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.     

Experimental and modeling study of Newtonian and non-Newtonian fluid flow in pore network micromodels

The in situ rheology of polymeric solutions has been studied experimentally in etched silicon micromodels which are idealizations of porous media. The rectangular channels in these etched networks have dimensions typical of pore sizes in sandstone rocks. Pressure drop/flow rate relations have been measured for water and non-Newtonian hydrolyzed-polyacrylamide (HPAM) solutions in both individual straight rectangular capillaries and in networks of such capillaries. Results from these experiments have been analyzed using pore-scale network modeling incorporating the non-Newtonian fluid mechanics of a Carreau fluid. Quantitative agreement is seen between the experiments and the network calculations in the Newtonian and shear-thinning flow regions demonstrating that the 'shift factor,'alpha, can be calculated a priori. Shear-thickening behavior was observed at higher flow rates in the micromodel experiments as a result of elastic effects becoming important and this remains to be incorporated in the network model.     

Electroosmosis through a Cation-Exchange Membrane: Effect of an ac Perturbation on the Electroosmotic Flow

The viscous behavior of oil-in-water (O/W) emulsions is studied over a broad range of dispersed-phase concentrations (φ) using a controlled-stress rheometer. At low-to-moderate values of φ (φ<0.60), emulsions exhibit Newtonian behavior. The droplet size does not exert any influence on the viscosity of Newtonian emulsions. However, at higher values of φ, emulsions exhibit shear-thinning behavior. The viscosity of shear-thinning emulsions is strongly influenced by the droplet size; a significant increase in the viscosity occurs when the droplet size is reduced. With the decrease in droplet size, the degree of shear thinning in concentrated emulsions is also enhanced. The viscosity data of Newtonian emulsions are described reasonably well by the cell model of Yaron and Gal-Or (Rheol. Acta 11, 241 (1972)), which takes into account the effects of the dispersed-phase concentration as well as the viscosity ratio of the dispersed phase to continuous phase. The relative viscosities of non-Newtonian emulsions having different droplet sizes but the same dispersed-phase concentration are scaled with the particle Reynolds number. The high shear viscosities of non-Newtonian emulsions can be predicted fairly well by the cell model of Yaron and Gal-Or (Rheol. Acta 11, 241 (1972)). Copyright 2000 Academic Press.     

Rheology of Water-in-Oil Emulsions with Different Drop Sizes

Systemic experiments have been conducted to investigate the effect of drop sizes on the rheology of water-in-oil (W/O) emulsions. Three sets of emulsions with different average drop sizes were first prepared and then the corresponding rheologies were determined using a concentric viscometer. Results indicated that the flow behavior of concentrated emulsions changes qualitatively from Newtonian flow to non-Newtonian flow with shear rates. In Newtonian flow regime, a smaller drop size leads to a higher viscosity, and the increments are more pronounced at high dispersed phase volume fractions. Two local remarkable increases of the emulsion viscosity with dispersed phase volume fractions correspond to the percolation and glass-transition, respectively. In non-Newtonian flow regime, emulsions show shear-thinning behavior and can be fitted well by the power law model. For emulsions with volume fractions between 0.132 and 0.325, the flow index and consistency constant show power law relationship with the water content. Furthermore, the shear-thinning effect becomes stronger in the emulsions with smaller drop sizes. A correlation has been successfully developed for determining the clusters’ sizes in W/O emulsions and shows excellent agreement with the experimental data. As a consequence, a microscopic understanding (cluster level) was presented for the shear-thinning behavior of the emulsions in this study.     

Determination of the pressure coefficient and pressure effects in capillary flow

General expressions for determining the pressure coefficient and axial distribution of the viscosity and pressure in capillary flow are derived for Newtonian and shear-thinning fluids. The pressure-dependent viscosity model is obtained from the WLF equation as derived from Doolittle's free volume theory. The model has also been derived from Eyring's hole theory for viscosity. Poiseuille's equation is modified to correct for the pressure effect on viscosity. A Newtonian, low-molecular-weight polystyrene and a shear-thinning, high-molecular-weight polystyrene were tested in an Instron capillary rheometer. The axial velocity distribution was found to be negligibly affected by pressure whereas the viscosity was shown to increase markedly with a decrease in volume. The resulting pressure effects on the viscosity of both samples were analyzed by using the derived expressions.     

Pressure-driven motion of surfactant-laden drops through cylindrical capillaries: effect of surfactant solubility

The effect of bulk-soluble surfactants on the dynamics of a drop translating through a cylindrical tube under low-Reynolds-number conditions is investigated. Interfacial surfactant adsorption/desorption is modeled according to the Frumkin adsorption framework, and the bulk-insoluble surfactant limit is recovered as the rate of surfactant sorption becomes large compared to that of bulk diffusion. As the equilibrium surface coverage is increased, the mechanism by which drop mobility is reduced changes from uniform retardation at low surface coverage to the formation of a stagnant cap at high surface coverage. For large capillary numbers, the drop does not achieve a steady shape, and eventually it breaks up either through the formation of a penetrating viscous jet of suspending fluid, or by continuous elongation and pinch-off. Surfactants have a destabilizing effect on transient drop shapes by accelerating the formation and development of the penetrating viscous jet that leads to drop breakup. The critical conditions for drop breakup, as well as the mode of breakup, depend on the manner in which the strength of the flow (i.e., the capillary number) is increased.     

Rheology of high internal phase emulsions

The mechanical dispersion technology used in this study employs rotor-stator mixers that produce water-continuous high internal phase emulsions (HIPEs) with narrow drop size distributions and small drop sizes, even when the internal phase (oil) viscosity is quite high. Analysis of these HIPEs reveals trends that are consistent with formation by a capillary instability mechanism in which a shear deformation produces highly elongated drops that rupture to form uniform, small droplets. In the search for a predictive tool to aid in the manufacture and use of HIPEs, rheology data for these shear-thinning HIPEs have been compared to data for models in the literature. Existing models do not correctly account for the effect of a high internal phase viscosity on the rheological properties of the HIPE. Another shortcoming is failure to correctly address the shear-thinning exponent. Whereas internal phase viscosity does not seem to affect the shear-thinning exponent, the surfactant apparently plays an important role, possibly through its modification of the interfacial tension and continuous phase rheology.     

Forced impregnation of a capillary tube with drop impact

We experimentally investigate how the impregnation of porous media can be forced using the initial kinetic energy of an impacting drop. We focus on the scale of a single pore – either hydrophilic or hydrophobic – and thus study the impact of a single drop falling on vertical cylindrical capillary tubes. This experimental configuration therefore differs from the impregnation of a porous media because of the finite volume of the drop and its initial kinetic energy. We observe different limit regimes: at low impact velocity, we recover the classical results for impregnation. The liquid does not impregnate the hydrophobic pore while it is totally sucked into the hydrophilic one. At high impact velocities, the drop is broken in two parts: one part spreads at the top of the surface while an isolated slug is trapped within the pore. We determine the critical speeds for these regimes and obtain a full phase-diagram for our observations. We also stress the characteristics of impregnating slugs namely their volume and their motion within the pores.     

Large Scale Porous Structure in Gels and Relationship with Their Plastic Behavior

Silica gels (classical aerogels and composite aerogels) have been prepared by classical gelation and addition of silica soot in the gelifying solution before gelation. Due to the aggregation mechanisms, these structures are characterized by a fractal organization. The fractal network previously described in the literature (1–100 nm) which results from the aggregation mechanism of the organosiloxane is affected by the addition of the silica soots. Ultra Small Angle X-ray Scattering (USAXS) experiments (done at ESRF) shows that besides the fractal network built by the organosiloxane, the silica soots are forming another porous structure at a higher scale.The mechanical properties seem to be dependent on this large pore structure. Under isostatic pressure, aerogels display an irreversible shrinkage caused by plastic deformation. As a consequence of this plastic shrinkage it is possible to densify, by the pore collapse tending towards the silica glass. The densification mechanism is different from the one obtained by a sintering at high temperature. The pore collapse mechanism is favored by the large pores structure of the composite aerogels, in contrast to viscous sintering.     

部分水解聚丙烯酰胺与蠕虫状胶束在微米级毛细管中的驱替粘度

部分水解聚丙烯酰胺(HPAMs)被大量地用作三次采油中驱替液的增稠剂,表面活性剂在一定的条件下可以通过自组装形成蠕虫状胶束,具有与高分子相似的增稠的作用。本文在半径为1–10 μm的毛细管中,分别考察了HPAMs与蠕虫状胶束的微观驱替行为,研究结果表示毛细管内腔的尺寸限制了这些非牛顿流体的增稠作用。随着毛细管半径的减小,聚合物溶液的剪切变稀越剧烈,甚至从非牛顿流体转变为牛顿流体的流体行为。结合驱替研究和超滤、电镜的结果,证明了高分子的缠绕结构在毛细管中已被破坏。通过对比驱替数据,蠕虫状胶束在毛细管中能够更大程度地保留宏观的粘度,我们提出表面活性剂能够通过自组装修复被破坏的缠绕结构,比高分子聚合物在微观有限空间中有更好的增稠能力。     

Spreading of liquid drops over dry surfaces

Spreading of thin, axisymmetric, non-volatile, Newtonian liquid drops over a dry, smooth, flat solid surface is considered both theoretically and experimentally in the case of complete wetting. The drop profile is solved analytically by matching the “outer” solution for large film thicknesses, where only the capillary effects are important, with the “inner” solution for small film thicknesses, where the viscous and disjoining pressure effects are comparable to capillary effects. It is shown that the apparent radius of the wetted spot, the apex height of the drop, and the apparent advancing dynamic contact angle follow different power laws in time and the advancing dynamic contact angle follows a power law in capillary number. Both the prefactor and the exponent of each power law are derived theoretically. Good agreement between the theory predictions and experimental measurements is shown for both the prefactor and exponent of each power law. It is necessary to emphasize that the theory suggested does not include any fitting parameters.     

Estimation of diffusion parameters in functionalized silicas with modulated porosity. Part II: pore network modeling

In this work, the pore structure of those five (5) silicas SiO2-X (see Part I) which have suffered gradual functionalization with functional groups X of increasing length (X = psi, [triple bond]Si-H, [triple bond]Si-CH2OH, [triple bond]Si-(CH2)3OH, [triple bond]Si-(CH2)11CH3), is modeled as a three-dimensional cubic network of cylindrical pores. Those hybrids organic-inorganic SiO2-X samples are characterized by different extent of pore blocking effects. The pores of samples are represented in a 9 x 9 x 9 lattice by the nodes as well the bonds that are interconnected in a so-called dual site-bond model, DSBM, network. The pore network is developed using a Monte Carlo statistical method where the cylindrical pores (nodes and bonds) are randomly assigned into the lattice, until matching of the theoretical results to the experimental data of N2 adsorption-desorption measurements. Thus, a visual picture of the porous solid is possible. This realistic network is used next in order to study the steady-state gas transport (Knudsen gas-phase and viscous diffusion) properties for the examined materials and how flow processes depend on the morphology of the pore structure. The pore diffusivity Dp and total permeability P of each porous medium is determined based on theoretical calculations and the structural statistical parameters, such as porosity epsilonp, tortuosity factor tau and connectivity c of pores is discussed with the corresponding experimental data described in Part I of this work. The results indicate clearly that the diffusion model made it possible to predict pore effective diffusivity in these porous media in very good agreement with the corresponding experimental results for all the examined solids (Part I). The pore diffusivity increases significantly as the value of the pore connectivity increases but the transport properties of the network are influenced strongly at lowest connectivity. Also the predicted tortuosity factor is related inversely to the extent of interconnection of pores in these solids, which indicates that the influence of pore branching to the tortuosity factor of the pore network decreases, as connectivity increases.     

Factors influencing the transport of short-chain alcohols through mesoporous gamma-alumina membranes

The pressure-driven transport of water, ethanol, and 1-propanol through supported gamma-alumina membranes with different pore diameters is reported. Water and alcohols had similar permeabilities when they were transported through gamma-alumina membranes with average pore diameters of 4.4 and 6.0 nm, and the permeability coefficient was found to be proportional to the square of pore size, in accordance with a viscous flow mechanism. For transport through membranes with an average diameter of 3.2 nm, the behavior of water was in accordance with the viscous flow mechanism, but the permeability of the membrane for ethanol and 1-propanol was much smaller than expected and could not be explained in terms of viscous flow. Although the low permeability of the membrane with 3.2 nm pores for ethanol and 1-propanol was partly due to the presence of small amounts of water in the alcohols, the permeability coefficients were still substantially smaller when water was absent. This intrinsic difference between water and alcohol may be due to differences in molecular size, chemisorption of alcohols on the oxide pore wall, which would lead to a reduction of the effective pore size, and/or a certain degree of translational ordering of the alcohol molecules inside the membrane pores, which leads to an effectively higher viscosity and, therefore, to a higher transport resistance.     

Shape relaxation of an elongated viscous drop

The shape relaxation of a distorted viscous drop suspended in a quiescent immiscible liquid is analyzed in the creeping flow limit. The shape of the drop is axisymmetric, but otherwise arbitrary. The relaxation process is assumed to be driven by a constant interfacial tension and rate-limited by the Newtonian viscosities of the dispersed and continuous phases. For analysis, a least squares technique is developed which, compared to the more common boundary integral methods, is simpler to implement and especially suited for systems where one liquid is much more viscous than the other (i.e., when the viscosity ratio lambda, defined as the ratio of the dispersed to continuous phase viscosities, approaches either zero or infinity). To demonstrate the validity of the proposed least squares technique, its results are shown to agree well with boundary integral calculations for moderate values of lambda, and with experimental data when lambda is much larger than unity (approximately 10(6)). Predictions at infinite viscosity ratio--the regime in which the least squares technique is most useful--are then used to evaluate interfacial tensions associated with a system of practical importance, namely, the dispersion of heavy crude oil in an aqueous environment. This amounts to a novel and accurate technique for determining interfacial tensions--especially those of low values (1 mN/m or less)--between density-matched liquids where at least one of the phases is highly viscous. The experimental part of this study involves the use of suction pipettes to manipulate the shapes of individual micrometer-sized droplets, thus avoiding the need for complex flow-generating devices to create drop deformations.     

Adsorption of Fluids in Pores Formed between Two Hard Cylinders

We study adsorption in pores with curved hard walls that are made of two uniaxial cylinders by using a density functional approach. Two cases are considered: adsorption of hard spheres and adsorption of a Lennard-Jones fluid. In the case of hard spheres, we perform a comparison with the results of grand canonical ensemble Monte Carlo data. This comparison indicates that the applied approach is capable of reproducing the fluid structure quite satisfactorily. For hard spheres, we also make a comparison of the total adsorption effect (expressed as the average density of a confined fluid) inside pores with curved walls with that evaluated for a slitlike pore. We have found that the differences between adsorption in pores with curved walls and in slits with the same wall-to-wall distance are quite low. The calculations for the Lennard-Jones fluid have been concerned with the investigation of the capillary evaporation and with the evaluation of phase diagrams for different pores, including slitlike pores. We have found that the curvature of the pore walls shifts the transition toward lower values of the chemical potential and increases slightly the value of the critical temperature in comparison with the values obtained for a slitlike pore. Copyright 2000 Academic Press.     

Electric-field-controlled water and ion permeation of a hydrophobic nanopore

The permeation of hydrophobic, cylindrical nanopores by water molecules and ions is investigated under equilibrium and out-of-equilibrium conditions by extensive molecular-dynamics simulations. Neglecting the chemical structure of the confining pore surface, we focus on the effects of pore radius and electric field on permeation. The simulations confirm the intermittent filling of the pore by water, reported earlier under equilibrium conditions for pore radii larger than a critical radius R(c). Below this radius, water can still permeate the pore under the action of a strong electric field generated by an ion concentration imbalance at both ends of the pore embedded in a structureless membrane. The water driven into the channel undergoes considerable electrostriction characterized by a mean density up to twice the bulk density and by a dramatic drop in dielectric permittivity which can be traced back to a considerable distortion of the hydrogen-bond network inside the pore. The free-energy barrier to ion permeation is estimated by a variant of umbrella sampling for Na(+), K(+), Ca(2+), and Cl(-) ions, and correlates well with known solvation free energies in bulk water. Starting from an initial imbalance in ion concentration, equilibrium is gradually restored by successive ion passages through the water-filled pore. At each passage the electric field across the pore drops, reducing the initial electrostriction, until the pore, of radius less than R(c), closes to water and hence to ion transport, thus providing a possible mechanism for voltage-dependent gating of hydrophobic pores.     

Numerical investigation of the effect of insoluble surfactants on drop deformation and breakup in simple shear flow

The effect of insoluble surfactants on drop deformation and breakup in simple shear flow is studied using a combination of a three-dimensional boundary-integral method and a finite-volume method to solve the coupled fluid dynamics and surfactant transport problem over the evolving interface. The interfacial tension depends nonlinearly on the surfactant concentration, and is described by the equation of state for the Langmuir isotherm. Results are presented over the entire range of the viscosity's ratio lambda and the surface coverage x, as well as the capillary number Ca that spans from that for small deformation to values that are beyond the critical one Ca(cr). The values of the elasticity number E, which reflects the sensitivity of the interfacial tension to the maximum surfactant concentration, are chosen in the interval 0.1 < or = E < or = 0.4 and a convection dominated regime of surfactant transport, where the influence of the surfactant on drop deformation is the most significant, is considered. For a better understanding of the processes involved, the effect of surfactants on the drop dynamics is decoupled into three surfactant related mechanisms (dilution, Marangoni stress and stretching) and their influence is separately investigated. The dependence of the critical capillary number Ca(cr)(lambda) on the surface coverage is obtained and the boundaries between different modes of breakup (tip-streaming and drop fragmentation) in the (lambda; x) plane are searched for. The numerical results indicate that at low capillary number, even with a trace amount of surfactant, the interface is immobilized, which has also been observed by previous studies. In addition, it is shown that for large Péclet numbers the use of the small deformation theory to measure the interfacial tension in the case where surfactants are present can introduce a significant error.     

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.