelles coexist with acid-soap crystallites, so that the application of other methods is difficult. The results indicate that the micelles of greater aggregation number have a lower degree of ionization, which can be explained with the effect of counterion binding. The proposed method is applicable to the concentration range, in which the films stratify and the micelles are spherical. This is satisfied for numerous systems representing scientific and practical interest.

Interfacial layers from the protein HFBII hydrophobin: Dynamic surface tension, dilatational elasticity and relaxation times

The pendant-drop method (with drop-shape analysis) and Langmuir trough are applied to investigate the characteristic relaxation times and elasticity of interfacial layers from the protein HFBII hydrophobin. Such layers undergo a transition from fluid to elastic solid films. The transition is detected as an increase in the error of the fit of the pendant-drop profile by means of the Laplace equation of capillarity. The relaxation of surface tension after interfacial expansion follows an exponential-decay law, which indicates adsorption kinetics under barrier control. The experimental data for the relaxation time suggest that the adsorption rate is determined by the balance of two opposing factors: (i) the barrier to detachment of protein molecules from bulk aggregates and (ii) the attraction of the detached molecules by the adsorption layer due to the hydrophobic surface force. The hydrophobic attraction can explain why a greater surface coverage leads to a faster adsorption. The relaxation of surface tension after interfacial compression follows a different, square-root law. Such behavior can be attributed to surface diffusion of adsorbed protein molecules that are condensing at the periphery of interfacial protein aggregates. The surface dilatational elasticity, E, is determined in experiments on quick expansion or compression of the interfacial protein layers. At lower surface pressures (<11 mN/m) the experiments on expansion, compression and oscillations give close values of E that are increasing with the rise of surface pressure. At higher surface pressures, E exhibits the opposite tendency and the data are scattered. The latter behavior can be explained with a two-dimensional condensation of adsorbed protein molecules at the higher surface pressures. The results could be important for the understanding and control of dynamic processes in foams and emulsions stabilized by hydrophobins, as well as for the modification of solid surfaces by adsorption of such proteins.

Stability of evaporating two-layered liquid film in the presence of surfactant—I. The equations of lubrication approximation

In this study we consider the stability of horizontal two-layered liquid film attached to a heated solid substrate. The film can contain surfactant that is soluble in both liquid phases. The evaporation of solvent from the upper film is also taken into account. Thus, the two-layered film can exhibit both thermocapillary and Marangoni instabilities coupled with the e⁄ect of solvent mass loss. The problem is solved in the framework of the lubrication approximation. We derive a system of partial di⁄erential equations describing the evolution of long-wave disturbances in the presence of surfactant and evaporation. Appropriate rescaling is proposed and a numerical analysis of the dimensionless groups for particular system of water-light oil film upon a horizontal PVC plate is performed. The model allows one to investigate the role of di⁄erent factors on the film stability: the surfactant concentration and distribution coeƒcient, the critical concentrations of micellization, the surface viscosities, the adsorption isotherms of the surfactant at the liquid surfaces and the intensity of evaporation. Based on this model the full linear analysis of the stability is given in Part II (see Danov et al. (1997b) Chem. Engng Sci., submitted). The non-linear e⁄ects are also taken into account in Part III (see Paunov et al. (1997) Chem. Engng Sci. submitted), where these e⁄ects are studied numerically for a particular case of PVC/tetrachlorethane/water/vapour system. ( 1998 Elsevier Science Ltd. All rights reserved.