Oscillating drop/bubble tensiometry: effect of viscous forces on the measurement of interfacial tension

The oscillating drop/bubble technique is increasingly popular for measuring the interfacial dilatational properties of surfactant/polymer-laden fluid/fluid interfaces. A caveat of this technique, however, is that viscous forces are important at higher oscillation frequencies or fluid viscosities; these can affect determination of the interfacial tension. Here, we experimentally quantify the effect of viscous forces on the interfacial-tension measurement by oscillating 100 and 200 cSt poly(dimethylsiloxane) (PDMS) droplets in water at small amplitudes and frequencies ranging between 0.01 and 1 Hz. Due to viscous forces, the measured interfacial tension oscillates sinusoidally with the same frequency as the oscillation of the drop volume. The tension oscillation precedes that of the drop volume, and the amplitude varies linearly with Capillary number, Ca=DeltamuomegaDeltaV/gammaa(2), where Deltamu=mu(D)-mu is the difference between the bulk Newtonian viscosities of the drop and surrounding continuous fluid, omega is the oscillation frequency of the drop, DeltaV is the amplitude of volume oscillation, gamma is the equilibrium interfacial tension between the PDMS drop and water, and a is the radius of the capillary. A simplified model of a freely suspended spherical oscillating-drop well explains these observations. Viscous forces distort the drop shape at Ca>0.002, although this criterion is apparatus dependent.     

Interfacial tension of blends containing thermotropic liquid crystalline polymers

A method is proposed to determine the interfacial tension of immiscible blends containing a liquid crystalline polymer (LCP) and a flexible-molecule polymer, under flow conditions. The method is based on Taylor's theorem for immiscible fluids, i.e., that a suspended drop of liquid A in liquid matrix B is deformed in shear or elongational flow in proportion to the ratio of interfacial to viscous stresses. Taylor's theorem, as originally derived, applies to low concentrations, Newtonian fluids and small deformations. Thus, the theorem was modified to account for “Power Law” fluids in elongational flow and large deformations, more applicable to the system under investigation. The elongational viscosities of the LCP and the flexible polymer (polycarbonate) as a function of elongational rate were determined using converging type flow. The two polymers exhibited a Power-Law behavior in elongational flow and, hence, the experimental constitutive equations of state were used to quantify the viscous stresses. The interfacial stresses were modified for large deformations by taking into consideration the deformed shape and hence increased surface area of the elongated LCP particle. Using the modified expression, the interfacial tension of LCP and PC was determined to be in the range of 5–6.6 dyne/cm.     

Experimental observation of oscillatory effects on the relaxation of a sheared liquid drop

This work deals with the experimental observation of the shape oscillations followed by a viscous liquid drop immersed in another viscous fluid matrix when retracting from a deformed state into the spherical shape under the action of interfacial forces. The droplet is firstly deformed into an ellipsoidal shape by a shear flow and later allowed to recover the equilibrium shape after cessation of the flow. It is observed that such an oscillatory process occurs for a wide range of viscosity ratios and it may be described by a dampened oscillation. Viscous components dominate the drop retraction, just allowing few oscillations. The dampening factor, frequency and amplitude of the oscillations are affected by the drop viscosity. Frequencies and amplitudes are also influenced by the initial drop deformation.     

界面流变性质对小液滴聚并过程的影响

对表面活性剂溶液中两个小液滴的聚并现象进行理论分析，并考虑相界面上质量传递对该过程的影响，得到聚并时间与界而张力和界面张力梯度、界面粘度、表面活性剂界面扩散系数、连续相和分散相的主体性质、范德华力及液滴半径的关系．     

Dielectric spectroscopy of liquid crystalline dispersions

We describe dielectric spectroscopy measurements on dispersions of two thermotropic liquid crystals (5CB and 8CB) in a poly(dimethylsiloxane) matrix. 5CB exhibits nematic and isotropic phases, while 8CB exhibits smectic, nematic, and isotropic phases. The spectra of the dispersions exhibit a temperature-dependent dielectric relaxation in the interval from 100 to 1000 Hz, with relaxation times that depend strongly on whether the dispersed phase is isotropic, nematic, or smectic. The dielectric relaxation times also depend on the viscosity of the matrix fluid. These results suggest a coupling between the electric field and the mechanics of the interface that affects the spectrum of the dispersed phase and shifts the Maxwell-Wagner interfacial polarization peak.     

The influence of internal phase viscosity on the viscosity of concentrated water-in-oil emulsions

Summary The influence of the viscosity of the internal phase on the viscosity of concentrated water-in-oil emulsions has been investigated and found to be negligible. It is indicated that thechemical nature of the dispersed medium may be of importance, however, with particular reference to its relationship to the stabilising agent, and an example of this is given. In liquid suspensions the ratio of the viscosities of the two phases is of importance in the transmission of viscous effects from the continuous to the disperse medium. This is not found to be the case for the emulsions examined, and the significance of the rigid structure of the interfacial film in this respect is discussed.

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Zusammenfassung Der Einflu? der Viskosit?t der inneren Phase auf die Viskosit?t von konzentriertem Wasser-in-?lemulsion wurde untersucht. Er ist vernachl?ssigbar. Dagegen ist die chemische Struktur des dispergierten Mediums wichtig, besonders im Zusammenhang mit dem Stabilisator, wie ein Beispiel zeigt. Da in flüssigen Suspensionen das Verh?ltnis der Viskosit?ten der beiden Phasen für die Berechnung der Viskosit?t der Dispersion aus denen der beiden Medien eine Rolle spielen sollte und dies bei den untersuchten Emulsionen nicht der Fall war, wird eine Wirkung von festen Grenzfl?chenfilmen für eine Erkl?rung diskutiert.

     

小角躺滴法测定低界面张力

在测定界面张力,特别是测定低界面张力的各种方法中,躺滴法占有相当重要的位置。但一般的躺滴法都要求获得赤道半径(图1中的x_e)数据.故躺滴与基底之间的接触角必须大于90°.这在低界面张力体系中常常难以实现,致使躺滴法的应用受到限制。本文提出一种新的躺滴法,它不依赖于接触角的大小,只需测定躺滴轮廓线上两个相关点的坐标,根据所给数值表即可计算出界面张力,从而为躺滴法应用于低界面张力,特别是     

Interfacial dilational behaviour of adsorbed β-lactoglobulin layers at the different fluid interfaces

β-Lactoglobulin adsorption layers at the interfaces solution/air, /tetradecan and /sunflower oil were characterised by dynamic interfacial tension measurements and harmonic drop oscillation experiments in a time scale of some seconds. Axialsymmetric drop shape analysis (ADSA) was used to calculate drop volume, area and interfacial tension. Within a definite range of drop volume amplitude, the oscillation of the surface tension is harmonic and interfacial dilation parameters can be determined. Dependence of the dilational parameters on the amplitude and frequency of drop volume oscillation were determined and methodical demands are given for this special kind of ADSA application. The concentration of interfacial saturation is minimal at the interface with sunflower oil. Interfacial dilational elasticities, and viscosities are maximal at the saturation concentration of all systems investigated. The dilational viscosities are maximal in the frequency range 0.007–0.011 Hz and characterise molecular rearrangement processes in the adsorption layer. Interfacial dilational elasticity and viscosity are the largest at the interface with air. They are the smallest at the interface with sunflower oil. Similarities and differences of the systems investigated are discussed by taking into account the adsorption behaviour and the solvatation of different apolar and polar parts of the protein molecules in the neighbouring phase.     

Compression/expansion rheology of oil/water interfaces with adsorbed proteins. Comparison with the air/water surface

Dynamic interfacial tensions and surface dilational moduli were measured for four proteins at three fluid interfaces, as a function of time and concentration. The proteins-beta-casein, beta-lactoglobulin, bovine serum albumin, and ovalbumin-were adsorbed from aqueous solution against air, n-tetradecane, and a triacylglycerol oil. The sinusoidal interfacial compression/expansion, at frequencies ranging from 0.005 to 0.5 Hz, was effected in a dynamic drop tensiometer suited to viscous oil phases. Generally, at interfacial pressures up to 15 mN/m, dilational moduli were purely elastic at frequencies from 0.1 Hz. In this elastic range, in-surface relaxation either was essentially completed or had not yet started within a time on the order of 10 s. Within this time span, protein exchange with the bulk solution was negligible. In cases where in-surface relaxation was completed in the imposed time, the moduli depended only on the equilibrium Pi(Gamma) relationship. We interpret these results in terms of a simple two-dimensional solution model, based on a Gibbs dividing surface, accounting for nonideal mixing to the first order with respect to both entropy and enthalpy. Interfacial mixing enthalpy is shown to have a major effect on the elasticity, with both quantities increasing in the sequence triacylglycerol < tetradecane < air. We also suggest a strong correlation between enthalpy and clean-interface tension that increases in the same order. At each interface, the enthalpy increases with increasing molecular rigidity: beta-casein < beta-lactoglobulin < bovine serum albumin < ovalbumin. Best agreement with the experimental data was obtained with a recently extended version of the model accounting for proteins adopting smaller molecular areas with increasing surface pressure. For interfacial pressures above 15 mN/m, the moduli were generally no longer purely elastic, with viscous loss angles ranging up to 36 degrees. In this range of high pressures, the moduli depended on relaxation mechanisms for which specific kinetic models must be developed.     

Role of surfactants on the approaching velocity of two small emulsion drops

Here we present the exact solution of two approaching spherical droplets problem, at small Reynolds and Peclet numbers, taking into account surface shear and dilatational viscosities, Gibbs elasticity, surface and bulk diffusivities due to the presence of surfactant in both disperse and continuous phases. For large interparticle distances, the drag force coefficient, f, increases only about 50% from fully mobile to tangentially immobile interfaces, while at small distances, f can differ several orders of magnitude. There is significant influence of the degree of surface coverage, θ, on hydrodynamic resistance β for insoluble surfactant monolayers. When the surfactant is soluble only in the continuous phase the bulk diffusion suppresses the Marangoni effect only for very low values of θ, while in reverse situation, the bulk diffusion from the drop phase is more efficient and the hydrodynamic resistance is lower. Surfactants with low value of the critical micelle concentration (CMC) make the interfaces tangentially immobile, while large CMC surfactants cannot suppress interfacial mobility, which lowers the hydrodynamic resistance between drops. For micron-sized droplets the interfacial viscosities practically block the surface mobility and they approach each other as solid spheres with high values of the drag coefficient.     

Localized electric field induced transition and miniaturization of two‐phase flow patterns inside microchannels

Strategic application of external electrostatic field on a pressure‐driven two‐phase flow inside a microchannel can transform the stratified or slug flow patterns into droplets. The localized electrohydrodynamic stress at the interface of the immiscible liquids can engender a liquid‐dielectrophoretic deformation, which disrupts the balance of the viscous, capillary, and inertial forces of a pressure‐driven flow to engender such flow morphologies. Interestingly, the size, shape, and frequency of the droplets can be tuned by varying the field intensity, location of the electric field, surface properties of the channel or fluids, viscosity ratio of the fluids, and the flow ratio of the phases. Higher field intensity with lower interfacial tension is found to facilitate the oil droplet formation with a higher throughput inside the hydrophilic microchannels. The method is successful in breaking down the regular pressure‐driven flow patterns even when the fluid inlets are exchanged in the microchannel. The simulations identify the conditions to develop interesting flow morphologies, such as (i) an array of miniaturized spherical or hemispherical or elongated oil drops in continuous water phase, (ii) “oil‐in‐water” microemulsion with varying size and shape of oil droplets. The results reported can be of significance in improving the efficiency of multiphase microreactors where the flow patterns composed of droplets are preferred because of the availability of higher interfacial area for reactions or heat and mass exchange.     

A Model for the Viscous Coalescence of Amorphous Particles

A model is presented for coalescence by viscous flow in two-particle systems, a phenomenon of interest in such diverse processes as the coagulation of air pollutant aerosols, glass and polymer sintering, and the coagulation of liquid suspensions. The model achieves computational efficiency by incorporating an empirical analytical function to describe the fluid interface, making it particularly suited to incorporation into aerosol dynamics models under conditions where coalescence-limited growth can occur. The dynamics of the interfacial evolution in the coalescing pair are approximated by employing a modification to the boundary integral approach in which a single surface point is used to solve the equations for the surface velocities. Model predictions of dimensionless shrinkage and neck growth obtained using this modeling approach compare favorably to those of existing finite-element models reported in the literature and provide a basis for more complex models to approximate multiple particle coalescence. Copyright 2001 Academic Press.     

Simulations of gravity-induced trapping of a deformable drop in a three-dimensional constriction

An efficient algorithm is developed to determine the three-dimensional shape of a deformable drop trapped under gravity in a constriction, employing an artificial evolution to a steady state. During the simulation, the drop surface is advanced using a rationally-devised normal "velocity", based on local deviation from the Young-Laplace equation and the adjacent solid shape, to approach the trapped drop shape. The artificial "time-dependent" evolution of the drop to the static, trapped shape requires that the free portions of the drop interface eventually satisfy the Young-Laplace equation, and the drop-solid contact portions of the drop interface conform to the solid surface. The significant advantage of this solution method is that a simple, numerically-efficient "velocity" is used to construct the evolution to the steady state; the coated areas where the drop is in near contact with solid boundaries of the constriction do not have to be specified a priori, but are found in the course of the solution. Alternative methods (e.g., boundary integral) based on realistic time-marching would be much more costly for determining the trapped state. Trapping conditions and drop shapes are studied for gravity-induced settling of a deformable drop into a three-dimensional constriction. For conditions near critical, where the trapped-drop steady state ceases to exist, severe surface-mesh distortions are treated by a combination of 'passive mesh stabilization', mesh relaxation and topological mesh transformations through node reconnections. For Bond numbers above a critical value, the drop is deformable enough to pass through the hole of the constriction, with no trapping. Critical Bond numbers are determined by linearly fitting minima of the root-mean-squared (rms) surface velocities versus corresponding Bond numbers greater than critical, and then extrapolating the Bond number to where the minimum rms velocity is zero (i.e., the drop becomes trapped). For ring and hyperbolic-tube constrictions, with axes parallel to the gravity vector, the results for trapped drops and critical Bond numbers are in close agreement with those obtained by the previous, highly-accurate axisymmetric method [1]. Also, the three-dimensional Young-Laplace and boundary-integral methods show good agreement for the static shape of a drop trapped in a tilted three-sphere constriction. For all constriction types studied, including circular rings, hyperbolic tubes and agglomerates of three and four spheres, the critical Bond number increases nearly linearly with an increase in the drop-to-hole size ratio. In contrast, the constriction type and tilt angle, which is the angle between the gravity vector and the normal to the plane of the constriction hole, have generally a weaker effect on the critical Bond number.     

Viscoelastic theory for nematic polymer interfaces

A macroscopic theory for the dynamics of compressible nematic polymer‐viscous fluid interfaces is developed from first principles. The theory is used to define and characterize the basic interfacial viscoelastic material properties of the ordered interfaces. The theory is based on a decomposition of the kinematic fields and nematic tensor order parameter that takes into account the symmetry breaking of the interface. The interfacial rate of entropy production used to identify the interfacial viscoelastic modes is given in terms of surface rate of deformation tensor and the surface Jaumann derivative of the tangential component nematic tensor order parameter. The derived surface viscous stress tensor is asymmetric and thus describes surface flow‐induced changes in the tensor order parameter. Consistency with the Boussinesq surface fluid appropriate for Newtonian interfaces is established. The interfacial material functions are identified as the dynamic surface tension, the interfacial dilational viscosities, and the interfacial shear viscosities. The interfacial material functions depend on the surface tensor order parameter and as a consequence anisotropy is their characteristic feature. Two characteristic interfacial tensions and two dilational viscosities are predicted depending on the director orientation. In addition six interfacial shear viscosities arise as the directors sample the velocity, velocity gradient, and vorticity directions. Finally the theory provides for the necessary theoretical tools needed to describe the interfacial dynamics of nematic polymer interfaces, such as capillary instabilities, Marangoni flows, and wetting phenomena.     

Particle self-assembly in ionic liquid-in-water Pickering emulsions

We report the self-assembly of a single species or a binary mixture of microparticles in ionic liquid-in-water Pickering emulsions, with emphases on the interfacial self-assembled particle structure and the partitioning preference of free particles in the dispersed and continuous phases. The particles form monolayers at ionic liquid-water interfaces and are close-packed on fully covered emulsion droplets or aggregated on partially covered droplets. In contrast to those at oil-water interfaces, no long-range-ordered colloidal lattices are observed. Interestingly, other than equilibrating at the ionic liquid-water interfaces, the microparticles also exhibit a partitioning preference in the dispersed and continuous phases: the sulfate-treated polystyrene (S-PS) and aldehyde-sulfate-treated polystyrene (AS-PS) microparticles are extracted to the ionic liquid phase with a high extraction efficiency, whereas the amine-treated polystyrene (A-PS) microparticles remain in the water phase.     

Adsorption kinetics of asphaltenes at the oil-water interface and nanoaggregation in the bulk

Asphaltenes constitute high molecular weight constituents of crude oils that are insoluble in n-heptane and soluble in toluene. They contribute to the stabilization of the water-in-oil emulsions formed during crude oil recovery and hinder drop-drop coalescence. As a result, asphaltenes unfavorably impact water-oil separation processes and consequently oil production rates. In view of this there is a need to better understand the physicochemical effects of asphaltenes at water-oil interfaces. This study elucidates aspects of these effects based on new data on the interfacial tension in such systems from pendant drop experiments, supported by results from nuclear magnetic resonance (NMR) and dynamic light scattering (DLS) studies. The pendant drop experiments using different asphaltene concentrations (mass fractions) and solvent viscosities indicate that the interfacial tension reduction kinetics at short times are controlled by bulk diffusion of the fraction of asphaltenes present as monomer. At low mass fractions much of the asphaltenes appear to be present as monomers, but at mass fractions greater than about 80 ppm they appear to aggregate into larger structures, a finding consistent with the NMR and DLS results. At longer times interfacial tension reduction kinetics are slower and no longer diffusion controlled. To investigate the controlling mechanisms at this later stage the pendant drop experiment was made to function in a fashion similar to a Langmuir trough with interfacial tension being measured during expansion of a droplet aged in various conditions. The interfacial tension was observed to depend on surface coverage and not on time. All observations indicate the later stage transition is to an adsorption barrier-controlled regime rather than to a conformational relaxation regime.     

Viscoelastic interfacial properties of compatibilized poly(ε‐caprolactone)/polylactide blend

Poly(ε‐caprolactone)/polylactide blend (PCL/PLA) is an interesting biomaterial because the two component polymers show good complementarity in their physical properties. However, PCL and PLA are incompatible thermodynamically and hence the interfacial properties act as the important roles controlling the final properties of their blends. Thus, in this work, the PCL/PLA blends were prepared by melt mixing using the block copolymers as compatibilizer for the studies of interfacial properties. Several rheological methods and viscoelastic models were used to establish the relations between improved phase morphologies and interfacial properties. The results show that the interfacial behaviors of the PCL/PLA blends highly depend on the interface‐located copolymers. The presence of copolymers reduces the interfacial tension and emulsified the phase interface, leading to stabilization of the interface and retarding both the shape relaxation and the elastic interface relaxation. As a result, besides the relaxation of matrices (τ_m) and the shape relaxation of the dispersed PLA phase (τ_F), a new relaxation behavior (τ_β), which is attribute to the relaxation of Marangoni stresses tangential to the interface between dispersed PLA phase and matrix PCL, is observed on the compatibilized blends. In contrast to that of the diblock copolymers, the triblock copolymers show higher emulsifying level. However, both can improve the overall interfacial properties and enhance the mechanical strength of the PCL/PLA blends as a result. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 756–765, 2010     

Friccohenics of Continuum and Non‐Continuum Models for Liquid Flow Applied for Heteromolecular Interaction of DNA Bases and Sugars Estimated with Mansingh Equation

Newtonian and non‐Newtonian liquids widely characterize continuum and non‐continuum models for flows, thus, viscous (continuum) and drop wise (non‐continuum) flows of water and aqueous nucleotides (2‐deoxy adenosine‐DOA, thymidine‐TMD) and nucleosides (guanosine monophosphate‐GMP, adenosine triphosphate‐ATP) with integral unites‐2‐deoxy ribose‐DOR (referred as DNA bases and sugars) have been studied with Survismeter. Time data for viscous (t and drop wise (dt) flows along with drop counts (n) for aqueous solutions of 0.4–1.4 millimol (mm) DNA base and sugars with survismetere at 288.15, 293.15, and 298.15 K are measured for viscosities and surface tension, respectively. The t and n are fitted in Mansingh equation for Friccohesity (σ) calculation that determines dipole moment (µ). The t, dt, and n data are measured for water from 15 to 70°C at an interval of 5°C for standard equation for dipole moment calculation. The t, dt and n values decrease with temperature where the σ is directly proportional to μ values with slight increase with compositions and decreases with temperatures. A continuous decrease in μ values with compositions is noted with slightly higher decrease at 288.15 with both millimol and temperature. The higher decrease with temperatures weakens Coulombic forces ((q₁ · q₂)/r², with charges q₁ and q₂, and radii r)) where σ increase.     

Stability of the Shape of a Viscous Drop under Buoyancy-Driven Translation in a Hele-Shaw Cell

It has been shown (N. R. Gupta, A. Nadim, H. Haj-Hariri, and A. Borhan, J. Colloid Interface Sci. 218, 338 1999) that a circular drop translating in a Hele-Shaw cell under the action of gravity is linearly stable for nonzero interfacial tension. In this paper, we use the boundary integral method to examine the nonlinear evolution of the shape of initially noncircular drops translating in a Hele-Shaw cell. For prolate initial deformations, it is found that the drop reverts to a circular shape for all finite Bond numbers considered. Initially oblate drops, on the other hand, are found to become unstable and break up if the initial shape perturbation is of sufficiently large magnitude. The critical conditions for the onset of drop breakup are examined in terms of the magnitude of the initial deformation as a function of Bond number. Two branches of marginal stability are identified and the effects of viscosity ratio and asymmetric initial perturbations on the stability diagram are discussed. Copyright 2000 Academic Press.