Surface Shear Viscosity Research Articles

Thermocapillary migration of a planar droplet at small and large Marangoni numbers: effects of interfacial rheology

In this paper, roles of interfacial rheology on thermocapillary migration of a planar droplet at small and large Marangoni numbers are analyzed. Under quasi-steady-state assumption, the time-independent momentum and energy equations of thermocapillary droplet migration with boundary conditions are determined. An exact solution of the steady thermocapillary migration of the deformed droplet at small Marangoni numbers is obtained. It is found that the deformed droplet has an oblate shape. The deviation from the circular section depends on the Weber number and the migration speed. The surface shear viscosity, the dilatational viscosity and the surface internal energy parameter affect the deformation of the droplet through reducing the migration speed. The validity of the steady thermocapillary droplet migration at small Marangoni numbers is confirmed by determining the conservative overall integral energy equations. At large Marangoni numbers, the non-conservative overall integral energy equations imply that thermocapillary droplet migration is always an unsteady process.

Surface Shear Viscosity and Interleaflet Friction from Nonequilibrium Simulations of Lipid Bilayers.

Nonequilibrium simulation protocols based on shear deformations are applied to determine the surface viscosity and interleaflet friction of lipid bilayers. At high shear rates, a non-Newtonian shear thinning regime is observed, but lower shear rates yield a Newtonian plateau and results that are consistent with equilibrium measurements based on fluctuation-dissipation theorems. Application to all-atom bilayers modeled with the CHARMM36 parameter set yields values for the surface viscosity that are consistent with microscopic measurements based on membrane protein diffusion but are approximately 10 times lower than more macroscopic experimental measurements. The interleaflet friction is about 10 times lower than experimental measurements. Trends across different lipids, temperatures, and ternary liquid-disordered phase mixtures produce results that are consistent with experimental diffusion constants. Application of the protocol to the liquid-ordered phase fails to yield a Newtonian plateau, suggesting more complex rheology.

Egg white protein microgels as aqueous Pickering foam stabilizers: Bubble stability and interfacial properties

The aim of this study was to design and characterize aqueous foams stabilized by egg white protein microgels (EWPM) and compare their stability with conventional foams stabilized by egg white protein (EWP). Sub-micron sized EWPM (hydrodynamic diameter = 359 ± 21 nm) were designed using a top-down approach involving the formation of a thermally-crosslinked egg white protein hydrogel (90 °C/30 min, pH 7.0) followed by controlled shearing using jet homogenization (300 bar, two passes). Microstructural evaluation at multiple length scales (confocal laser scanning microscopy and cryogenic scanning electron microscopy) indicated that the EWPM stabilized the aqueous foams via a Pickering-type mechanism. Foamability was higher in EWP-stabilized foams compared to EWPM-stabilized foams, irrespective of the protein concentrations tested (0.5–3.0 wt%). However, EWPM-stabilized foams exhibited higher stability to disproportionation over long periods (p < 0.05), even though the initial air bubble size was smaller than with EWP. Bubble coalescence experiments also confirmed that the fraction of the coalescence was much lower in EWPM systems as compared to the EWP counterparts. Changes of surface shear viscosities of EWP at the air-water interface indicated that EWP films were more brittle, exhibiting shear thinning during the measurements, whereas the viscosities of the EWPM films were independent of shear after 24 h of ageing. In summary, our study demonstrates for the first time that microgels of EWP have distinct advantages over EWP itself in terms of generating edible foams with ultra-high stability against disproportionation.

Molecular Dynamics Simulation Studies on Structure, Dynamics, and Thermodynamics of Uranyl Nitrate Solution at Various Acid Concentrations.

The structural and dynamical characteristics of uranyl ions in an aqueous acidic environment are of immense importance in the field of nuclear fuel reprocessing. In view of that, the structural and dynamical behavior of the uranyl ion in water has been investigated by performing molecular dynamics (MD) simulations using different force fields. All the force fields have depicted similar structural and dynamical properties except the free energy of hydration where the Guilbaud-Wipff (GW) model performs well over the others. The calculated density using MD simulations is found to be in excellent agreement with the measured experimental density, which ensures the accuracy of the adopted GW force field. The calculated surface tension and shear viscosity are seen to be increased with uranyl nitrate concentrations. At a higher concentration of about 4.0 mol/L, the supersaturation effect has been captured by an inflection in the plot of surface tension and shear viscosity against concentration because of the solution heterogeneity, which was correlated by an inflection in the scattering intensity observed by performing the dynamic light scattering experiment. The binding mode of nitrate ions with the uranyl ion is found to be concentration-dependent, and at higher concentration, it is predominantly monodentate.

Flow in a containerless liquid system: Ring-sheared drop with finite surface shear viscosity

In microgravity a stationary contact ring can constrain a large liquid drop and a second contact ring in rotation can impose shear. With numerical simulations we show that significant flow occurs for finite surface interfacial viscosity, as for example, when protein is adsorbed to the interface.

Influence of pressure-dependent surface viscosity on dynamics of surfactant-laden drops in shear flow

We study numerically the dynamics of an insoluble surfactant-laden droplet in a simple shear flow taking surface viscosity into account. The rheology of drop surface is modelled via a Boussinesq–Scriven constitutive law with both surface tension and surface viscosity depending strongly on the surface concentration of the surfactant. Our results show that the surface viscosity exhibits non-trivial effects on the surfactant transport on the deforming drop surface. Specifically, both dilatational and shear surface viscosity tend to eliminate the non-uniformity of surfactant concentration over the drop surface. However, their underlying mechanisms are entirely different; that is, the shear surface viscosity inhibits local convection due to its suppression on drop surface motion, while the dilatational surface viscosity inhibits local dilution due to its suppression on local surface dilatation. By comparing with previous studies of droplets with surface viscosity but with no surfactant transport, we find that the coupling between surface viscosity and surfactant transport induces non-negligible deviations in the dynamics of the whole droplet. More particularly, we demonstrate that the dependence of surface viscosity on local surfactant concentration has remarkable influences on the drop deformation. Besides, we analyse the full three-dimensional shape of surfactant-laden droplets in simple shear flow and observe that the drop shape can be approximated as an ellipsoid. More importantly, this ellipsoidal shape can be described by a standard ellipsoidal equation with only one unknown owing to the finding of an unexpected relationship among the drop’s three principal axes. Moreover, this relationship remains the same for both clean and surfactant-laden droplets with or without surface viscosity.

Capillary waves with surface viscosity

Experiments over the last 50 years have suggested a tentative correlation between the surface (shear) viscosity and the stability of a foam or emulsion. We examine this link theoretically using small-amplitude capillary waves in the presence of a surfactant solution of dilute concentration, where the associated Marangoni and surface viscosity effects are modelled via the Boussinesq–Scriven formulation. The resulting integro-differential initial value problem is solved analytically, and surface viscosity is found to contribute an overall damping effect to the amplitude of the capillary wave with varying degree depending on the length scale of the system. Numerically, we find that the critical damping wavelength increases for increasing surface concentration but the rate of increase remains different for both the surface viscosity and the Marangoni effect.

Mixing within drops via surface shear viscosity

A new strategy for mixing inside drops is introduced utilizing the action of surface shear viscosity. A drop is constrained by two sharp-edged contact rings that are differentially rotating. Differential rotation of the rings is conveyed by surface shear viscosity into the bulk fluid, thus enhancing the mixing when compared to the quiescent case. Primarily, mixing was considered in a configuration where one hemisphere is initially at a different concentration than the other. When inertia becomes important, the mixing time is reduced by an order of magnitude compared to the case where the two rings are stationary. Various driving speeds of one ring or counter rotation of two rings are considered for the hemispherical initial concentration. Mixing of a core–shell initial concentration was also considered. This approach to mixing in a drop is found to be an effective containerless mixer and may be utilized in chemical and biological applications where solid-wall interactions are deleterious.

Slow viscous flow past cylindrical particles with thin liquid layer: Cell model

In order to investigate the hydrodynamic interaction between an interface and a cylindrical particle, it is essential to compute the drag and other physical properties exerted on the cylinder in the vicinity of the interface. The present study examines the analytical solution of slow viscous flow past a swarm of cylindrical particles, where each particle consists of a solid core covered by a liquid shell coated with thin monomolecular layer of surfactant using cell model technique. We have assumed that each particle is enclosed by a hypothetical cell. The boundary conditions of Happel, Kuwabara, Kvashnin and Mehta–Morse models are considered on hypothetical cell. The effects of Surfactants are accommodated by considering the Scriven boundary conditions at the shell involving Surface Shear viscosity and Surface Dilatational viscosity. The variation of drag force and hydrodynamic permeability with various parameters is graphically presented. The result reveals in all cases the strong influence of surface viscosity on the motion of cylindrical particle, following cell model technique. It is seen that the presence of surfactant layer increases drag force on the contrary decreases hydrodynamic permeability. In the limiting cases, the analytical solutions describing the drag force reduces to known results of Happel, Kuwabara, Kvashin and Mehta-Morse.

Influence of complex interfacial rheology on the thermocapillary migration of a surfactant-laden droplet in Poiseuille flow

The effect of surface viscosity on the motion of a surfactant-laden droplet in the presence of a non-isothermal Poiseuille flow is studied, both analytically and numerically. The presence of bulk-insoluble surfactants along the droplet surface results in interfacial shear and dilatational viscosities. This, in turn, is responsible for the generation of surface-excess viscous stresses that obey the Boussinesq-Scriven constitutive law for constant values of surface shear and dilatational viscosities. The present study is primarily focused on finding out how this confluence can be used to modulate droplet dynamics in the presence of Marangoni stress induced by nonuniform distribution of surfactants and temperature along the droplet surface, by exploiting an intricate interplay of the respective forcing parameters influencing the interfacial stresses. Under the assumption of negligible fluid inertia and thermal convection, the steady-state migration velocity of a non-deformable spherical droplet, placed at the centerline of an imposed unbounded Poiseuille flow, is obtained for the limiting case when the surfactant transport along the interface is dominated by surface diffusion. Our analysis proves that the droplet migration velocity is unaffected by the shear viscosity whereas the dilatational viscosity has a significant effect on the same. The surface viscous effects always retard the migration of a surfactant-laden droplet when the temperature in the far-field increases in the direction of the imposed flow although the droplet always migrates towards the hotter region. On the contrary, if a large temperature gradient is applied in a direction opposite to that of the imposed flow, the direction of droplet migration gets reversed. However, for a sufficiently high value of dilatational surface viscosity, the direction of droplet migration reverses. For the limiting case in which the surfactant transport along the droplet surface is dominated by surface convection, on the other hand, surface viscosities do not have any effect on the motion of the droplet. These results are likely to have far-reaching consequences in designing an optimal migration path in droplet-based microfluidic technology.

Low Rm magnetohydrodynamics as a means of measuring the surface shear viscosity of a liquid metal: A first attempt on Galinstan.

This paper introduces an experimental apparatus which generates the end-driven annular flow of a liquid metal pervaded by a uniform magnetic field. Unlike past viscometers involving an annular channel with particular values of the depth-to-width ratio, the present experiment enables us to drive the viscous shear at the surface of an annular liquid metal bath put in rotation. The magnetic interaction parameter N and the Boussinesq number related to the surface shear viscosity can be monitored from the magnitude of the applied magnetic field; the latter being set large enough for avoiding artefacts related to centrifugation and surface dilatation. This essential feature is obtained due to the ability of the magnetic field to set dimensionality of the annular flow in the channel between 2D-1/2 (swirling flow) and 2D axisymmetric (extinction of the overturning flow if N is large enough). By tracking the azimuthal velocity of tracers seeded along the oxidised surface of liquid Galinstan, an estimate for the surface shear viscosity of a liquid metal can be given.

High Internal Phase Emulsion Gels Stabilized by Natural Casein peptides.

The surface and interfacial properties of casein-hydrolyzed peptides were evaluated using measurement of surface and interfacial tensions, surface viscosity, dynamic light scattering (DLS), and freeze-fracture transmission electron microscopy (FF-TEM). In this study, high internal oil phase emulsion (HIPE) gels were successfully prepared, using the surface and interfacial properties of casein peptides. The casein peptides exhibited surface and interfacial activities. The estimated critical micelle concentration (CMC) and γCMC values were 3.0 mg/mL and 47.8 mN/m, and the average size of casein peptide micelles was 13.2 ± 1.7 nm. The surface shear viscosity of an aqueous casein peptide solution at 10 mg/mL was 1603 µPa ms, which is fifteen times larger than that of sodium dodecyl sulfate (SDS, 106 µPa ms). The larger surface viscosity of casein peptide adsorbed layer could stabilize emulsions and prevent flocculation and coalescence. High internal oil phase gel emulsions were then prepared by slowly adding oil and polyisobutene into an aqueous casein peptide solution/glycerol mixture with different compositions. Based on the pseudo ternary 15 wt% aqueous casein peptide solution/polyisobutene/glycerol phase diagram, the HIPE containing the maximum 88.1 wt% (91.5 vol%) of oil is obtained by the addition of 0.36 wt% of casein peptides. The use of only a small amount of protein-hydrolyzed peptides instead of the commonly used synthetic surfactants for HIPE preparation has great advantages for the widespread application of HIPE technology.

Study the Characterization of Adding Polymer-Surfactant Agent on the Drag Reduction Phenomena in Pipeline Flow System

Abstract &#x0D; In this study, the effect of carboxylic methyl cellulose (CMC), and sodium dodcyl benzene sulfonate (SDBS) as an aqueous solution on the drag reduction was investigated. Different concentrations of (CMC) and (SDBS) such as (50, 100, 150, 200, 250, 300, 350, 400, 450, and 500 ppm) were used to analyze the aqueous solution properties, including surface tension, conductivity, and shear viscosity. The optimum four concentrations (i.e., 50, 100, 200, and 300 ppm) of fluid properties were utilized to find their effect on the drag reduction. Two different PVC pipe diameters (i.e., 1" and 3/4") were used in this work. The results showed that blending CMC with SDBS gives a good drag reduction percent about (58%) more than using them individually, friction factor decreasing with increasing Reynolds number and gives good agreement with von Karamn equation and maximum drag reduction (MDR) asymptote. Reynolds number, pipe diameter, and polymer-surfactant concentrations were considered as influencing factors. In addition, critical micelle concentration, the onset of drag reduction, and the interactions between the mixed additives were discussed. &#x0D; Keyword: CMC, SDBS, drag reduction, friction factor, blending of additives.

Irreversible particle motion in surfactant-laden interfaces due to pressure-dependent surface viscosity

The surface shear viscosity of an insoluble surfactant monolayer often depends strongly on its surface pressure. Here, we show that a particle moving within a bounded monolayer breaks the kinematic reversibility of low-Reynolds-number flows. The Lorentz reciprocal theorem allows such irreversibilities to be computed without solving the full nonlinear equations, giving the leading-order contribution of surface pressure-dependent surface viscosity. In particular, we show that a disc translating or rotating near an interfacial boundary experiences a force in the direction perpendicular to that boundary. In unbounded monolayers, coupled modes of motion can also lead to non-intuitive trajectories, which we illustrate using an interfacial analogue of the Magnus effect. This perturbative approach can be extended to more complex geometries, and to two-dimensional suspensions more generally.

Erratum to: Modeling of complex interfaces for pendant drop experiments

The original version of this article unfortunately contained mistakes. Theo A. Tervoort was not listed among the authors. The correct information is given above. In Balemans et al. (2016), an axisymmetric finite element model is presented to study the behaviour of complex interfaces in pendant drop experiments. While the bulk fluid of the pendant drop is modeled as a Newtonian fluid, the interface behaviour is described using a quasi-linear Kelvin-Voigt constitutive model. To study the influence of the five model parameters of this constitutive model, a parameter study is performed. Furthermore, small amplitude oscillatory measurements are simulated to demonstrate the applicability of the numerical model. The quasi-linear two-dimensional Kelvin-Voigt viscoelastic constitutive equation as proposed by Verwijlen et al. (2014) and used in Balemans et al. (2016) is not material frame indifferent, because the Cauchy-Green deformation tensor Cs is directly coupled to the surface stress tensor ς. Instead the Finger tensor Bs should be used to construct a material frame indifferent constitutive equation. The correct formulation of the quasi-linear twodimensional Kelvin-Voigt constitutive equation becomes (Formula presented.) where J = det(Bs). The constitutive equation has both viscous and elastic properties, and all simulations for Balemans et al. (2016) have been repeated after implementation of Eq. 1 into the numerical model. The results show minor differences for small deformations and small values of the surface elasticity parameters. However, the results presented in Figure 18 (only K = 100 μN/mm) and Figure 21 are significantly different. These deviating results are summarized in Fig. 1, where the apex length in time for G = 1, 10, 50, 100 μN/mm is shown at a surface tension γ = 50 μN/mm, surface dilatational viscosity κ = 1 μNs/mm, surface shear viscosity μ = 1 μNs/mm, and surface dilatational elasticityK = 100 μN/mmas presented before using the Cauchy-Green tensor Cs (dotted lines) and with the use of the Finger tensor Bs (solid lines). Using the new results, Figures 18 and 21 of the article by Balemans et al. (2016) should be replaced with Figs. 2 and 3, respectively. The conclusions of the article do not change. (Figure presented.).

Modelling steady shear flows of Newtonian liquids with non-Newtonian interfaces

In countless biological and technological processes, the flow of Newtonian liquids with a non-Newtonian interface is a common occurrence, such as in monomolecular films in ‘solid’ phases atop of aqueous bulk fluid. There is a lack of models that can predict the flow under conditions different from those used to measure the rheological response of the interface. Here, we present a model which describes interfacial hydrodynamics, including two-way coupling to a bulk Newtonian fluid described by the Navier–Stokes equations, that allows for shear-thinning response of the interface. The model includes a constitutive equation for the interface under steady shear that takes the Newtonian functional form but where the surface shear viscosity is generalized to be a function of the local shear rate. In the limit of a highly viscous interface, the interfacial hydrodynamics is decoupled from the bulk flow and the model can be solved analytically. This provides not only insight into the flow but also a means to validate the numerical technique for solving the two-way coupled problem. The numerical results of the coupled problem shed new light on existing experimental results on steadily sheared monolayers of dipalmitoylphosphatidylcholine (DPPC), the primary constituent of lung surfactant and the bilayers of mammalian cell walls. For low packing density DPPC monolayers, a Newtonian shear-independent surface shear viscosity model can reproduce the interfacial flows, but at high packing density, the shear-thinning properties of the new model presented here are needed.

Simulation Studies on the Role of Lauryl Betaine in Modulating the Stability of AOS Surfactant-Stabilized Foams Used in Enhanced Oil Recovery

The stability of foam in the presence of oil is of fundamental interest in enhanced oil recovery processes using foam for mobility control. Experimentally, it is known that lauryl betaine (LB) increases foam stability of certain anionic surfactants, and LB is referred to as a foam booster. However, the molecular basis for this effect is not well understood. Using molecular dynamics simulations, here we study a system of LB and alpha olefin sulfonate (AOS-14), an anionic surfactant that is used as a foam stabilizer. We monitor the area per molecule, a quantity that correlates with the surface shear viscosity, and the surface dilatational modulus to infer the stability of the various mixtures. We find that the influence of LB is nonmonotonic: the area per molecule and surface dilatational modulus have a minimum and maximum, respectively, around 30% LB in the monolayer. We show that this net effect has its basis in two competing effects: the favorable interaction between LB and AOS-14 that tends to shrink th...

Influence of the Surface Viscosity on the Breakup of a Surfactant-Laden Drop.

We examine both theoretically and experimentally the breakup of a pendant drop loaded with an insoluble surfactant. The experiments show that a significant amount of surfactant is trapped in the resulting satellite droplet. This result contradicts previous theoretical predictions, where the effects of surface tension variation were limited to solutocapillarity and Marangoni stresses. We solve numerically the hydrodynamic equations, including not only those effects but also those of surface shear and dilatational viscosities. We show that surface viscosities play a critical role to explain the accumulation of surfactant in the satellite droplet.

Surface shear viscosity as a macroscopic probe of amyloid fibril formation at a fluid interface.

Amyloidogenesis of proteins is of wide interest because amyloid structures are associated with many diseases, including Alzheimer's and type II diabetes. Dozens of different proteins of various sizes are known to form amyloid fibrils. While there are numerous studies on the fibrillization of insulin induced by various perturbations, shearing at fluid interfaces has not received as much attention. Here, we present a study of human insulin fibrillization at room temperature using a deep-channel surface viscometer. The hydrodynamics of the bulk flow equilibrates in just over a minute, but the proteins at the air-water interface exhibit a very slow development during which the surface (excess) shear viscosity deduced from a Newtonian surface model increases slightly over a period of a day and a half. Then, there is a very rapid increase in the surface shear viscosity to effectively unbounded levels as the interface becomes immobilized. Atomic force microscopy shows that fibrils appear at the interface after it becomes immobilized. Fibrillization in the bulk does not occur until much later. This has been verified by concurrent atomic force microscopy and circular dichroism spectroscopy of samples from the bulk. The immobilized interface has zero in-plane shear rate, however due to the bulk flow, there is an increase in the strength of the normal component of the shear rate at the interface, implicating this component of shear in the fibrillization process ultimately resulting in a thick weave of fibrils on the interface. Real-time detection of fibrillization via interfacial rheology may find utility in other studies of proteins at sheared interfaces.

Artificial viscosity model to mitigate numerical artefacts at fluid interfaces with surface tension

Abstract The numerical onset of parasitic and spurious artefacts in the vicinity of fluid interfaces with surface tension is an important and well-recognised problem with respect to the accuracy and numerical stability of interfacial flow simulations. Issues of particular interest are spurious capillary waves, which are spatially underresolved by the computational mesh yet impose very restrictive time-step requirements, as well as parasitic currents, typically the result of a numerically unbalanced curvature evaluation. We present an artificial viscosity model to mitigate numerical artefacts at surface-tension-dominated interfaces without adversely affecting the accuracy of the physical solution. The proposed methodology computes an additional interfacial shear stress term, including an interface viscosity, based on the local flow data and fluid properties that reduces the impact of numerical artefacts and dissipates underresolved small scale interface movements. Furthermore, the presented methodology can be readily applied to model surface shear viscosity, for instance to simulate the dissipative effect of surface-active substances adsorbed at the interface. The presented analysis of numerical test cases demonstrates the efficacy of the proposed methodology in diminishing the adverse impact of parasitic and spurious interfacial artefacts on the convergence and stability of the numerical solution algorithm as well as on the overall accuracy of the simulation results.