Stability of Streaming in an Electrified Maxwell Fluid Sheet Influenced by a Vertical Periodic Field in the Absence of Surface Charges

The problem of electroviscoelastic Kelvin-Helmholtz waves of Maxwellian fluids under the influence of a vertical periodic electric field is studied in the absence of surface charges. The system is composed of a streaming dielectric fluid sheet of finite thickness embedded between two different streaming semi-infinite dielectric fluids. Due to the streaming flow and the influence of a periodic force, a mathematical simplification is considered. The weak viscoelastic effects are taken into account so that their contributions are demonstrated in the boundary conditions. The approximate equations of motion are solved in the absence of viscoelastic effects. The solutions of the linearized equations of motion and boundary conditions lead to two simultaneous Mathieu equations of damping terms having complex coefficients. Symmetric or antisymmetric deformation that relaxes the coupled Mathieu equations and yields a single Mathieu equation is considered. Stability criteria are discussed and numerical estimation shows that the increase in the sheet thickness plays a destabilizing effect in the presence or in the absence of the field frequency as well as the field intensity. In the absence of the field frequency the velocity ratio between the upper fluid velocity and the sheet velocity has a destabilizing influence, while that between the velocity of the lower fluid and the velocity of the sheet has a stabilizing influence. Moreover, the viscosity ratios have a damping influence while the elasticity ratios have a destabilizing influence. Furthermore, a range of general deformations of the surface deflections is studied. Moreover, the stability behavior for the resonance cases is studied and discussed. The coupled Mathieu equations are analyzed by the multiple scale method. The numerical examination for stability yields some changes in the stability behavior. The fluid sheet thickness plays a stabilizing role in the presence of a constant field while the damping role is observed for the resonance case. Similar results are found for both the stratified velocities and the stratified relaxation times. The dual role of the stratified viscosities is observed in the presence or the absence of the field frequency. Copyright 2000 Academic Press.     

Electrorheological Kelvin-Helmholtz instability of a fluid sheet

The present work deals with the gravitational stability of an electrified Maxwellian fluid sheet shearing under the influence of a vertical periodic electric field. The field produces surface charges on the interfaces of the fluid sheet. Due to the rather complicated nature of the problem a mathematical simplification is considered where the weak effects of viscoelastic fluids are taken into account. The solutions of the linearized equations of motion and boundary conditions lead to two simultaneous Mathieu equations with damping terms and having complex coefficients. Stability criteria are discussed through the assumption of symmetric and anti-symmetric deformations. The disappearance of surface charges from the interfaces obeys a certain relation derived in the marginal state. Furthermore, the case dealing with general deformation is discussed through marginal state analysis. The stability behavior in resonant and nonresonant cases are studied. In addition, the stability picture in the case of absence of the field frequency is studied. The numerical examination for stability showed that the relaxation time ratio plays a destabilizing influence in the case of anti-symmetric deformation or in the general deformation. The stabilizing effect for the relaxation time ratio is saved in the case of general deformation in the presence of the field frequency. In the later case the viscosity, the velocity, and the thickness parameter play a stabilizing influence. A dual role is readied for these parameters in the absence of the field frequency or in the anti-symmetric deformation. The field frequency still plays a destabilizing role in both cases.     

Stability conditions of an electrified miscible viscous fluid sheet

The Kelvin-Helmholtz problem of viscous fluids under the influence of a normal periodic electric field in the absence of surface charges is studied. The system is composed of a streaming dielectric fluid sheet of finite thickness embedded between two different streaming finite dielectric fluids. The interfaces permit mass and heat transfer. Because of the complexity of the considered system, a mathematical simplification is adopted. The weak viscous effects are taken into account so that their contributions are incorporated into the boundary conditions. Therefore, the equations of motion are solved in the absence of viscous effects. The boundary value problem leads to two simultaneous Mathieu equations of damped terms having complex coefficients. The symmetric and antisymmetric deformations reduced the coupled Mathieu equations to a single Mathieu equation. The classical stability criterion is found to be substantially modified due to the effect of mass and heat transfer. The analytical results are numerically confirmed. It is found that the sheet thickness and mass and heat transfer parameters have a dual influence on the stability criteria. It is also found that the field frequency has a stabilizing influence especially at small values of the wave number. In contrast to the case of a pure inviscid fluid, it is found that the uniform normal electric field plays a dual role in the stability criteria. This role depends on the choice of the numerical values of the physical parameters of the system under consideration.     

Destabilizing effect of time-dependent oblique magnetic field on magnetic fluids streaming in porous media

The present work studies Kelvin-Helmholtz waves propagating between two magnetic fluids. The system is composed of two semi-infinite magnetic fluids streaming throughout porous media. The system is influenced by an oblique magnetic field. The solution of the linearized equations of motion under the boundary conditions leads to deriving the Mathieu equation governing the interfacial displacement and having complex coefficients. The stability criteria are discussed theoretically and numerically, from which stability diagrams are obtained. Regions of stability and instability are identified for the magnetic fields versus the wavenumber. It is found that the increase of the fluid density ratio, the fluid velocity ratio, the upper viscosity, and the lower porous permeability play a stabilizing role in the stability behavior in the presence of an oscillating vertical magnetic field or in the presence of an oscillating tangential magnetic field. The increase of the fluid viscosity plays a stabilizing role and can be used to retard the destabilizing influence for the vertical magnetic field. Dual roles are observed for the fluid velocity in the stability criteria. It is found that the field frequency plays against the constant part for the magnetic field.     

Flow of Multicomponent Electrolyte Solutions through Narrow Pores of Nanofiltration Membranes

The slow flow of a multicomponent electrolyte solution in a narrow pore of a nanofiltration membrane is considered. The well-known semiempirical method of subdivision of electrical potential into quasi-equilibrium and streaming parts and the definition of streaming concentrations and pressure are discussed. The usefulness of this tool for solving the electrohydrodynamic equations is shown and justified: the use of a small parameter enables a system of electrohydrodynamic partial differential equations to be reduced to a system of ordinary differential equations for streaming functions. Boundary conditions for streaming functions at both the capillary inlet and outlet are derived. The proposed model is developed for the flow of a multicomponent electrolyte solution with an arbitrary number of ions. This is coupled with (i) the introduction of specific interactions between all ions and the pore wall and (ii) the inclusion of the dissociation of water in both conservation and transport equations. Effective distribution coefficients of ions are introduced that are functions of both the specific interaction potentials and the surface potential of the nanofiltration membrane material. The axial dependency of surface potential is expressed by the use of a charge regulation model from which the discontinuity in electric potential and ion pore concentrations at the pore inlet and outlet can be described.A relation between the frequently used capillary and homogeneous models of nanofiltration membranes is developed. An example of application of the homogeneous model for interpretation of experimental data on nanofiltration separation of electrolyte solutions is presented, which shows a reasonable predictive ability for the homogeneous model.     

Investigation of Calcium Carbonate Scaling Inhibition and Scale Morphology by AFM

The calcium carbonate scale inhibition by two inhibitors, polyacrylic acid (PAA) and 2-phosphonobutane-1,2,4-tricarboxylic acid (PBTCA), has been studied in two heat transfer systems: recirculating cooling water and pool boiling systems. It is found that PBTCA has a better inhibition effect than PAA under identical conditions. The inhibition effect increases with increasing fluid velocity for the cooling water system, whereas in the presence of inhibitors, the fluid velocity has less effect on the scaling behavior. When the initial surface temperature increases, the inhibition efficiency decreases. In the presence of inhibitors, the scaling behavior is insensitive to the change of surface temperature. The relationship between the inhibition effect and the fractal dimension has also been investigated. The results show that the fractal dimension is higher in the presence of inhibitors. The better the inhibition effect, the higher the fractal dimension. XRD and FTIR analyses demonstrate that for the CaCO₃ formed in the pool boiling system, the content of vaterite increases with the increase of inhibition effects. The metastable crystal forms of vaterite and aragonite are stabilized kinetically in the presence of inhibitors. The step morphology has been observed by atomic force microscopy. It is shown that the step space on the CaCO₃ surface increases in the presence of inhibitors. Moreover, with the increase in inhibition effect, both the step space and the fractal dimension increase. Step bunching is also found and discussed in this paper.     

Effect of Insoluble Surfactants on Drainage and Rupture of a Film between Drops Interacting under a Constant Force

The deformation, drainage, and rupture of an axisymmetrical film between colliding drops in the presence of insoluble surfactants under the influence of van der Waals forces is studied numerically at small capillary and Reynolds numbers and small surfactant concentrations. Constant-force collisions of Newtonian drops in another Newtonian fluid are considered. The mathematical model is based on the lubrication equations in the gap between drops and the creeping flow approximation of Navier–Stokes equations in the drops, coupled with velocity and stress boundary conditions at the interfaces. A nonuniform surfactant concentration on the interfaces, governed by a convection–diffusion equation, leads to a gradient of the interfacial tension which in turn leads to additional tangential stress on the interfaces (Marangoni effects). The mathematical problem is solved by a finite-difference method on a nonuniform mesh at the interfaces and a boundary-integral method in the drops. The whole range of the dispersed to continuous-phase viscosity ratios is investigated for a range of values of the dimensionless surfactant concentration, Peclét number, and dimensionless Hamaker constant (covering both “nose” and “rim” rupture). In the limit of the large Peclét number and the small dimensionless Hamaker constant (characteristic of drops in the millimeter size range) a fair approximation to the results is provided by a simple expression for the critical surfactant concentration, drainage being virtually uninfluenced by the surfactant for concentrations below the critical surfactant concentration and corresponding to that for immobile interfaces for concentrations above it.     

Multilayer Charged Structures in Nonpolar Dielectric Liquids

Theory of the multilayer charged structures adjacent to an electrode surface in nonpolar dielectric liquids with low conductivity under the action of an electric field is developed. Structures of this kind have been revealed by the probe measurements of the field strength in the vicinity of the flat electrode in hydrocarbon liquids.     

Nonlinear EHD Stability of the Interfacial Waves of Two Superposed Dielectric Fluids

The slow modulation of the interfacial capillary–gravity waves of two superposed dielectric fluids with uniform depths and solid horizontal boundaries, under the influence of a normal electric field and in the absence of surface charges at their interface, is investigated by using the multiple-time scales method. It is found that the complex amplitude of quasi-monochromatic traveling waves can be described by a nonlinear Schrödinger equation in a frame of reference moving with the group velocity. The stability characteristics of a uniform wave train are examined analytically and numerically on the basis of the nonlinear Schrödinger equation, and some limiting cases are recovered. Three cases appear, depending on whether the depth of the lower fluid is equal to, greater than, or less than the depth of the upper fluid. The effect of the normal electric field is determined for the three stability regions of the pure hydrodynamic case. It is found that the normal electric field has a destabilizing influence in the first stability region and a stabilizing effect in the second and third stability regions. Moreover, one new unstable region or two new stable and unstable regions appear, all of which increase when the electric field increases. On the other hand, the complex amplitude of quasi-monochromatic standing waves near the cutoff wavenumber is governed by a similar type of nonlinear Schrödinger equation in which the roles of time and space are interchanged. This equation makes it possible to estimate the nonlinear effect on the cutoff wavenumber.     

Removal of proteinaceous soils using hydroxyl radicals generated by the electrolysis of hydrogen peroxide

We have developed here for the first time a novel method to generate hydroxyl radicals, *OH, by applying slightly negative electric potentials (-0.2--0.8 V vs Ag/AgCl) to the surface of a metal (or metal oxide) that is in contact with hydrogen peroxide solution containing a supporting electrolyte. Namely, *OH radicals were generated at the surface by the electrolysis of hydrogen peroxide according to the equation, H2O2+e- --> *OH+OH-. This method was used to clean a stainless steel fouled with a model protein, beta-lactoglobulin. The *OHs generated at the surface were effective in removing beta-lactoglobulin that had been irreversibly adsorbed, by several minutes of treatment at room temperature (22+/-2 degrees C). The removal rates measured for various concentrations of H2O2 and supporting electrolyte and different potentials were determined exclusively by the electric current.     

Effect of structural stress on the intercalation rate of kaolinite

Particle size in kaolinite intercalation showed an inverse reactivity trend compared with most chemical reactions: finer particles had lower reactivity and some of the fine particles cannot be intercalated. Although this phenomenon was noted in the early 1960s and several hypotheses have been reported, there is no widely accepted theory about the unusual particle size response in the intercalation. We propose that structural stress is a controlling factor in the intercalation and the stress contributes to the higher reactivity of the coarser particles. In this study, we checked the structural deformation spectroscopically and indirectly proved the structural stress hypothesis. A Georgia kaolinite was separated into nine size fractions and their intercalations by hydrazine monohydrate and potassium acetate were investigated with X-ray diffraction (XRD) and Fourier-transform infrared (FTIR) analyses. The apical Si-O band of kaolinite at 1115 cm(-1) shifted to 1124 cm(-1) when the mineral was intercalated to 1.03 nm by hydrazine monohydrate, and its strong pleochroic properties became much weaker. Similar reduction in pleochroism was observed on the surface OH bands of kaolinite after intercalation. Both the bending vibrations of the inner OH group at 914 cm(-1) and of the surface OH group at 937 cm(-1) shifted to 903 cm(-1) after intercalation by hydrazine. A new band for the inner OH group appeared at 3611 cm(-1) during the deintercalation of the 1.03 nm hydrazine kaolinite complex. Pleochroism change in the apical Si-O band suggested the tetrahedra had increased tilt with respect to the (001) plane. The tilt of the Si-O apical bond could occur only if the octahedra had also undergone structural rearrangement during intercalation. These changes in the octahedral and tetrahedral sheets represent some change in the manner of compensation for the structural misfit of the tetrahedral sheet and octahedral sheet. As the lateral dimensions of a kaolinite particle increases, the cumulative degree of misfit increases. Intercalation breaks the hydrogen bonds between layers and allows for the structure to reduce the accumulated stress in some other manner. The reversed size effect on intercalation probably was not caused by crystallinity differences as reported in the literature, because the Hinckley and Lietard crystallinity indices of the four clay fractions were very close to each other. Impurities, such as dickite- or nacrite-like phases are not significant in the studied sample as suggested by the XRD and IR results, they are not the main reasons for the lower reactivity of the finer particles.     

Electrooptics of β-FeOOH Particles in Aqueous Media: 1. Reversing-Pulse Electric Birefringence in the Low Field Region

Reversing-pulse electric birefringence (RPEB) of a nearly monodisperse iron(III) hydroxide oxide sample in the β-form (β-FeOOH) was measured at 25°C and at a wavelength of 633 nm in aqueous media in the presence of NaCl. The concentrations of β-FeOOH and added NaCl varied between 0.00111 and 0.0555 g/L and 0.03 and 2.0 mM, respectively. Except for the suspensions with high salt concentrations, each RPEB signal showed a dip or minimum in the reverse process upon electric field reversal, together with a smooth rise in the buildup and a fall in the decay process. The observed signals were analyzed with a new RPEB theory, which takes into account not only the permanent electric dipole moment (μ) but also the root-mean-square ionic dipole moment (m^21/2) due to the ion fluctuation in ion atmosphere, in addition to the field-induced electronic (covalent) dipole moment Δα′ E. The results showed that the slowly fluctuating moment of m^21/2 is by far the most predominant one for the field orientation of the β-FeOOH particle, though the permanent dipole moment μ may not be completely excluded. The rotational relaxation time of the whole particle was evaluated from the decay signal, while the relaxation time for fluctuating ions was estimated from RPEB signal fitting. The sign of the steady-state birefringence for β-FeOOH suspensions was positive without exception under the present conditions. The birefringence signals in the steady state (δ/d) were proportional to the second power of the applied field strength (E) in the low field region; thus, the Kerr law was verified to hold for β-FeOOH suspensions. The specific Kerr constant was evaluated for each suspension by extrapolating the values of δ/d to zero field (E→0).     

Numerical simulations of capillary-driven flows in nonuniform cross-sectional capillaries

In this study the wetting behavior of converging-diverging and diverging-converging capillaries is investigated numerically using an in-house written, finite-element code. An interface tracking procedure based on the predicted change in the total liquid volume, to update the interface location, and Cox's formulation, to determine the dynamic contact angle and the interface shape, is proposed and used. Flow simulations revealed that both converging-diverging and diverging-converging capillaries exhibit significantly slower wetting behavior than straight capillaries and that any deviation in the capillary diameter necessarily tends to slow the overall wetting speed. This behavior was attributed to local regions of very low capillary pressure and high viscous retardation force when the capillary diameter at the interface was significantly larger than the capillary diameter over the upstream fluid. Though the local wetting velocities were different, when equivalent capillaries were compared it was found that both converging-diverging and diverging-converging capillaries had the same total fill time independent of the number of irregular regions, suggesting that the simple model is sufficient for predicting the overall effect. The influence of surface tension and contact angle on the total wetting time was found to be similar for both straight and irregularly shaped capillaries.     

Adsorption Isotherms of Cetylpyridinium Chloride with Iron III Salts at Air/Water and Silica/Water Interfaces

The interaction of iron III salts and cetylpyridinium chloride (CPC) has been studied at the air/water and silica/water interfaces. The surface tension of cetylpyridinium chloride has been determined in aqueous solutions in the presence of iron III chloride and iron III nitrate at two constant pH values, namely, 3.5 and 1.2. It is shown that the surface tension of the cationic surfactant depends upon the ionic strength of the solution through the pH adjustment in the presence of the former salt but not in the presence of the latter. The effect of iron III nitrate on the surface tension of CPC is similar to that of potassium nitrate, indicating that the iron III various-hydrolyzed species do not interfere with the composition of the air/water interface. The competitive adsorption of iron III nitrate salt and the cationic surfactant at a silica/water interface was next investigated. The adsorption isotherms were determined at pH 3.5. It is shown that although the iron III ions, which were added to the silica dispersion in the presence of the cetylpyridinium ions, were strongly bound to the anionic surface sites, the surfactant ions are not salted out in the solution but remain in close vicinity of the silica surface. Conversely as the cationic surfactant is added first to the silica dispersion in the presence of the adsorbed iron III ions, the metal ions and the surfactant ions are both coadsorbed onto the silica surface. It is suggested that iron III hydrolyzed or free cations and the cationic surfactant molecules may not compete for the same adsorption sites onto the silica surface.     

Analysis of the Silica Surface Free Energy by the Imbibition Technique

The surface free energy of silica and its components have been evaluated from imbibition experiments performed with liquids of differing surface properties by the distance–time method. Data were analyzed by a parabolic fit to Washburn's equation, because of the uncertainty in the exact position and time at which penetration begins in these kinds of experiments. In addition to the mathematical treatment of the experimental results, the influence of the components and parameters of the surface tension of the liquids used on the values of the solid surface free-energy components has been analyzed.     

A Novel Method for Surface Free-Energy Determination of Powdered Solids

Interfacial solid/liquid interactions play a crucial role in wetting, spreading, and adhesion processes. In the case of a flat solid surface, contact angle measurements are commonly utilized for the determination of the solid surface free energy and its components. However, if such a surface cannot be obtained, then the contact angle can not be measured directly. Usually methods based on imbibition of probe liquids into a thin porous layer or column are applied. In this paper a novel method, also based on the capillary rise, is proposed for the solid surface free-energy components determination. Actually, it is a modification of the thin column wicking method; similar theoretical background can be applied together with that appropriate for the capillary rise method of liquid surface tension determination. The proposed theoretical approach and procedure are verified by using single glass capillaries, and then alumina and ground glass powders were used for the method testing. Thus obtained surface free-energy components for these solids, for both glass and alumina, agree well with the literature values.     

Wetting Study of Hydrophobic Membranes via Liquid Entry Pressure Measurements with Aqueous Alcohol Solutions

A new concept of liquid entry pressure measurements is applied to study the hydrophobicity of microporous membranes for aqueous alcohol solutions. The effects of alcohol concentration, type of alcohol, and temperature on liquid entry pressure of the membrane have been studied. Two theoretical equations for the determination of membrane pore size have been proposed. The former equation was developed taking into account the deviation from the Laplace–Young equation due to the membrane structure by means of the structure angle. The latter equation was established considering only the range of alcohol concentration in which the dispersion component of liquid surface tension remains practically constant. Hydrophobicity has been expressed in terms of wetting surface tension, γ_L^w. Based on these measurements, the maximum concentration before the spontaneous wetting occurs would be predicted.     

A Phenomenon of the Change in Particle Drift Velocity Direction in High-Field Electrophoresis

The sign–alternating electric field in rectangular impulses has been used to eliminate linear electrophoresis and to study nonlinear electrophoresis in water at strong fields. We found out that the particle drift velocity could change its direction with the growth of the strength of the field. This new phenomenon has obtained its explanation in the framework of the Debye–Hückel theory of strong electrolyte where we consider a particle as a “heavy” effective ion and take into account all relevant nonlinear effects, grounding ourselves on basic physics. With the help of our theory we have succeeded in good fitting of our experimental data on black oil and Al₂O₃ particles in distilled water using reasonable values for the basic parameters such as the Debye screening length.     

Dynamic electrophoretic mobility of a concentrated dispersion of particles with a charge-regulated surface at arbitrary potential

The dynamic electrophoretic mobility of a concentrated dispersion of biocolloids such as cells and microorganisms is modeled theoretically. Here, a biological particle is simulated by a particle, the surface of which contains dissociable functional groups. The results derived provide basic theory for the quantification of the surface properties of a biocolloid through an electroacoustic device, which has the merit of making direct measurement on a concentrated dispersion without dilution. Two key parameters are defined to characterize the phenomenon under consideration: the first, A, is associated with the pH of the dispersion, and the second, B, is associated with the equilibrium constant of the dissociation reaction of the functional group. We show that if A is large and/or B is small, the surface potential is high, and the effect of double-layer polarization becomes significant. In this case the dynamic electrophoretic mobility may have a local maximum and a phase lead as the frequency of the applied electric field varies. Due to the hydrodynamic interaction between neighboring particles, the dynamic electrophoretic mobility decreases with the concentration of dispersion.