Free energy of colloidal particles at the surface of sessile drops

The influence of finite system size on the free energy of a spherical particle floating at the surface of a sessile droplet is studied both analytically and numerically. In the special case that the contact angle at the substrate equals $\pi/2$ a capillary analogue of the method of images is applied in order to calculate small deformations of the droplet shape if an external force is applied to the particle. The type of boundary conditions for the droplet shape at the substrate determines the sign of the capillary monopole associated with the image particle. Therefore, the free energy of the particle, which is proportional to the interaction energy of the original particle with its image, can be of either sign, too. The analytic solutions, given by the Green's function of the capillary equation, are constructed such that the condition of the forces acting on the droplet being balanced and of the volume constraint are fulfilled. Besides the known phenomena of attraction of a particle to a free contact line and repulsion from a pinned one, we observe a local free energy minimum for the particle being located at the drop apex or at an intermediate angle, respectively. This peculiarity can be traced back to a non-monotonic behavior of the Green's function, which reflects the interplay between the deformations of the droplet shape and the volume constraint.Comment: 24 pages, 19 figure

Surface shear rheology of hydrophobin adsorption layers: laws of viscoelastic behaviour with applications to long-term foam stability

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

Shear rheology of hydrophobic adsorption layers at oil/water interfaces and data interpretation in terms of a viscoelastic thixotropic model

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''

Shear rheology of mixed protein adsorption layers vs their structure studied by surface force measurements

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

Surface Pressure and Elasticity of Hydrophobin HFBII Layers on the Air-Water Interface: Rheology Versus Structure Detected by AFM Imaging

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

Competitive adsorption of the protein hydrophobin and an ionic surfactant: Parallel vs sequential adsorption and dilatational rheology

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

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