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Traditionally, stress fluctuations in flowing and deformed materials are overlooked, with an obvious focus on average stresses in a continuum mechanical approximation. However, these fluctuations, often dismissed as "noise," hold the potential to provide direct insights into the material structure and its structure-stress coupling, uncovering detailed aspects of fluid transport and relaxation behaviors. Despite advancements in experimental techniques allowing for the visualization of these fluctuations, their significance remains largely untapped as modeling efforts continue to target Newtonian fluids within the confines of Gaussian noise assumptions. In the present work, a comparative analysis of stress fluctuations in two distinct microstructural models is carried out: the temporary network model and the hydrodynamic dumbbell model. Despite both models conforming to the upper convected Maxwell model at a macroscopic level, the temporary network model predicts non-Gaussian fluctuations. We find that stress fluctuations within the temporary network model exhibit more pronounced abruptness at the local scale, with only an enlargement of the control volume leading to a gradual Gaussian-like noise, diminishing the differences between the two models. These findings underscore the heightened sensitivity of fluctuating rheology to microstructural details and the microstructure–flow coupling, beyond what is captured by macroscopically averaged stresses. [ABSTRACT FROM AUTHOR]

Determination of the rheological properties and the interfacial structure–property relationships for complex fluid–fluid interfaces can be of crucial importance for the understanding of physiological and biomedical systems, designing and engineering industrial processes, and developing environmental remediation technologies. For the measurement of interfacial shear rheological material functions, it has been determined that the control of the surface pressure during the application of deformation is essential for obtaining reproducible data especially when measuring complex interfaces, such as particle- and polymer-laden interfaces. Moreover, the study of complex fluid interfaces is complicated by kinematically mixed interfacial flow fields, which include both shear and dilatation (shape and area changes), leading to a possible complex flow history. To address this, specialized rheometers have been developed to provide clear kinematic conditions. For instance, a radial trough has been introduced to enhance the study of dilatational interfacial rheology, effectively solving the challenges posed by the mixed flow fields typical in standard rectangular Langmuir–Pockels (LP) troughs or pendant drops. In the present work, we utilize a new trough instrument, the Quadrotrough (QT), capable of performing on the same device (and sample) independent dilatational and shear deformations at the air/liquid interface under strain and surface pressure control. Brewster angle microscopy (BAM) imaging is carried out in situ simultaneously with rheological measurements. Thus, the QT embodies the combined advantages of the circular trough and the controlled surface pressure shear interfacial rheometer. The interfacial rheology of poly(tert-butyl methacrylate) at the air/water interface was measured for both pure dilatation and pure shear in steady and small amplitude oscillatory (SAO) dilatation (D) and shear (S) modes on the same interface. BAM images were obtained during shear and compression. The results obtained by the QT were highly reproducible and in good agreement with measurements performed previously using the LP trough-mounted double wall ring rheometer and the radial trough. The Hencky strain model was employed to derive steady shear and dilatational interfacial moduli. Very good agreement was observed between the steady and complex shear moduli. However, the dilatational moduli measured under steady compression were markedly smaller than those measured by small amplitude oscillatory dilatational at fixed molecular areas, further highlighting the complicating factor of deformation history on material properties for complex interfaces. In summary, the QT has been shown to be a valuable tool for exploring interfacial rheology and providing insights into complex interfacial systems. [ABSTRACT FROM AUTHOR]

Film drainage, essential in droplet and bubble coalescence and surface wetting, is influenced strongly by the stress boundary condition, in particular, when interfacial stresses are present. These stresses, caused by ubiquitous surface-active components, significantly impact the dynamics of liquid films. Through dynamic thin film balance experiments, we compare the effects of Marangoni stresses, interfacial viscosity, and interfacial viscoelasticity on the drainage of free-standing thin liquid films. These data serve to demonstrate that film deformation intricately depends on the interplay between these stresses and capillarity, resulting in widely varied drainage times. Seemingly subtle changes, especially in the local stress-carrying capacity of the interface, can lead to significant differences in film dynamics. This makes it a promising area for research into interfacial-rheologically active materials for stabilizing potentially more sustainable multiphase materials. [ABSTRACT FROM AUTHOR]

When surface-active molecules or particles assemble at fluid–fluid interfaces, these interfaces acquire complex rheological properties that are of importance in processes that involve flow and deformation of interfaces. Although much progress has been made, interfacial rheology measurements and, in particular, the measurement of interfacial rheological properties of polymers at the air-water interface remain challenging. These are due to weak interactions with the water subphase, the polymer backbone conformation, the glass transition of the interfacial layer, and memory effects. In the present work, we describe systematic rheological measurements of polymer-laden interfaces. The measurements were performed with four different interfacial shear rheometers that can be classified into two types: rheometers in which the surface pressure can be controlled independently, and devices based on fixtures mounted on standard rotational rheometers and lacking control of the surface pressure. We use poly(tert-butyl methacrylate) and poly(methyl methacrylate), two high glass transition temperature, hydrophobic polymers anchored to the water subphase by means of the acrylate group. Using a Langmuir–Pockels (LP) trough, we identify the transition of the polymer monolayer from a viscous to a solid elastic or soft-glassy interface as the polymer surface concentration increases by compression. Then, we compare the linear viscoelastic properties of the interface as obtained by each rheometer. Our results show poor reproducibility and comparability of the rheological data as obtained by different rheometers for the same polymer. This is mainly due to differences in the method used to prepare the layers. For LP-based devices, spreading under dilute conditions and subsequent compression yields layers of compressed glassy blobs with reproducible results. On the other hand, for devices without surface pressure control, deposition of the amount needed to reach a desired concentration may lead to the formation of ill-defined layers resulting in irreproducible data. Furthermore, we find that only when spreading the polymer to form a dilute layer and then controlling the surface pressure by compression, we can clearly distinguish the fluidlike from solidlike interfaces, and a clear correlation is observed between the surface pressure (or interfacial polymer concentration) and the rheological properties of the interface. [ABSTRACT FROM AUTHOR]

Understanding the interfacial structure–property relationship of complex fluid–fluid interfaces is increasingly important for guiding the formulation of systems with targeted interfacial properties, such as those found in multiphase complex fluids, biological systems, biopharmaceuticals formulations, and many consumer products. Mixed interfacial flow fields, typical of classical Langmuir trough experiments, introduce a complex interfacial flow history that complicates the study of interfacial properties of complex fluid interfaces. In this article, we describe the design, implementation, and validation of a new instrument capable of independent application of controlled interfacial dilation and shear kinematics on fluid interfaces. Combining the Quadrotrough with both in situ Brewster angle microscopy and neutron reflectometry provides detailed structural measurements of the interface at the mesoscale and nanoscale in relationship to interfacial material properties under controlled interfacial deformation histories. [ABSTRACT FROM AUTHOR]

We investigate the flow of viscous interfaces carrying an insoluble surface active material, using numerical methods to shed light on the complex interplay between Marangoni stresses, compressibility, and surface shear and dilatational viscosities. We find quantitative relations between the drag on a particle and interfacial properties as they are required in microrheology, i.e., going beyond the asymptotic limits. To this end, we move a spherical particle probe at constant tangential velocity, symmetrically immersed at either the incompressible or compressible interface, in the presence and absence of surfactants, for a wide range of system parameters. A full three-dimensional finite element calculation is used to reveal the intimate coupling between the bulk and interfacial flows and the subtle effects of the different physical effects on the mixed-type velocity field that affects the drag coefficient, both in the bulk and at the interface. For an inviscid interface, the directed motion of the particle leads to a gradient in the concentration of the surface active species, which in turn drives a Marangoni flow in the opposite direction, giving rise to a force exerted on the particle. We show that the drag coefficient at incompressible interfaces is independent of the origin of the incompressibility (dilatational viscosity, Marangoni effects or a combination of both) and that its higher value can not only be related to the Marangoni effects, as suggested earlier. In confined flows, we show how the interface shear viscosity suppresses the vortex at the interface, generates a uniform flow, and consequently increases the interface compressibility and the Marangoni force on the particle. We mention available experimental data and provide analytical approximations for the drag coefficient that can be used to extract surface viscosities. [ABSTRACT FROM AUTHOR]

Attractive colloidal glasses are unique as their dynamical arrest is a combination of entropic crowding effects and energetic bonds formation. When such systems are subjected to flow, their dynamics are activated in a way which differs from hard-sphere glasses that melt through a "convective cage release mechanism." Here, we investigate the microscopic dynamics by measuring the relaxation spectrum during flow using orthogonal superposition rheometry. A small amplitude oscillatory strain is imposed perpendicularly to a steady shear flow, and superposition moduli are measured. Brownian dynamic simulations are utilized complementary to extract the moduli from mean-squared displacements using the generalized Stokes–Einstein relation. At low Péclet number, a crossover frequency between elastic and viscous moduli is detected, representing the relaxation time associated with shear-induced particles escape from their frustration (localization) under flow. For the repulsive glass, this is related to shear-induced cage renewal of particles. For attractive glasses, however, when particles escape their localized length (bonds), they move with no further hindrance with the escape time, which is independent of attraction strength and interestingly faster than that in the repulsive glass. This is attributed to particle localization at shorter length scales due to bonding. At high Péclet, a second low frequency crossover is observed and a low frequency elastic dominated response emerges. This elastic response may originate from slow relaxation of hydroclusters or be a consequence of more intricate nature of superposition moduli. At high frequencies, both orthogonal moduli increase relative to quiescent state due to shear-induced cage deformation, which slows down in-cage dynamics. [ABSTRACT FROM AUTHOR]

The steady state flow of a concentrated dispersion of starlike micelles above the colloidal glass transition concentration is interrogated by superimposing a small amplitude straining motion orthogonal to the main flow direction. Strain amplitude sweeps reveal that the linear response region of the orthogonal perturbation increases with increasing flow rate, consistent with a fluidization of the materials. Orthogonal dynamic frequency sweeps (ODFSs) are obtained for a wide range of shear rates probing the full flow curve. The shear-induced fluidization of the initially glassy suspension is more clearly evidenced by the appearance of a crossover frequency ω c in ODFS, which steadily increases, reflecting a faster structural relaxation under shear. The dependence of ω c on the shear rate is sublinear and follows a power law with an exponent of 0.8. We show that the shape of the orthogonal viscoelastic spectrum changes at a critical shear rate γ ˙ cr , indicative of a structural relaxation modulus that changes from exponential at lower shear rates to multistep with alternating exponential and power law response at higher shear rates. We finally provide a theoretical framework which explains the observed sublinear power law dependence of the crossover frequency and relates it with the shear rate dependence of the viscosity measured by the flow curve. [ABSTRACT FROM AUTHOR]

Multiphase fluids and highly non-Newtonian fluids often show wall slip. The typical approach to reduce wall slip in experiments is to use roughened geometries, which are thin porous layers. However, the presence of the roughness introduces in itself an apparent wall slip due to the flow within the porous layer. To account for wall slip typically, measurements must be run at several gaps in a plate-plate device. With Newtonian fluids, the apparent wall slip can be conveniently accounted for in the measurements at a single gap since it can be accurately predicted using models describing the flow of Newtonian fluids through and over porous media. Here, we extend this approach to viscoelastic fluids by using Minale's model [Phys. Fluids 28, 023102 and 023103 (2016)] for the flow of second order fluids (SOFs) through and over a porous medium. In this work, we first validate the theoretical predictions and then propose an experimental protocol to measure a SOF with rough geometries by executing the experiments at a single chosen gap. Two Boger fluids are used as model SOFs, and three different rough geometries are considered: Two commercial crosshatched plates and a homemade pillared one. The apparent wall slip is shown to be reduced for the viscoelastic fluids, with respect to the Newtonian case, and agreement with the theoretical predictions is excellent. [ABSTRACT FROM AUTHOR]

Gelling colloidal suspensions represent an important class of soft materials. Their mechanical response is characterized by a solid-to-liquid transition at a given shear stress level. Moreover, they often exhibit a complex time-dependent rheological behavior known as thixotropy. The viscosity changes find their origin in the microstructure, which depends on flow history. Yet, the structural response of colloidal gels to flow differs fundamentally from most complex fluids, where flow induces orientation. Upon yielding, low to intermediate volume fraction gels break down in a spatially anisotropic way. Bonds in the velocity-velocity gradient plane are broken, whereas microstructural features in other planes are less affected. The subsequent flow-induced microstructural anisotropy is characterized by typical butterfly scattering patterns. However, as yet there was no evidence for the pertinence of this anisotropy for the rheological properties of these systems. In the present work, orthogonal superposition rheometry was first used to evaluate how the flow-induced microstructure affects the viscoelastic properties. It was shown to retain significant elasticity in the velocity-vorticity plane, even when the structure liquefied. Further, the shearinduced mechanical anisotropy was measured using two-dimensional small amplitude oscillatory shear, exploiting the fact that for suitable thixotropic samples the recovery after arresting the flow is relatively slow. It was hence possible to measure the anisotropy of the moduli upon cessation of flow. The mechanical anisotropy was shown to be spectacular, with the storage moduli in perpendicular directions differing by as much as 2 orders of magnitude. [ABSTRACT FROM AUTHOR]

A geometrically simple flow cell is proposed to generate different types of stagnation flows, using a separation flow and small variations of the geometric parameters. Flows with high local deformation rates can be changed from purely rotational, over simple shear flow, to extensional flow in a region surrounding a stagnation point. Computational fluid dynamic calculations are used to analyse how variations of the geometrical parameters affect the flow field. These numerical calculations are compared to the experimentally obtained streamlines of different designs, which have been determined by high speed confocal microscopy. As the flow type is dictated predominantly by the geometrical parameters, such simple separating flow devices may alleviate the requirements for flow control, while offering good stability for a wide variety of flow types. [ABSTRACT FROM AUTHOR]

When surface-active molecules or particles assemble at fluid–fluid interfaces, these interfaces acquire complex rheological properties that are of importance in processes that involve flow and deformation of interfaces. Although much progress has been made, interfacial rheology measurements and, in particular, the measurement of interfacial rheological properties of polymers at the air-water interface remain challenging. These are due to weak interactions with the water subphase, the polymer backbone conformation, the glass transition of the interfacial layer, and memory effects. In the present work, we describe systematic rheological measurements of polymer-laden interfaces. The measurements were performed with four different interfacial shear rheometers that can be classified into two types: rheometers in which the surface pressure can be controlled independently, and devices based on fixtures mounted on standard rotational rheometers and lacking control of the surface pressure. We use poly(tert-butyl methacrylate) and poly(methyl methacrylate), two high glass transition temperature, hydrophobic polymers anchored to the water subphase by means of the acrylate group. Using a Langmuir–Pockels (LP) trough, we identify the transition of the polymer monolayer from a viscous to a solid elastic or soft-glassy interface as the polymer surface concentration increases by compression. Then, we compare the linear viscoelastic properties of the interface as obtained by each rheometer. Our results show poor reproducibility and comparability of the rheological data as obtained by different rheometers for the same polymer. This is mainly due to differences in the method used to prepare the layers. For LP-based devices, spreading under dilute conditions and subsequent compression yields layers of compressed glassy blobs with reproducible results. On the other hand, for devices without surface pressure control, deposition of the amount needed to reach a desired concentration may lead to the formation of ill-defined layers resulting in irreproducible data. Furthermore, we find that only when spreading the polymer to form a dilute layer and then controlling the surface pressure by compression, we can clearly distinguish the fluidlike from solidlike interfaces, and a clear correlation is observed between the surface pressure (or interfacial polymer concentration) and the rheological properties of the interface. [ABSTRACT FROM AUTHOR]

A common approach to prevent or alleviate wall slip in rotational rheometry is to utilize roughened geometries. While this is a helpful strategy, the presence of the surface roughness introduces a fundamentally different boundary condition, as the flow trough the porous structure needs to be accounted for. In the present work, we investigate the use of rough surfaces in rheometry, starting with simple Newtonian fluids. Both structured and randomly structured surfaces are used, i.e., a cross-hatched plate and a sandpaper disk, respectively. We show that the fluid flows within the roughened layer and that the flow in the gap of the rheometer can be modeled as a flow over and through a porous medium. Stokes' equation and Brinkman's equation can be coupled at the interface through a suitable stress boundary condition recently developed in the literature that takes the momentum transfer to both the fluid and the solid substrate properly into account [Minale, Phys Fluids 26, 123102 (2014b)]. The predictions of this n ew model are compared with the experimental results on Newtonian reference fluids and show excellent agreement for the case of the crosshatched geometry, and satisfactory agreement for the geometry with sandpaper. The analysis provides a way to correct the apparent viscosity by dealing with the extra dissipation in the rough layer using an extrapolation length. [ABSTRACT FROM AUTHOR]

An X-ray flexure-based microgap rheometer (X-FMR) has been designed for combining rheology and in situ small-angle X-ray scattering from the vorticity plane. The gap distance can be varied continuously from 500 μm down to several μm, which provides the unique possibility to generate a strong confinement for many complex fluids. A singular advantage of this setup is the possibility to directly probe the vorticity direction of the flow field with a microfocus X-ray beam and to probe the structural response of the fluid to combined shear and confinement in the vorticity plane. The sliding-plate setup operates over a wide range of shear rates of ... = 10-3-10³ s-1 and strains in the range of 10-4-10². The flexure-based bearing maintains the plate parallelism within 10-5 rad. The X-FMR requires very small sample volumes on the order of 10 μl. The applicability of the device is demonstrated here with limited examples of a nematic suspension of fd virus (rods), and a crystalline suspension containing sterically stabilized polystyrene-butylacrylate latex particles. [ABSTRACT FROM AUTHOR]

When particles are dispersed in a rheologically complex medium, a striking alignment of particles into strings can be observed during shear flow. This occurs even under conditions where the suspensions would be considered to be dilute. However, a conclusive explanation for the specific role of the rheological properties of the suspending medium has not been given since the phenomenon was first discovered, now around 40 years ago. The present work aims to elucidate the role of the fluid properties as well as the effect of geometrical conditions by performing experiments, which separate the different factors that could play a role in string formation. First, the presence of significant normal stress differences is shown to help, but it is not a necessary condition for string formation. Second, moderate confinement is shown to be enhancing alignment as well. Third, shear thinning and its effect on lubrication forces are identified to be the crucial factor for alignment. In particular, shear thinning allows to maintain the individual rotation of each particle in a string. This is a requirement to meet the zero torque condition; otherwise, the string would tumble as a whole. In confirmation of this it is observed that when small particles are added as depleting agent to push larger particles closer together, at a critical concentration the flow induced alignment is suppressed. Particle doublets and triplets are then observed to rotate as a whole and tumble on drifting Jeffery orbits ending up in a log-rolling state, oriented along the vorticity direction. The suppression of the string formation upon increasing attraction confirms that enabling the rotation of the separate particles within the string is crucial for maintaining the structure aligned in the flow direction. This suggests that the pertinent rheological parameters of the suspending fluids are those related to the lubrication flows occurring in the gap, i.e., the overall level of the viscosity and the amount of shear thinning. [ABSTRACT FROM AUTHOR]

Aggregated suspensions of rodlike particles are commonly encountered in soft biological materials and their solidlike response at extremely low volume fractions is also exploited technologically. Understanding the link between the physicochemical parameters such as size, aspect ratio, volume fraction, and interparticle forces with the resulting microstructure and the subsequent rheological response remains challenging. In the present work, suspensions of monodisperse rodlike virus particles, whose surface is modified by grafting with a thermoreversible polymer poly(N-isopropylacrylamide), are used as a model system. The repulsive and attractive contributions to the total interaction potential can be changed independently by varying the ionic strength and the temperature. The effects of these changes on the strength and structure of gels have been studied near the gel transition using a combination of rheological and scattering measurements. Rheological measurements of the near critical gel properties as a function of concentration and ionic strength proved to be more sensitive compared to scattering in resolving the structural differences. A percolating structure can be formed at very low volume fractions, which show a weak dependence on the ionic strength with the anisotropy of the repulsive interactions playing the main role in creating more 'open' structures. The intrinsic stiffness of the rodlike particles does not affect the moduli of the gel states very strongly. [ABSTRACT FROM AUTHOR]

Colloidal gels can undergo a solid to liquid transition, and the yielding and subsequent microstructural reorganizations are responsible for the complex rheological properties of these materials. In the present work, video microscopy is used to study the details of the microstructure during the yielding transition, using planar monolayers of model aggregated suspensions subjected to homogeneous interfacial shear flows. The microstructural heterogeneity of the quiescent structure on both local and larger length scales is characterized in detail. The pertinent length scales can be directly linked to the aggregation pathway. The large scale heterogeneity in the microstructure, rather than the local scale properties, determines the length scales observed during the initial yielding of the gel structure. The break-up and subsequent reaggregation leads to a local compaction and increasingly more heterogeneous structure. As the surface coverage increases, the heterogeneity and deformations become more and more localized. The experiments shed light on the pertinent length scales in colloidal gels and how they evolve upon initial yielding, which should be relevant for understanding the thixotropic response and guiding modeling efforts of the macroscopic rheological behavior of flocculated suspensions. [ABSTRACT FROM AUTHOR]

Nonaqueous layered silicate suspensions have a complex rheological behavior due to the presence of a microstructure on multiple length scales, which is sensitive to flow and flow history. In the present work, the flow-induced orientation and anisotropy of the nonequilibrium metastable structures in nonaqueous layered silicate suspensions has been studied using a combination of light scattering, scattering dichroism, and advanced rheometric measurements, including two dimensional small amplitude oscillatory shear (2D-SAOS) flow experiments. The nature of the structures during flow was mainly studied by means of small angle light scattering patterns. Linear dichroism measurements in the vorticity and velocity gradient directions were used to assess the microstructural anisotropy. The changes observed in the vorticity plane developed in the same range of shear rate as the shear-thinning behavior of the suspensions. Scattering dichroism was used to demonstrate that the flow-induced anisotropy was locked in upon cessation of flow. To verify that this also leads to an anisotropy of the rheological properties, the linear viscoelastic moduli were measured using (2D-SAOS) experiments. This new technique proved to be particularly sensitive to the anisotropic nature of the metastable microstructure of organoclay suspensions. Both the flow-induced orientation and larger scale microstructural rearrangements are shown to contribute to the transient rheological response of the nonaqueous layered silicate suspensions. [ABSTRACT FROM AUTHOR]

The effect of the viscoelastic nature of the suspending medium on the rotation of spherical particles in a simple shear flow is studied experimentally using a counter-rotating device. To evaluate the effect of variations in rheological properties of the suspending media, fluids have been selected which highlight specific constitutive features. These include a reference Newtonian fluid, a constant viscosity, high elasticity Boger fluid, a single relaxation time wormlike micellar surfactant solution, and a broad spectrum shear-thinning elastic polymer solution. It is shown that particle rotation slows down, when compared to the Newtonian case, as elasticity increases, in qualitative agreement with computer simulation studies. Despite the variation in constitutive properties and the wide range of time scales of the fluids, it is found that the Weissenberg number suffices to scale the data: the dimensionless rotation speed of the spheres in the different fluids scales onto a single master curve as a function of the Weissenberg number. This indicates that the slowing down in rotation finds its main origin in (indirect) normal stress effects. [ABSTRACT FROM AUTHOR]

In inertialess suspensions of rigid particles, the rotational motion of each particle is governed by the so-called freely rotating condition, whereby the total torque acting on the particle must be zero. In this work, we study the effect of viscoelasticity of the suspending liquid on the rotation period of a sphere by means of three-dimensional finite element simulations, for conditions corresponding to a macroscopic shear flow. The simulation results capture the slowing down of the rotation, relative to the Newtonian case, which was recently observed in experiments. It is shown that such a phenomenon depends on the specific constitutive equation adopted for the viscoelastic liquid. Analysis of transients shows a clear correlation between rotation rate and the development of first normal stress difference. [ABSTRACT FROM AUTHOR]

The magnetic interfacial needle stress rheometer is a device capable of sensitive rheological interfacial measurements. Yet even for this device, when measuring interfaces with low elastic and viscous moduli, the system response of the instrument contributes significantly to the measured response. To determine the operation limits of the magnetic rod rheometer, we analyze the relative errors that are introduced by linearly subtracting the instrument contribution from the measured response. An analysis of the fluid mechanics demonstrates the intimate coupling between the flow field at the two-dimensional interface and in the bulk at low Boussinesq number. A nonzero Reynolds number is observed to have a similar order of magnitude effect. The resulting nonlinear interfacial deformation profiles lead to an error, which depends on the magnitude of the interfacial modulus, as well as on the phase angle. The conditions under which reliable measurements can be obtained are identified. Based on the analysis of the effects of system response, the Boussinesq and Reynolds numbers, small modifications to the measurement probe are proposed. A reduction of the mass and localization of the magnetic material result in even further improved instrument sensitivity. This is demonstrated experimentally for two cases, i.e., a purely viscous interface of known viscosity, as produced by spreading thin silicon oil films on a water layer, and a time-dependent viscoelastic interface, generated by the surface gelation of a lysozyme solution. [ABSTRACT FROM AUTHOR]