Drop Tensiometry Research Articles

Interfacial Activity of Nonamphiphilic Particles in Fluid-Fluid Interfaces.

Surfactants can adsorb in fluid-fluid interfaces and lower the interfacial tension. Like surfactants, particles with appropriate wettability can also adsorb in fluid-fluid interfaces. Despite many studies of particle adsorption at fluid interfaces, some confusion persists regarding the ability of (simple, nonamphiphilic) particles to reduce the interfacial tension. In the present work, the interfacial activity of silica nanoparticles at air-water and hexadecane-water interfaces and of ethyl cellulose particles at the interface of water with trimethylolpropane trimethacrylate was analyzed through pendant drop tensiometry. Our measurements strongly suggest that the particles do significantly affect the interfacial tension provided that they have a strong affinity to the interface by virtue of their wettability and that no energy barrier to adsorption prevents them from reaching the interface. A simplistic model that does not explicitly account for any particle-particle interactions is found to yield surprisingly good predictions for the effective interfacial tension in the presence of the adsorbed particles. We further propose that interfacial tension measurements, when combined with information about the particles' wetting properties, can provide a convenient way to estimate the packing density of particles in fluid-fluid interfaces. These results may help to understand and control the assembly of nonamphiphilic nanoparticles at fluid-fluid interfaces, which is relevant to applications ranging from surfactant-free formulations and food technology to oil recovery.

Nano-thin walled micro-compartments from transmembrane protein-polymer conjugates.

The high interfacial activity of protein-polymer conjugates has inspired their use as stabilizers for Pickering emulsions, resulting in many interesting applications such as synthesis of templated micro-compartments and protocells or vehicles for drug and gene delivery. In this study we report, for the first time, the stabilization of Pickering emulsions with conjugates of a genetically modified transmembrane protein, ferric hydroxamate uptake protein component A (FhuA). The lysine residues of FhuA with open pore (FhuA ΔCVFtev) were modified to attach an initiator and consequently controlled radical polymerization (CRP) carried out via the grafting-from technique. The resulting conjugates of FhuA ΔCVFtev with poly(N-isopropylacrylamide) (PNIPAAm) and poly((2-dimethylamino)ethyl methacrylate) (PDMAEMA), the so-called building blocks based on transmembrane proteins (BBTP), have been shown to engender larger structures. The properties such as pH-responsivity, temperature-responsivity and interfacial activity of the BBTP were analyzed using UV-Vis spectrophotometry and pendant drop tensiometry. The BBTP were then utilized for the synthesis of highly stable Pickering emulsions, which could remain non-coalesced for well over a month. A new UV-crosslinkable monomer was synthesized and copolymerized with NIPAAm from the protein. The emulsion droplets, upon crosslinking of polymer chains, yielded micro-compartments. Fluorescence microscopy proved that these compartments are of micrometer scale, while cryo-scanning electron microscopy and scanning force microscopy analysis yielded a thickness in the range of 11.1 ± 0.6 to 38.0 ± 18.2 nm for the stabilizing layer of the conjugates. Such micro-compartments would prove to be beneficial in drug delivery applications, owing to the possibility of using the channel of the transmembrane protein as a gate and the smart polymer chains as trigger switches to tune the behavior of the capsules.

Graphene oxide at oil-water interfaces: Adsorption, assembly & demulsification

Graphene oxide (GO) has gathered widespread interest within the scientific community due to its unique properties. Understanding the adsorption behaviors of GO at the oil–water interface has become increasingly important both in terms of fundamental science and applications of GO in emulsions. In the present work, the adsorption dynamics of GO sheets at the toluene/water interface were explored by using pendant drop tensiometry to trace the evolution of oil/water interfacial tensions. A shift from diffusion-controlled to kinetic controlled feature was observed during the aging of the interface, indicating the irreversible adsorption of GO to the interface. Assembly of GO at oil/water interfaces in the presence of surfactants were discussed. Robust large-area films could be prepared by taking advantage of the assembly of GO at the oil/water interface in the presence of cetyltrimethylammonium bromide and octane phenol polyoxyethylene-10. Corresponding interaction mechanisms were discussed. Ultimately, the acquired insights on the interfacial adsorption and the interfacial assembly behavior of GO sheets were combined to reveal the demulsification performance of GO for different emulsions. The findings in the present study are crucial for fully understanding the interfacial activity of GO in emulsions and might provide a facile way to prepare large-area graphene oxide thin films.

Synthesis and interfacial activity of PMMA/PtBMA Janus and homogeneous nanoparticles at water/oil interfaces

Polymethylmethacrylate/poly-tert-butylmethacrylate Janus nanoparticles were synthesized by the electrohydrodynamic co-jetting method. The Janus character of these nanoparticles was visualized through super-resolution imaging with Structured Illumination Microscopy. The Janus nanoparticles, and the corresponding homogeneous sets, were then morphologically characterized to assess their size, distribution, and concentrations. All nanoparticles presented high interfacial activity as measured by pendant drop tensiometry at water/decane interfaces. At high concentrations and compression states, the Janus nanoparticles exhibited higher interfacial activity than the homogeneous nanoparticles. This is in agreement with theoretical and experimental works in which Janus nanoparticles present higher interfacial activity than homogeneous nanoparticles.

Interfacial Activity of Gold Nanoparticles Coated with a Polymeric Patchy Shell and the Role of Spreading Agents.

Gold patchy nanoparticles (PPs) were prepared under surfactant-free conditions by functionalization with a binary ligand mixture of polystyrene and poly(ethylene glycol) (PEG) as hydrophobic and hydrophilic ligands, respectively. The interfacial activity of PPs was compared to that of homogeneous hydrophilic nanoparticles (HPs), fully functionalized with PEG, by means of pendant drop tensiometry at water/air and water/decane interfaces. We compared interfacial activities in three different spreading agents: water, water/chloroform, and pure chloroform. We found that the interfacial activity of PPs was close to zero (∼2 mN/m) when the spreading agent was water and increased to ∼14 mN/m when the spreading agent was water/chloroform. When the nanoparticles were deposited with pure chloroform, the interfacial activity reached up to 60 mN/m by compression. In all cases, PPs exhibited higher interfacial activity than HPs, which were not interfacially active, regardless of the spreading agent. The interfacial activity at the water/decane interface was found to be significantly lower than that at the water/air interface because PPs aggregate in decane. Interfacial dilatational rheology showed that PPs form a stronger elastic shell at the pendant drop interface, compared to HPs. The significantly high interfacial activity obtained with PPs in this study highlights the importance of the polymeric patchy shell and the spreading agent.

The Conformation of Interfacially Adsorbed Ranaspumin-2 Is an Arrested State on the Unfolding Pathway

Ranaspumin-2 (Rsn-2) is a surfactant protein found in the foam nests of the túngara frog. Previous experimental work has led to a proposed model of adsorption that involves an unusual clam-shell-like unhinging of the protein at an interface. Interestingly, there is no concomitant denaturation of the secondary structural elements of Rsn-2 with the large-scale transformation of its tertiary structure. In this work we use both experiment and simulation to better understand the driving forces underpinning this unusual process. We develop a modified Gō-model approach where we have included explicit representation of the side chains to realistically model the interaction between the secondary structure elements of the protein and the interface. Doing so allows for the study of the underlying energy landscape that governs the mechanism of Rsn-2 interfacial adsorption. Experimentally, we study targeted mutants of Rsn-2, using the Langmuir trough, pendant drop tensiometry, and circular dichroism, to demonstrate that the clam-shell model is correct. We find that Rsn-2 adsorption is in fact a two-step process: the hydrophobic N-terminal tail recruits the protein to the interface after which Rsn-2 undergoes an unfolding transition that maintains its secondary structure. Intriguingly, our simulations show that the conformation Rsn-2 adopts at an interface is an arrested state along the denaturation pathway. More generally, our computational model should prove a useful, and computationally efficient, tool in studying the dynamics and energetics of protein-interface interactions.

Phase-field modelling of a miscible system in spinning droplet tensiometer

The spinning drop tensiometry is used for measurements of surface tension coefficients, especially, when interfaces are characterised by low and ultra-low interfacial stresses. A droplet of lighter liquid is introduced into a rotating capillary that was initially saturated with another heavier liquid. The tube is subject to axial rotation that results in droplet’s elongation along the tube’s axis. The equilibrium shape of the droplet is used to determine the surface tension coefficient. In this work, the evolution of a slowly miscible droplet introduced into a spinning capillary is investigated. This technique is frequently employed for studies of the dynamics of miscible systems, even despite the fact that a strict equilibrium is never achieved in a mixture of fully miscible liquids. The numerical modelling of a miscible droplet is fulfilled on the basis of the phase-field (Cahn-Hilliard) approach. The numerical results are compared against the experimental data pursuing two objectives: (i) to verify the use of the phase-field approach as a consistent physics-based approach capable of accurate tracking of the short- and long-term evolution of miscible systems, and (ii) to estimate the values of the phenomenological parameters introduced within the phase-field approach, so making this approach a practical tool for modelling of thermohydrodynamic changes in miscible systems within various configurations.

The apparently anomalous effects of surfactants on interfacial tension in the IBA/water system near its upper critical solution temperature

We studied the effect of anionic, cationic, and nonionic surfactants on the interfacial tension between the two phases of the isobutyric acid/water system using spinning drop tensiometry. It has been found that interfacial tension decreases with increasing concentration of the surfactant in the case of sodium dodecyl sulfate (SDS) and of dodecyltrimethylammonium chloride (DTAC). However, in the case of Triton X-100 an increase of surfactant concentration leads to an increase of the interfacial tension. Such results are consistent with the upper critical solution temperature (UCST) in the presence of these surfactants: the UCST decreases with increasing SDS and DTAC concentrations while it increases in the case of Triton X-100. This apparently anomalous effect has been explained by considering the molecular structure of Triton X-100, which possesses a short polymeric chain that promotes its partitioning toward one of the two phases making them less compatible and thus raises the UCST and the interfacial tension.

Interactions between a triblock copolymer and hydroxyethyl cellulose in aqueous solution and their use in the solubilization of Amiodarone

A physicochemical characterization of the mixtures of triblock copolymer PEO20-PPO70-PEO20, (P123) and hydroxyethyl cellulose (HEC) in aqueous solutions, with and without the hydrophobic drug amiodarone (ADA), was performed by pendant drop tensiometry, differential scanning calorimetry (DSC) and dynamic light scattering (DLS). The results allowed us to propose a detailed diagram for the formation of the different aggregates in water. The equilibrium surface tension values showed that adding HEC to P123 solutions promotes the aggregation of the P123 monomers on the HEC polymer until saturation. By adding ADA into the P123 micelles, the same equilibrium surface tension values were obtained as the ones found in the pure solution of P123. This suggests that the drug is mostly encapsulated. The DSC experiments showed that the critical micelle temperature and the enthalpy of aggregation of P123 were not modified by the presence of HEC. But the incorporation of ADA to the micelles showed a reduction of 40% in the enthalpy of aggregation, indicating a strong interaction between P123 and ADA. In contrast to the empty micelles, when HEC is added to the loaded micelles, the enthalpy of aggregation increases and the interaction of HEC-P123 becomes evident. The DLS results support that the hydrodynamic diameter of the ADA-loaded micelles is 17% smaller than the diameter of the empty P123 micelles. In the presence of HEC, the empty or loaded micelles form a larger complex. This suggests that HEC surrounds the micelles and provides the drug with a second protecting shell. This system could be a good candidate for the hydrophobic drug delivery.

The effects of alkylammonium counterions on the aggregation of fluorinated surfactants and surfactant ionic liquids

The effects of organic counterions with varying carbon number on surfactant aggregation have been analysed by coupling perfluorooctanoate surfactant anions with various alkylammonium counterions. Both the degree of substitution (primary to tertiary) and alkyl chain length (0–3 carbons) of the counterions were varied to provide a comprehensive matrix of geometries and lipophilicities. Surface activity was measured using pendant drop tensiometry, while temperature-controlled small-angle neutron scattering was used to probe changes in aggregation morphology. It was found that the use of such alkylammonium counterions resulted in a strong preference for bilayer formation even at low surfactant concentration (<2wt%), when compared to simple inorganic counterions such as sodium which favour near-spherical micelles. At increased temperatures, some counterions led to unique phase behaviour wherein a transition between two structurally different lamellar phases is seen, rationalised as a transition into a microscopic phase separation wherein a surfactant-rich lamellar phase coexists with a dilute micellar phase. The results indicate that aggregation is controlled by a delicate balance of counterion size, hydrophilicity and diffuseness of charge, providing new methods for the subtle control of surfactant solutions.

Functional properties of pea protein hydrolysates in emulsions and spray-dried microcapsules

In the present study the impact of partial enzymatic hydrolysis on the functional properties of pea protein isolate (PPI) was investigated. PPI and pea protein hydrolysates (PPH) with various degrees of hydrolysis (DH) were characterised by molecular weight distribution, interfacial activity and dilatational rheology (pendant drop tensiometry) and emulsion properties (oil droplet size and ζ-potential). Their suitability for the microencapsulation of nutritional oils by spray-drying and prevention of hydroperoxide formation during storage was evaluated. Only at very low DH (1%), could stable emulsions be produced using alcalase PPH as emulsifier, most likely due to enhanced bulk aggregation, however the oil droplet size was increased compared to PPI-stabilised emulsions. In contrast, trypsin PPH-stabilised emulsions exhibited smaller oil droplets and an increased surface charge (ζ-potential) with increasing DH in comparison to PPI-stabilised emulsions. Differences observed were reflected in dilatational rheological experiments. Depending on the enzyme used to produce PPH, the dilatational moduli increased and the phase angle decreased (trypsin), i.e. stronger and more elastic interfacial layers were formed, or vice versa (alcalase). The PPI- and trypsin-derived PPH-containing emulsions were stable during atomisation and drying, resulting in high microencapsulation efficiencies (94.5–95.6%). Trypsin PPH exhibited a higher potential than PPI to reduce lipid oxidation of rapeseed oil in spray-dried emulsions during storage as demonstrated by hydroperoxide formation. This effect may be attributed to the altered physical properties of the interfacial film as well as the antioxidative effects of the hydrolysed proteins.

Nano ellipsoids at the fluid-fluid interface: effect of surface charge on adsorption, buckling and emulsification.

In this contribution, we discuss the role of surface charge on the adsorption of shape anisotropic particles to fluid-fluid interfaces in the context of their application in particle-stabilized emulsions. Starting with a pendent aqueous drop containing nano-ellipsoids of known surface charge density suspended in an oil medium, we study the kinetics of adsorption of the ellipsoids to the water-decane interface using pendant drop tensiometry. The interfacial tension of the drop is recorded as a function of time by analyzing the shape of the drop. We show that the particles that are weakly charged readily adsorb to the water-decane interface and the adsorption behavior is influenced by the particle surface charge density. Furthermore, as the area available for the particles deposited at the interface is reduced, the interface populated with self-assembled ellipsoids shows wrinkles indicating buckling of the particle-laden interface under compression. However, the buckling is not observed if nano-ellipsoids are highly charged confirming that the particles do not adsorb to the interface when they are highly charged. This suggests that in several examples where the particles at interfaces concept is exploited, the repulsive energy barrier due to the particle surface charge plays a key role in the adsorption of particles to the interfaces. However, once the particles are adsorbed, the interfacial properties of the monolayer depend on the particle-particle interactions. Thus a combination of these interactions determines the concentration of particles at the interface, their microstructure and interfacial properties. The effect of these interactions on the quantity and size of the emulsion drops stabilized by ellipsoidal particles is also explored.

Vitamin D3 and phytosterols affect the properties of polyglycerol polyricinoleate (PGPR) and protein interfaces

The present work tested the effect of addition of hydrophobic compounds at interfaces containing polyglycerol polyricinoleate (PGPR) and β-lactoglobulin or sodium caseinate, using drop tensiometry. Vitamin D3 or phytosterols were also tested on a model double emulsion stabilized with PGPR and sodium caseinate. Emulsions were prepared using a high pressure homogenizer, and changes in particle size were followed using light scattering. The encapsulation efficiency of the double emulsions was estimated by adding Mg2+ and measuring its release from the inner droplet. PGPR dominated the oil-water interfacial properties. In the presence of proteins there was a decrease of the interfacial tension, with little changes in the viscoelastic properties. The presence of vitamin D3 and phytosterols further affected the interfacial properties. Double emulsions were then prepared with 2% PGPR. While control emulsions showed limited stability with an increase in the particle size after one week of storage, emulsions containing 0.05% (w/w) of vitamin D3 or phytosterol resulted in better stability over the storage period. Results suggested that vitamin D3 and phytosterol molecules may interact with the emulsifiers at the interface, affecting the physico-chemical properties, and possibly their release during digestion.

Extraction of EPA/DHA from 18/12EE Fish Oil Using AgNO3(aq): Composition, Yield, and Effects of Solvent Addition on Interfacial Tension and Flow Pattern in Mini-Fluidic Systems

Solvent extraction of Omega-3 polyunsaturated fatty acids (PUFA) ethyl esters (Et) from 18/12EE fish oil was performed with an aqueous silver nitrate solution in a mini-fluidic reactor framework. The resulting extraction was compared within conventional stirred-tank reactors, with practical extraction yields of EPA-Et and DHA-Et approaching 60 to 70 wt %. Equilibrium was reached in less than 36 s at 10 °C, despite stratified flow being observed rather than previously reported slug-flow profiles in idealized fluid pairs at these scales. The deviation in flow pattern was attributed to a measured order of magnitude reduction in the interfacial tension between fish oils and AgNO3 solution relative to idealized solvent mixtures using hexane/heptane as a carrier for purified EPA/DHA. The impact of solvent addition to fish oils on interfacial tension with silver nitrate solutions was subsequently explored through spinning drop tensiometry, suggesting that the heterogeneous nature of raw fish oils will yield sign...

Interfacial Activity and Contact Angle of Homogeneous, Functionalized, and Janus Nanoparticles at the Water/Decane Interface.

Surface heterogeneity affects the behavior of nanoparticles at liquid interfaces. To gain a deeper understanding on the details of these phenomena, we have measured the interfacial activity and contact angle at water/decane interfaces for three different types of nanoparticles: homogeneous poly(methyl methacrylate) (PMMA), silica functionalized with a capping ligand containing a methacrylate terminal group, and Ag-based Janus colloids with two capping ligands of different hydrophobicity. The interfacial activity was analyzed by pendant drop tensiometry, and the contact angle was measured directly by freeze-fracture shadow-casting cryo-scanning electron microscopy. The silver Janus nanoparticles presented the highest interfacial activity, compared to the silica nanoparticles and the homogeneous PMMA nanoparticles. Additionally, increasing the bulk concentration of the PMMA and silica nanoparticles up to 100-fold compared to the Janus nanoparticles led to silica particles forming fractal-like structures at the interface, contrary to the PMMA particles that did not show any spontaneous adsorption.

Tea polyphenols association to caseinate-stabilized oil–water interfaces

Tea Catechins associate with proline rich proteins such as caseins. In this work, the interactions between epigallocatechin-gallate (EGCG), one of the main tea catechins, and caseins at an oil water interface were studied. The association of EGCG with sodium caseinate was quantified by measuring the amount of EGCG adsorbed on the emulsion droplets. In addition, the viscoelastic properties of the protein and EGCG–protein layers formed at the interface were studied using drop tensiometry. Different concentrations of EGCG were added to a model emulsion to obtain final concentrations of 10% soybean oil, 0.5% sodium caseinate and 0–9 mg/mL EGCG. At concentrations < 2 mg/mL EGCG, more than 90% was adsorbed at the interface. At higher concentrations, below 5 mg/mL, about 70% of EGCG was adsorbed. The surface load reached about 1 mg/m2 at 9 mg/mL of EGCG. The dissociation constant for the complex formed, was estimated using schatchard plot, and was 3.7 × 10−5 M for less than 20 mol bound EGCG/protein. The interactions of EGCG with sodium caseinate did not affect the interfacial tension but increased the dilational modulus of the EGCG-protein layer at the interface. This study demonstrated that sodium caseinate emulsions could be employed as carriers for EGCG, and that the complexes formed at the interface are affecting the physico-chemical properties of the emulsions. The results are of significance in the development of dairy based beverages containing tea polyphenols.

Tensiometry and dilational rheology of mixed β-lactoglobulin/ionic surfactant adsorption layers at water/air and water/hexane interfaces

Oscillating drop tensiometry was applied to study adsorbed interfacial layers at water/air and water/hexane interfaces formed from mixed solutions of β-lactoglobulin (BLG, 1μM in 10mM buffer, pH 7 – negative net charge) and the anionic surfactant SDS or the cationic DoTAB. The interfacial pressure Π and the dilational viscoelasticity modulus |E| of the mixed layers were measured for mixtures of varying surfactant concentrations. The double capillary technique was employed which enables exchange of the protein solution in the drop bulk by surfactant solution (sequential adsorption) or by pure buffer (washing out). The first protocol allows probing the influence of the surfactant on a pre-adsorbed protein layer thus studying the protein/surfactant interactions at the interface. The second protocol gives access to the residual values of Π and |E| measured after the washing out procedure thus bringing information about the process of protein desorption.The DoTAB/BLG complexes exhibit higher surface activity and higher resistance to desorption in comparison with those for the SDS/BLG complexes due to hydrophobization via electrostatic binding of surfactant molecules. The neutral DoTAB/BLG complexes achieve maximum elastic response of the mixed layer. Mixed BLG/surfactant layers at the water/oil interface are found to reach higher surface pressure and lower maximum dilational elasticity than those at the water/air surface. The sequential adsorption mode experiments and the desorption study reveal that binding of DoTAB to pre-adsorbed BLG globules is somehow restricted at the water/air surface in comparison with the case of complex formation in the solution bulk and subsequently adsorbed at the water/air surface. Maximum elasticity is achieved with washed out layers obtained after simultaneous adsorption, i.e. isolation of the most surface active DoTAB/BLG complex. These specific effects are much less pronounced at the W/H interface.

Release of Surfactant Cargo from Interfacially-Active Halloysite Clay Nanotubes for Oil Spill Remediation

Naturally occurring halloysite clay nanotubes are effective in stabilizing oil-in-water emulsions and can serve as interfacially-active vehicles for delivering oil spill treating agents. Halloysite nanotubes adsorb at the oil-water interface and stabilize oil-in-water emulsions that are stable for months. Cryo-scanning electron microscopy (Cryo-SEM) imaging of the oil-in-water emulsions shows that these nanotubes assemble in a side-on orientation at the oil-water interface and form networks on the interface through end-to-end linkages. For application in the treatment of marine oil spills, halloysite nanotubes were successfully loaded with surfactants and utilized as an interfacially-active vehicle for the delivery of surfactant cargo. The adsorption of surfactant molecules at the interface serves to lower the interfacial tension while the adsorption of particles provides a steric barrier to drop coalescence. Pendant drop tensiometry was used to characterize the dynamic reduction in interfacial tension resulting from the release of dioctyl sulfosuccinate sodium salt (DOSS) from halloysite nanotubes. At appropriate surfactant compositions and loadings in halloysite nanotubes, the crude oil-saline water interfacial tension is effectively lowered to levels appropriate for the dispersion of oil. This work indicates a novel concept of integrating particle stabilization of emulsions together with the release of chemical surfactants from the particles for the development of an alternative, cheaper, and environmentally-benign technology for oil spill remediation.

Microemulsions with the ionic liquid ethylammonium nitrate: phase behavior, composition, and microstructure.

In this study, we investigate properties of microemulsions which consist of the ionic liquid (IL) ethylammonium nitrate (EAN), the nonionic surfactant C12E3 and an n-alkane, namely n-dodecane or n-octane. The compositions of the coexisting phases are calculated from the densities and volumes of the respective phases. Since the interfacial tension between the water-rich and the oil-rich phase in traditional microemulsions (containing water and oil) relates to the microstructure, spinning drop tensiometry is used to measure the interfacial tension σab and to estimate the domain sizes. Finally, measuring the self-diffusion coefficients of all components via the Fourier Transform Pulsed Gradient Spin Echo (FTPGSE) NMR technique allowed distinguishing between continuous and discrete structures. Our results indicate that the general principles underlying water-n-alkane-CiEj microemulsions can indeed be transferred to oil-in-EAN droplet and the respective bicontinuous microemulsions, while differences are observed for EAN-in-oil droplet microemulsions.

Regulation of chicken egg lysozyme functional properties by interaction with 5-methylresorcinol

The surface activity and dynamics of adsorption surface layer formation of individual solutions of 5-methylresorcinol (MR) and its mixed solutions with lysozyme on air/solution (0.05 M phosphate buffer, pH 6.0) interface under conditions of MR maximally exceeding hydrolytic activity of lysozyme are studied using method of dynamic drop tensiometry. The thermodynamic parameters of adsorption are determined based on the isotherms. It is established that MR possesses lower surface activity in comparison to traditional surfactants. Methylresorcinol increases the surface activity and lysozyme adsorption rate at the air/solution interface in the entire concentration range covered.