A finite element formulation of frequency-dependent electro-osmosis

In this paper, we model frequency-dependent electro-osmosis in a capillary using the fully nonlinear Navier-Stokes equation (NSE) for viscous, incompressible, and homogeneous flow. We simulate the NSE using the finite element method, computing the solution for a closed capillary and compare it to the closed form solutions. It is confirmed that the second velocity zero crossing is dependent of the capillary radius. The distance of the zero velocity crossing decreases with decreasing capillary radius. It is also shown that the AC electro-osmosis causes a circulation of fluid within the capillary with low frequencies generating the greatest net flow.     

Effect of capillary element aspect ratio on the dynamic imbibition within porous networks

The Washburn equation is widely accepted for describing capillary imbibition. It has, however, been shown to be insufficient at very short times due partly to the lack of inertial terms. Bosanquet (C. H. Bosanquet, Philos. Mag. ser. 645, 525 (1923)) applied an inertial term via momentum, Szekely et al. (J. Szekely, A. W. Neumann, and Y. K. Chang, J. Colloid Interface Sci.35, 273 (1971)) examined single capillaries based on a revised boundary-condition model, and Sorbie et al. (K. S. Sorbie, Y. Z. Wu, and S. R. McDougall, J. Colloid Interface Sci. 289 (1995)) reviewed and applied Szekely's work to examine the effects of comparative imbibition into a parallel pore doublet. The study here extends the work of Sorbie et al. by applying the equation of Bosanquet to a three-dimensional network model, Pore-Cor. All authors agree that, with the inclusion of inertial terms at short times, smaller radius capillaries will initially fill faster than larger radius capillaries which disagrees with the Washburn equation. It is shown that the aspect ratio of a capillary, defined as its length divided by its radius, plays an important role, in combination with the capillary radii themselves, in determining the filling rate of individual elements. The distribution of this ratio associated with the capillary throat elements within a network structure is investigated. The result is that a preferred pathway of permeation is observed under supersource imbibition conditions in the case where a broad size distribution of capillary elements occurs within a network structure.     

Laser excitation of high-frequency capillary waves

The laser-induced surface deformation (LISD) technique was applied to generate high-frequency capillary waves on liquid surfaces up to several tens of kHz in a noncontact manner. The dynamic response of the fluid near the surface was theoretically derived under the condition of periodical radiation pressure. The result of the numerical calculation predicts the propagation of induced capillary waves out from the excitation region. The efficiency of the wave generation was experimentally examined by changing the width of the excitation laser beam at the surface. The observed LISD spectra were well reproduced by the theory, showing that the effective frequency band can be extended up to over 100 kHz. The propagation of the optically generated wave was measured with a laser probe sweeping the position of the observation. The spatial profile gives the surface tension and the shear viscosity of the sample liquid. The frequency domain measurement was also carried out and the spectrum obtained at a fixed point agrees with the theory, demonstrating the rapid measurement of frequency-dependent phenomena.     

Oscillating laminar electrokinetic flow in infinitely extended rectangular microchannels

This paper has addressed analytically the problem of laminar flow in microchannels with rectangular cross-section subjected to a time-dependent sinusoidal pressure gradient and a sinusoidal electric field. The analytical solution has been determined based on the Debye-Hückel approximation of a low surface potential at the channel wall. We have demonstrated that Onsager's principle of reciprocity is valid for this problem. Parametric studies of streaming potential have shown the dependence of the electroviscous effect not only on the Debye length, but also on the oscillation frequency and the microchannel width. Parametric studies of electroosmosis demonstrate that the flow rate decreases due to an increase in frequency. The obtained solutions for both the streaming potential and electroosmotic flows become those for flow between two parallel plates in the limit of a large aspect ratio.     

Frequency-Dependent Streaming Potentials

An experimental apparatus and data acquisition system was constructed to measure the streaming potential coupling coefficients as a function of frequency. The purpose of the experiments was to measure, for the first time, the real and imaginary portion of streaming potentials. In addition, the measured frequency range was extended beyond any previous measurements. Frequency-dependent streaming potential experiments were conducted on one glass capillary and two porous glass filters. The sample pore diameters ranged from 1 mm to 34 μm. Two frequency-dependent models (Packard and Pride) were compared to the data. Both Pride's and Packard's models have a good fit to the experimental data in the low- and intermediate-frequency regime. In the high-frequency regime, the data fit the theory after being corrected for capacitance effects of the experimental setup. Pride's generalized model appears to have the ability to more accurately estimate pore sizes in the porous medium samples. Packard's model has one unknown model parameter while Pride's model has four unknown model parameters, two of which can be independently determined experimentally. Pride's additional parameters may allow for a determination of permeability. Copyright 2001 Academic Press.     

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.     

Oscillating laminar electrokinetic flow in infinitely extended circular microchannels

This article addresses the problem of oscillating laminar electrokinetic liquid flow in an infinitely extended circular microchannel. Based on the Debye-Huckel approximation for low surface potential at the channel wall, a complex variable approach is used to obtain an analytical solution for the flow. The complex counterparts of the flow rate and the current are linearly dependent on the pressure gradient and the external electric field. This property is used to show that Onsager's principle of reciprocity continues to be valid (involving the complex quantities) for the stated problem. During oscillating pressure-driven flow, the electroviscous effect for a given value of the normalized reciprocal electrical double-layer (EDL) thickness is observed to attain a maximum at a certain normalized frequency. In general, an increasing normalized frequency results in a reduction of EDL effects, leading to (i). a volumetric flow rate in the case of streaming potential approaching that predicted by the theory without EDL effects, and (ii). a reduction in the volumetric flow rate in the case of electroosmosis.     

ac electroosmosis in rectangular microchannels

Motivated by the growing interest in ac electroosmosis as a reliable no moving parts strategy to control fluid motion in microfluidic devices for biomedical applications, such as lab-on-a-chip, we study transient and steady-state electrokinetic phenomena (electroosmosis and streaming currents) in infinitely extended rectangular charged microchannels. With the aid of Fourier series and Laplace transforms we provide a general formal solution of the problem, which is used to study the time-dependent response to sudden ac applied voltage differences in case of finite electric double layer. The Debye-Huckel approximation has been adopted to allow for an algebraic solution of the Poisson-Boltzmann problem in Fourier space. We obtain the expressions of flow velocity profiles, flow rates, streaming currents, as well as expressions of the complex hydraulic and electrokinetic conductances. We analyze in detail the dependence of the electrokinetic conductance on the extension of linear dimensions relative to the Debye length, with an eye on finite electric double layer effects.     

Characterization of capillary inner surface conditions with streaming potential

Streaming potential is created when an electrolyte solution is forced to flow pass a charged surface. For an uncoated fused silica capillary, the streaming potential is measured between the inlet and outlet vials while applying a pressure across the capillary. The changes in streaming potential can be used to characterize the properties of the capillary inner surface. In this work, HCl, NaCl, and NaOH solutions ranging from 0.4 to 6 mM were used as the background electrolyte (BGE) at temperatures of 15 to 35 °C for the mesurements. The streaming potential decreases with the increase in BGE concentration, and the trend is amplified at higher temperatures. When buffer solutions in the pH range of 1.5 to 12.7 were used as the BGE, streaming potential was shown to be sensitive to changes in pH but reaches a maximum at around 9.5. At pH < 3.3, no streaming potentials were observed. The pH of zero surface charge (streaming potential equals 0) changes with temperature, and is measured to be 3.3 to 3.1 when the temperature is changed from 15 to 35°C. Zeta potentials can be calculated from the measured streaming potential, conductivity, and the solution viscosity. Surface charge densities were calculated in this work using the zeta potentials obtained. We demonstrated that capillary surface conditions can significantly change the streaming potential, and with three different solutions, we showed that analyte-dependent adsorption can be monitored and mitigated to improve the peak symmetry and migration times reproducibility.     

Electrochemistry of capillary systems with narrow pores. I. Overview

In capillary systems with narrow pores the Helmholtz electrochemical double layer located at the pore wall extends over the entire cross section of the pores. It loses its character as the “charge on the wall”. It will be shown that not only the electrokinetic phenomena but also the electrical conductivity and the dialysis potential of membranes with narrow pores can be understood from the same point of view, namely: the electrolyte solution in the pores of a membrane with narrow pores is considered to be an approximately homogeneous solution in contact with immobilised charges located at the pore wall. In this case the electrochemical equations contain the fixed ion concentration as a parameter instead of the ζ potential. This makes it possible to describe quantitatively to a good approximation data on the electroosmosis, the electrical conductivity, the streaming potential and the dialysis potential taken from the literature, as well as results of our own measurements, by using a single membrane constant.     

Electrochemistry of capillary systems with narrow pores. I. Overview

In capillary systems with narrow pores the Helmholtz electrochemical double layer located at the pore wall extends over the entire cross section of the pores. It loses its character as the “charge on the wall”. It will be shown that not only the electrokinetic phenomena but also the electrical conductivity and the dialysis potential of membranes with narrow pores can be understood from the same point of view, namely: the electrolyte solution in the pores of a membrane with narrow pores is considered to be an approximately homogeneous solution in contact with immobilised charges located at the pore wall. In this case the electrochemical equations contain the fixed ion concentration as a parameter instead of the ζ potential. This makes it possible to describe quantitatively to a good approximation data on the electroosmosis, the electrical conductivity, the streaming potential and the dialysis potential taken from the literature, as well as results of our own measurements, by using a single membrane constant.     

Streaming potential generated by a long viscous drop in a capillary

The streaming potential generated by motion of a long drop of viscosity mu(d) = lambdamu in a uniform circular capillary filled with fluid of viscosity mu is investigated by means of a model previously used to study electrophoresis of a charged mercury drop in water. The capillary wall is at potential zeta c relative to the bulk fluid within it, and the surface of the drop is at potential zeta(d). Potentials are assumed to be sufficiently small so that the charge cloud is described by the linearized Poisson-Boltzmann equation, and the Debye length characterizing the thickness of the charge cloud is assumed to be thin compared with the gap h(0) between the drop and the capillary wall. Ions in the external fluid are not allowed to discharge at the surface of the drop, and the wall of the capillary has a nonzero surface conductivity sigma c. The drop is assumed to be sufficiently long so that end effects can be neglected. Recirculation of fluid within the drop gives rise to an enhanced streaming current when zeta(d) is nonzero, leading to an anomalously high streaming potential. This vanishes as the drop viscosity becomes large. If V is the velocity of the drop and gamma is the coefficient of interfacial tension between the two fluids, then the capillary number is Ca = mu V/gamma, and the gap varies as h(0)planck'sCa(2/3). When Ca is small, the gap h(0) is small and electrical conduction along the narrow gap is dominated by the surface conductivity sigma(c) of the capillary wall, which is constant. The electrical current convected by flowing fluid is proportional to Ca, as is the change in streaming potential caused by the presence of the drop. If sigma(c) = 0, then the electrical conductance of the gap depends on its width h(0) and on the bulk fluid conductivity sigma and becomes small as h(0) approximately equal to Ca(2/3) --> 0. The streaming potential required to cancel the O(Ca) convection current therefore varies as Ca(1/3). If sigma(c) = 0 and the drop is rigid (lambda --> infinity), then the change in streaming potential over and above that expected due to the change in pressure gradient is proportional to the difference in potentials zeta(c)-zeta(d).     

Electrokinetic Measurements at High Electrolyte Concentrations

The method of capillary electrokinetics has for the first time been used to measure streaming current at high electrolyte concentrations. It has been shown that the streaming current is proportional to the applied pressure. At an electrolyte concentration of 1 M, the thickness of the diffuse layer is comparable with the size of a water molecule (0.3 nm); i.e., there is almost no diffuse layer. The existence of the streaming current in this case indicates that there are no hydrodynamically immobile layers near a smooth solid surface.     

Analysis of a quasi-elastic laser scattering spectrum using the maximum entropy method.

We have applied the maximum entropy method (MEM) to the analysis of quasi-elastic laser scattering (QELS) spectra and have established a technique for determining capillary wave frequencies with a higher time resolution than that of the conventional procedure. Although the QELS method has an advantage in time resolution over mechanical methods, it requires the averaging of at least 20-100 power spectra for determining capillary wave frequencies. We find that the MEM analysis markedly improves the S/N ratio of the power spectra, and that averaging the spectra is not necessary for determining the capillary wave frequency, i.e., it can be estimated from one power spectrum. The time resolution of the QELS attains the theoretical limit by using MEM analysis.     

Vergleichende Messungen des Zeta-Potentials von Faserstoffen durch Elektroosmose und Strömungsstrom/Strömungspotential

An apparatus for the determination of zetapotential is described, which allows measurement of both streaming potential and streaming current as well as electroosmosis with one and the same fiber diaphragm with various electrodes (calomel, Ag/AgCl, palladium). Measurements with glass fibers, fibers of polyacrylonitrile and of polyester, and with cellulose pulp show that identical values for the electrokinetic parameters are obtained independent of voltage applied during electroosmosis resp. pressure difference during streaming measurements. This allows the conclusion that the zetapotential in dilute electrolyte solution is here an unequivocally determinable figure.

Herrn Prof. Dr.R. C. Schulz mit den herzlichsten Glückwünschen zum 65. Geburtstag gewidmet.     

Solvent and pressure effects on quenching by oxygen of 9,10-dimethylanthracene fluorescence in liquid n-alkanes: a study on solvent cage effects

The fluorescence quenching by oxygen of 9,10-dimethylanthracene (DMEA) in liquid ethane and propane at pressures up to 60 MPa and 25 degrees C was investigated. The apparent activation volumes for the quenching rate constant, k(q),DeltaV++(q) , were 5.0 +/- 3.4 and 7.4 +/- 1.0 cm(3)/mol, whereas those for the solvent viscosity, eta,DeltaV++(eta) , were 190 +/- 22 and 42 +/- 1 cm(3)/mol in ethane and propane at 6.0 MPa, respectively. These results were discussed together with those in n-alkanes (C(4)-C(7)) and methylcyclohexane (MCH) that were previously reported, and it was found that DeltaV++(q) increases monotonically but DeltaV++(eta) decreases rapidly with increasing the number of carbon atoms in n-alkanes. The plot of ln k(q) against ln eta showed a leveling-off with decreasing eta. These observations were analyzed satisfactorily by the pressure dependence of the solvent viscosity on k(q) coupled with that of the radial distribution function, g(sigma), at contact with a hard sphere assumption. The apparent bimolecular rate constant, k(bim,0), for the quenching in the solvent cage was evaluated by extrapolating to g(sigma)eta = 0 in the plot of g(sigma)/k(q) against g(sigma)eta, and it was found that k(bim,0) decreased with increasing the radius of the solvent molecule. From the solvent size dependence of k(bim,0), the solvent cage effect was discussed phenomenologically.     

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.     

Exploring new scaling regimes for streaming potential and electroviscous effects in a nanocapillary with overlapping Electric Double Layers

In this paper, we unravel new scaling regimes for streaming potential and electroviscous effects in a nanocapillary with thick overlapping Electric Double Layers (EDLs). We observe that the streaming potential, for a given value of the capillary zeta (ζ) potential, varies with the EDL thickness and a dimensionless parameter R, quantifying the conduction current. Depending on the value of R, variation of the streaming potential with the EDL thickness demonstrates distinct scaling regimes: one can witness a Quadratic Regime where the streaming potential varies as the square of the EDL thickness, a Weak Regime where the streaming potential shows a weaker variation with the EDL thickness, and a Saturation Regime where the streaming potential ceases to vary with the EDL thickness. Effective viscosity, characterizing the electroviscous effect, obeys the variation of the streaming potential for smaller EDL thickness values; however, for larger EDL thickness the electroosmotic flow profile dictates the electroviscous effect, with insignificant contribution of the streaming potential.