Staff Publications

Staff Publications

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    'Staff publications' contains references to publications authored by Wageningen University staff from 1976 onward.

    Publications authored by the staff of the Research Institutes are available from 1995 onwards.

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Growth of wormlike micelles in nonionic surfactant solutions : Quantitative theory vs. experiment
Danov, Krassimir D. ; Kralchevsky, Peter A. ; Stoyanov, Simeon D. ; Cook, Joanne L. ; Stott, Ian P. ; Pelan, Eddie G. - \ 2018
Advances in Colloid and Interface Science 256 (2018). - ISSN 0001-8686 - p. 1 - 22.
Micelle free energy - Micelle growth - Nonionic surfactants - Polyoxyethylene alkyl ethers - Wormlike micelles
Despite the considerable advances of molecular-thermodynamic theory of micelle growth, agreement between theory and experiment has been achieved only in isolated cases. A general theory that can provide self-consistent quantitative description of the growth of wormlike micelles in mixed surfactant solutions, including the experimentally observed high peaks in viscosity and aggregation number, is still missing. As a step toward the creation of such theory, here we consider the simplest system – nonionic wormlike surfactant micelles from polyoxyethylene alkyl ethers, CiEj. Our goal is to construct a molecular-thermodynamic model that is in agreement with the available experimental data. For this goal, we systematized data for the micelle mean mass aggregation number, from which the micelle growth parameter was determined at various temperatures. None of the available models can give a quantitative description of these data. We constructed a new model, which is based on theoretical expressions for the interfacial-tension, headgroup-steric and chain-conformation components of micelle free energy, along with appropriate expressions for the parameters of the model, including their temperature and curvature dependencies. Special attention was paid to the surfactant chain-conformation free energy, for which a new more general formula was derived. As a result, relatively simple theoretical expressions are obtained. All parameters that enter these expressions are known, which facilitates the theoretical modeling of micelle growth for various nonionic surfactants in excellent agreement with the experiment. The constructed model can serve as a basis that can be further upgraded to obtain quantitative description of micelle growth in more complicated systems, including binary and ternary mixtures of nonionic, ionic and zwitterionic surfactants, which determines the viscosity and stability of various formulations in personal-care and house-hold detergency.
Hardening of particle/oil/water suspensions due to capillary bridges : Experimental yield stress and theoretical interpretation
Danov, Krassimir D. ; Georgiev, Mihail T. ; Kralchevsky, Peter A. ; Radulova, Gergana M. ; Gurkov, Theodor D. ; Stoyanov, Simeon D. ; Pelan, Eddie G. - \ 2018
Advances in Colloid and Interface Science 251 (2018). - ISSN 0001-8686 - p. 80 - 96.
Capillary bridges - Capillary suspensions - Pendular state - Rheology of suspensions - Wet granular materials - Yield stress
Suspensions of colloid particles possess the remarkable property to solidify upon the addition of minimal amount of a second liquid that preferentially wets the particles. The hardening is due to the formation of capillary bridges (pendular rings), which connect the particles. Here, we review works on the mechanical properties of such suspensions and related works on the capillary-bridge force, and present new rheological data for the weakly studied concentration range 30-55 vol% particles. The mechanical strength of the solidified capillary suspensions, characterized by the yield stress Y, is measured at the elastic limit for various volume fractions of the particles and the preferentially wetting liquid. A quantitative theoretical model is developed, which relates Y with the maximum of the capillary-bridge force, projected on the shear plane. A semi-empirical expression for the mean number of capillary bridges per particle is proposed. The model agrees very well with the experimental data and gives a quantitative description of the yield stress, which increases with the rise of interfacial tension and with the volume fractions of particles and capillary bridges, but decreases with the rise of particle radius and contact angle. The quantitative description of capillary force is based on the exact theory and numerical calculation of the capillary bridge profile at various bridge volumes and contact angles. An analytical formula for Y is also derived. The comparison of the theoretical and experimental strain at the elastic limit reveals that the fluidization of the capillary suspension takes place only in a deformation zone of thickness up to several hundred particle diameters, which is adjacent to the rheometer's mobile plate. The reported experimental results refer to water-continuous suspension with hydrophobic particles and oily capillary bridges. The comparison of data for bridges from soybean oil and hexadecane surprisingly indicate that the yield strength is greater for the suspension with soybean oil despite its lower interfacial tension against water. The result can be explained with the different contact angles of the two oils in agreement with the theoretical predictions. The results could contribute for a better understanding, quantitative prediction and control of the mechanical properties of three-phase capillary suspensions solid/liquid/liquid.
Rheology of particle/water/oil three-phase dispersions : Electrostatic vs. capillary bridge forces
Georgiev, Mihail T. ; Danov, Krassimir D. ; Kralchevsky, Peter A. ; Gurkov, Theodor D. ; Krusteva, Denitsa P. ; Arnaudov, Luben N. ; Stoyanov, Simeon D. ; Pelan, Eddie G. - \ 2018
Journal of Colloid and Interface Science 513 (2018). - ISSN 0021-9797 - p. 515 - 526.
Capillary bridges - Capillary suspensions - Pendular state - Silica particles - Suspension rheology - Wet granular materials - Yield stress
Hypothesis Particle/water/oil three-phase capillary suspensions possess the remarkable property to solidify upon the addition of minimal amount of the second (dispersed) liquid. The hardening of these suspensions is due to capillary bridges, which interconnect the particles (pendular state). Electrostatic repulsion across the oily phase, where Debye screening by electrolyte is missing, could also influence the hardness of these suspensions. Experiments We present data for oil-continuous suspensions with aqueous capillary bridges between hydrophilic SiO2 particles at particle volume fractions 35–45%. The hardness is characterized by the yield stress Y for two different oils: mineral (hexadecane) and vegetable (soybean oil). Findings and modelling The comparison of data for the “mirror” systems of water- and oil-continuous capillary suspensions shows that Y is lower for the oil-continuous ones. The theoretical model of yield stress is upgraded by including a contribution from electrostatic repulsion, which partially counterbalances the capillary-bridge attraction and renders the suspensions softer. The particle charge density determined from data fits is close to that obtained in experiments with monolayers from charged colloid particles at oil/water interfaces. The results could contribute for better understanding, quantitative prediction and control of the mechanical properties of solid/liquid/liquid capillary suspensions.
Production and characterization of stable foams with fine bubbles from solutions of hydrophobin HFBII and its mixtures with other proteins
Dimitrova, Lydia M. ; Petkov, Plamen V. ; Kralchevsky, Peter A. ; Stoyanov, Simeon D. ; Pelan, Eddie G. - \ 2017
Colloids and Surfaces. A: Physicochemical and Engineering Aspects 521 (2017). - ISSN 0927-7757 - p. 92 - 104.
Hydrophobins are proteins that are excellent foam stabilizers. We investigated the effects of pH and addition of other proteins on the foaminess, bubble size, and stability of foams from aqueous solutions of the protein HFBII hydrophobin. The produced stable foams have bubbles of radii smaller than 40 μm that obey the lognormal distribution. The overrun of most foams is in the range from 5 to 8, which indicates a good foaminess. The foam longevity is characterized by the time dependences of the foam volume and weight. A combined quantitative criterion for stability, the degree of foam conservation, is proposed. The produced foams are stable for at least 12–17 days. The high foam stability can be explained with the formation of dense hydrophobin adsorption layers, which are impermeable to gas transfer and block the Ostwald ripening (foam disproportionation). In addition, the population of small bubbles formed in the HFBII solutions blocks the drainage of water through the Plateau borders in the foam. The variation of pH does not essentially affect the foaminess and foam stability. The addition of “regular” proteins, such as beta-lactoglobulin, ovalbumin and bovine serum albumin, to the HFBII solutions does not deteriorate the quality and stability of the produced foams up to 94% weight fraction of the added protein. The results and conclusions from the present study could be useful for the applications of hydrophobins as foam stabilizers.
Limited coalescence and Ostwald ripening in emulsions stabilized by hydrophobin HFBII and milk proteins
Dimitrova, Lydia M. ; Boneva, Mariana P. ; Danov, Krassimir D. ; Kralchevsky, Peter A. ; Basheva, Elka S. ; Marinova, Krastanka G. ; Petkov, Jordan T. ; Stoyanov, Simeon D. - \ 2016
Colloids and Surfaces. A: Physicochemical and Engineering Aspects 509 (2016). - ISSN 0927-7757 - p. 521 - 538.
Drop size distribution - Emulsification - Emulsion stability - HFBII hydrophobin - Ostwald ripening

Hydrophobins are proteins isolated from filamentous fungi, which are excellent foam stabilizers, unlike most of the proteins. In the present study, we demonstrate that hydrophobin HFBII can also serve as excellent emulsion stabilizer. The HFBII adsorption layers at the oil/water interface solidify similarly to those at the air/water interface. The thinning of aqueous films sandwiched between two oil phases ends with the formation of a 6 nm thick protein bilayer, just as in the case of foam films, which results in strong adhesive interactions between the emulsion drops. The drop-size distribution in hydrophobin stabilized oil-in-water emulsions is investigated at various protein concentrations and oil volume fractions. The data analysis indicates that the emulsification occurs in the Kolmogorov regime or in the regime of limited coalescence, depending on the experimental conditions. The emulsions with HFBII are very stable – no changes in the drop-size distributions are observed after storage for 50 days. However, these emulsions are unstable upon stirring, when they are subjected to the action of shear stresses. This instability can be removed by covering the drops with a second adsorption layer from a conventional protein, like β-lactoglobulin. The HFBII surface layer is able to suppress the Ostwald ripening in the case when the disperse phase is oil that exhibits a pronounced solubility in water. Hence, the hydrophobin can be used to stabilize microcapsules of fragrances, flavors, colors or preservatives due to its dense adsorption layers that block the transfer of oil molecules.

Adhesion of bubbles and drops to solid surfaces, and anisotropic surface tensions studied by capillary meniscus dynamometry
Danov, Krassimir D. ; Stanimirova, Rumyana D. ; Kralchevsky, Peter A. ; Marinova, Krastanka G. ; Stoyanov, Simeon D. ; Blijdenstein, Theodorus B.J. ; Cox, Andrew R. ; Pelan, Eddie G. - \ 2016
Advances in Colloid and Interface Science 233 (2016). - ISSN 0001-8686 - p. 223 - 239.
Bubble and drop adhesion to walls - Capillary meniscus dynamometry - Disjoining pressure vs. transversal tension - Foams and emulsions - Isotropic and anisotropic interfaces - Protein and egg yolk solutions

Here, we review the principle and applications of two recently developed methods: the capillary meniscus dynamometry (CMD) for measuring the surface tension of bubbles/drops, and the capillary bridge dynamometry (CBD) for quantifying the bubble/drop adhesion to solid surfaces. Both methods are based on a new data analysis protocol, which allows one to decouple the two components of non-isotropic surface tension. For an axisymmetric non-fluid interface (e.g. bubble or drop covered by a protein adsorption layer with shear elasticity), the CMD determines the two different components of the anisotropic surface tension, σs and σϕ , which are acting along the "meridians" and "parallels", and vary throughout the interface. The method uses data for the instantaneous bubble (drop) profile and capillary pressure, but the procedure for data processing is essentially different from that of the conventional drop shape analysis (DSA) method. In the case of bubble or drop pressed against a substrate, which forms a capillary bridge, the CBD method allows one to determine also the capillary-bridge force for both isotropic (fluid) and anisotropic (solidified) adsorption layers. The experiments on bubble (drop) detachment from the substrate show the existence of a maximal pulling force, F max, that can be resisted by an adherent fluid particle. F max can be used to quantify the strength of adhesion of bubbles and drops to solid surfaces. Its value is determined by a competition of attractive transversal tension and repulsive disjoining pressure forces. The greatest F max values have been measured for bubbles adherent to glass substrates in pea-protein solutions. The bubble/wall adhesion is lower in solutions containing the protein HFBII hydrophobin, which could be explained with the effect of sandwiched protein aggregates. The applicability of the CBD method to emulsion systems is illustrated by experiments with soybean-oil drops adherent to hydrophilic and hydrophobic substrates in egg yolk solutions. The results reveal how the interfacial rigidity, as well as the bubble/wall and drop/wall adhesion forces, can be quantified and controlled in relation to optimizing the properties of foams and emulsions.

Capillary meniscus dynamometry - Method for determining the surface tension of drops and bubbles with isotropic and anisotropic surface stress distributions
Danov, K.D. ; Stanimirova, R.D. ; Kralchevsky, P.A. ; Marinova, K.G. ; Alexandrov, N.A. ; Stoyanov, S.D. ; Blijdenstein, T.B.J. ; Pelan, E.G. - \ 2015
Journal of Colloid and Interface Science 440 (2015). - ISSN 0021-9797 - p. 168 - 178.
Anisotropic interfacial layers - Drop shape analysis - Non-uniform surface tension - Pendant drops and buoyant bubbles - Protein adsorption layers - Surface stress balances

The stresses acting in interfacial adsorption layers with surface shear elasticity are, in general, anisotropic and non-uniform. If a pendant drop or buoyant bubble is covered with such elastic layer, the components of surface tension acting along the "meridians" and "parallels", σs and σϕ, can be different and, then, the conventional drop shape analysis (DSA) is inapplicable. Here, a method for determining σs and σϕ is developed for axisymmetric menisci. This method, called 'capillary meniscus dynamometry' (CMD), is based on processing data for the digitized drop/bubble profile and capillary pressure. The principle of the CMD procedure for data processing is essentially different from that of DSA. Applying the tangential and normal surface stress balance equations, σs and σϕ are determined in each interfacial point without using any rheological model. The computational procedure is fast and could be used in real time, during a given process. The method is applied to determine σs and σϕ for bubbles and drops formed on the tip of a capillary immersed in solutions of the protein HFBII hydrophobin. Upon a surface compression, meridional wrinkles appear on the bubble surface below the bubble "equator", where the azimuthal tension σϕ takes negative values. The CMD method allows one to determine the local tensions acting in anisotropic interfacial layers (films, membranes), like those formed from proteins, polymers, asphaltenes and phospholipids. The CMD is applicable also to fluid interfaces (e.g. surfactant solutions), for which it gives the same surface tension as the conventional methods.

Shear rheology of mixed protein adsorption layers vs their structure studied by surface force measurements
Danov, K.D. ; Kralchevsky, P.A. ; Radulova, G.M. ; Basheva, E.S. ; Stoyanov, S.D. ; Pelan, E.G. - \ 2015
Advances in Colloid and Interface Science 222 (2015). - ISSN 0001-8686 - p. 148 - 161.
nonlinear viscoelastic model - dependent relaxation-times - class-ii hydrophobin - low ionic-strength - beta-casein - interfacial rheology - air/water interface - liquid interfaces - bubble stability - hfbii
The hydrophobins are proteins that form the most rigid adsorption layers at liquid interfaces in comparison with all other investigated proteins. The mixing of hydrophobin HFBII with other conventional proteins is expected to reduce the surface shear elasticity and viscosity, Esh and ¿sh, proportional to the fraction of the conventional protein. However, the experiments show that the effect of mixing can be rather different depending on the nature of the additive. If the additive is a globular protein, like ß-lactoglobulin and ovalbumin, the surface rigidity is preserved, and even enhanced. The experiments with separate foam films indicate that this is due to the formation of a bilayer structure at the air/water interface. The more hydrophobic HFBII forms the upper layer adjacent to the air phase, whereas the conventional globular protein forms the lower layer that faces the water phase. Thus, the elastic network formed by the adsorbed hydrophobin remains intact, and even reinforced by the adjacent layer of globular protein. In contrast, the addition of the disordered protein ß-casein leads to softening of the HFBII adsorption layer. Similar (an even stronger) effect is produced by the nonionic surfactant Tween 20. This can be explained with the penetration of the hydrophobic tails of ß-casein and Tween 20 between the HFBII molecules at the interface, which breaks the integrity of the hydrophobin interfacial elastic network. The analyzed experimental data for the surface shear rheology of various protein adsorption layers comply with a viscoelastic thixotropic model, which allows one to determine Esh and ¿sh from the measured storage and loss moduli, G' and G¿. The results could contribute for quantitative characterization and deeper understanding of the factors that control the surface rigidity of protein adsorption layers with potential application for the creation of stable foams and emulsions with fine bubbles or droplets.
Shear rheology of hydrophobic adsorption layers at oil/water interfaces and data interpretation in terms of a viscoelastic thixotropic model
Radulova, G.M. ; Danov, K.D. ; Kralchevsky, P.A. ; Petkov, J.T. ; Stoyanov, S.D. - \ 2014
Soft Matter 10 (2014)31. - ISSN 1744-683X - p. 5777 - 5786.
oil-water interface - dependent relaxation-times - class-ii hydrophobin - protein hfbii - hexadecane/water interface - flexible proteins - bubble stability - beta-casein - surface - monolayers
Here, we investigate the surface shear rheology of class II HFBII hydrophobin layers at the oil/water interface. Experiments in two different dynamic regimes, at a fixed rate of strain and oscillations, have been carried out with a rotational rheometer. The rheological data obtained in both regimes comply with the same viscoelastic thixotropic model, which is used to determine the surface shear elasticity and viscosity, Esh and ¿sh. Their values for HFBII at oil/water interfaces are somewhat lower than those at the air/water interface. Moreover, Esh and ¿sh depend on the nature of oil, being smaller for hexadecane in comparison with soybean-oil. It is remarkable that Esh is independent of the rate of strain in the whole investigated range of shear rates. For oil/water interfaces, Esh and ¿sh determined for HFBII layers are considerably greater than for other proteins, like lysozyme and ß-casein. It is confirmed that the hydrophobin forms the most rigid surface layers among all investigated proteins not only for the air/water, but also for the oil/water interface. The wide applicability of the used viscoelastic thixotropic model is confirmed by analyzing data for adsorption layers at oil/water interfaces from lysozyme and ß-casein – both native and cross-linked by enzyme, as well as for films from asphaltene. This model turns out to be a versatile tool for determining the surface shear elasticity and viscosity, Esh and ¿sh, from experimental data for the surface storage and loss moduli, G' and G''.
Competitive adsorption of the protein hydrophobin and an ionic surfactant: Parallel vs sequential adsorption and dilatational rheology
Stanimirova, R. ; Marinova, K.G. ; Danov, K.D. ; Kralchevsky, P.A. ; Basheva, E.S. ; Stoyanov, S.D. ; Pelan, E.G. - \ 2014
Colloids and Surfaces. A: Physicochemical and Engineering Aspects 457 (2014). - ISSN 0927-7757 - p. 307 - 317.
air-water-interface - sodium dodecyl-sulfate - beta-casein - air/water interface - fluid interfaces - layers - hfbii - elasticity - stability - mixtures
The competitive adsorption of the protein HFBII hydrophobin and the anionic surfactant sodium dodecyl sulfate (SDS) is investigated in experiments on parallel and sequential adsorption of the two components. The dynamic surface tension and the surface storage and loss dilatational moduli are determined by the oscillating bubble method. A new procedure for data processing is proposed, which allows one to collect data from many different runs on a single master curve and to determine more accurately the dependence of the dilatational elasticity on the surface pressure. Experiments on sequential adsorption are performed by exchanging the HFBII solution around the bubble with an SDS solution. Experiments with separate thin foam films bring additional information on the effect of added SDS. The results indicate that if HFBII has first adsorbed at the air/water interface, it cannot be displaced by SDS at any concentration, both below and above the critical micellization concentration (CMC). In the case of parallel adsorption, there is a considerable difference between the cases below and above the CMC. In the former case, SDS cannot prevent the adsorption of HFBII at the interface, whereas in the latter case adsorption of HFBII is absent, which can be explained with hydrophilization of the hydrophobin aggregates by the SDS in the bulk. The surface dilatational elasticity of the HFBII adsorption layers markedly decreases in the presence of SDS, but it recovers after washing out the SDS. With respect to their dilatational rheology, the investigated HFBII layers exhibit purely elastic behavior, the effect of dilatational viscosity being negligible. As a function of surface tension, the elasticity of the investigated interfacial layers exhibits a high maximum, which could be explained with the occurrence of a phase transition in the protein adsorption layer.
Surface Pressure and Elasticity of Hydrophobin HFBII Layers on the Air-Water Interface: Rheology Versus Structure Detected by AFM Imaging
Stanimirova, R.D. ; Gurkov, T.D. ; Kralchevsky, P.A. ; Balashev, K.T. ; Stoyanov, S.D. ; Pelan, E.G. - \ 2013
Langmuir 29 (2013)20. - ISSN 0743-7463 - p. 6053 - 6067.
class-ii hydrophobins - air/water interface - langmuir monolayers - trichoderma-reesei - proteins - films - adsorption - stability - emulsions - mechanisms
Here, we combine experiments with Langmuir trough and atomic force microscopy (AFM) to investigate the reasons for the special properties of layers from the protein HFBII hydrophobin spread on the airwater interface. The hydrophobin interfacial layers possess the highest surface dilatational and shear elastic moduli among all investigated proteins. The AFM images show that the spread HFBII layers are rather inhomogeneous, (i.e., they contain voids, monolayer and multilayer domains). A continuous compression of the layer leads to filling the voids and transformation of a part of the monolayer into a trilayer. The trilayer appears in the form of large surface domains, which can be formed by folding and subduction of parts from the initial monolayer. The trilayer appears also in the form of numerous submicrometer spots, which can be obtained by forcing protein molecules out of the monolayer and their self-assembly into adjacent pimples. Such structures are formed because not only the hydrophobic parts, but also the hydrophilic parts of the HFBII molecules can adhere to each other in the water medium. If a hydrophobin layer is subjected to oscillations, its elasticity considerably increases, up to 500 mN/m, which can be explained with compaction. The relaxation of the layers tension after expansion or compression follows the same relatively simple law, which refers to two-dimensional diffusion of protein aggregates within the layer. The characteristic diffusion time after compression is longer than after expansion, which can be explained with the impedence of diffusion in the more compact interfacial layer. The results shed light on the relation between the mesoscopic structure of hydrophobin interfacial layers and their unique mechanical properties that find applications for the production of foams and emulsions of extraordinary stability; for the immobilization of functional molecules at surfaces, and as coating agents for surface modification.
Surface shear rheology of hydrophobin adsorption layers: laws of viscoelastic behaviour with applications to long-term foam stability
Danov, K.D. ; Radulova, G.M. ; Kralchevsky, P.A. ; Golemanov, K. ; Stoyanov, S.D. - \ 2012
Faraday Discussions 158 (2012). - ISSN 1359-6640 - p. 195 - 221.
class-ii hydrophobins - air-water-interface - hfbii hydrophobin - liquid interfaces - protein layers - beta-casein - films - elasticity - monolayers - viscosity
The long-term stabilization of foams by proteins for food applications is related to the ability of proteins to form dense and mechanically strong adsorption layers that cover the bubbles in the foams. The hydrophobins represent a class of proteins that form adsorption layers of extraordinary high shear elasticity and mechanical strength, much higher than that of the common milk and egg proteins. Our investigation of pure and mixed (with added beta-casein) hydrophobin layers revealed that their rheological behavior obeys a compound rheological model, which represents a combination of the Maxwell and Herschel-Bulkley laws. It is remarkable that the combined law is obeyed not only in the simplest regime of constant shear rate (angle ramp), but also in the regime of oscillatory shear strain. The surface shear elasticity and viscosity, E-sh and eta(sh), are determined as functions of the shear rate by processing the data for the storage and loss moduli, G' and G ''. At greater strain amplitudes, the spectrum of the stress contains not only the first Fourier mode, but also the third one. The method is extended to this non-linear regime, where the rheological parameters are determined by theoretical fit of the experimental Lissajous plot. The addition of beta-casein to the hydrophobin leads to softer adsorption layers, as indicated by their lower shear elasticity and viscosity. The developed approach to the rheological characterization of interfacial layers allows optimization and control of the performance of mixed protein adsorption layers with applications in food foams.
Interfacial layers from the protein HFBII hydrophobin: Dynamic surface tension, dilatational elasticity and relaxation times
Alexandrov, N.A. ; Marinova, K.G. ; Gurkov, T.D. ; Danov, K.D. ; Kralchevsky, P.A. ; Stoyanov, S.D. ; Blijdenstein, T.B.J. ; Arnaudov, L.N. ; Pelan, E.G. ; Lips, A. - \ 2012
Journal of Colloid and Interface Science 376 (2012). - ISSN 0021-9797 - p. 296 - 306.
class-ii hydrophobins - air-water-interface - trichoderma-reesei - structural-analysis - crystal-structures - curved interfaces - latex-particles - beta-casein - adsorption - rheology
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 (
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