A robust algorithm for the simultaneous parameter estimation of interfacial tension and contact angle from sessile drop profiles

The pendant and sessile drop profile analysis using the finite element method (PSDA-FEM) is an algorithm which allows simultaneous determination of the interfacial tension (gamma) and contact angle (theta(c)) from sessile drop profiles. The PSDA-FEM algorithm solves the nonlinear second-order spherical coordinate form of the Young-Laplace equation. Thus, the boundary conditions at the drop apex and contact position of the drop with the substrate are required to solve for the drop profile coordinates. The boundary condition at the position where the drop contacts the substrate may be specified as a fixed contact line or fixed contact angle. This paper will focus on the fixed contact angle boundary condition for sessile drops on a substrate and how this boundary condition is used in the PSDA-FEM curve-fitting algorithm. The PSDA-FEM algorithm has been tested using simulated drop shapes with and without the addition of random error to the drop profile coordinates. The random error is varied to simulate the effect of camera resolution on the estimates of gamma and theta(c) values obtained from the curve-fitting algorithm. The error in the experimental values for gamma from sessile drops of water on acrylic and Mazola corn oil on acrylic falls within the predicted range of errors obtained for gamma values from simulated sessile drop profiles with randomized errors that are comparable in magnitude to the resolution of the experimental setup.     

Determination of surface tension and contact angle from the shapes of axisymmetric fluid interfaces without use of apex coordinates

Drop shape techniques, such as axisymmetric drop shape analysis, are widely used to measure surface properties, as they are accurate and reliable. Nevertheless, they are not applicable in experimental studies dealing with fluid configurations that do not present an apex. A new methodology is presented for measuring interfacial properties of liquids, such as surface tension and contact angles, by analyzing the shape of an axisymmetric liquid-fluid interface without use of apex coordinates. The theoretical shape of the interface is generated numerically as a function of surface tension and some geometrical parameters at the starting point of the interface, e.g., contact angle and radius of the interface. Then, the numerical shape is fitted to the experimental profile, taking the interfacial properties as adjustable parameters. The best fit identifies the true values of surface tension and contact angle. Comparison between the experimental and the theoretical profiles is performed using the theoretical image fitting analysis (TIFA) strategy. The new method, TIFA-axisymmetric interfaces (TIFA-AI), is applicable to any axisymmetric experimental configuration (with or without apex). The versatility and accuracy of TIFA-AI is shown by considering various configurations: liquid bridges, sessile and pendant drops, and liquid lenses.     

Elliptic solution to the Young-Laplace differential equation

The Young-Laplace equation differential form can be solved under the elliptic representation for a fluid-fluid interface in the range 0 相似文献   

PREDICTION OF OIL SATURATION IN A FIBROUS BED COALESCER FROM PRESSURE DROP DATA

A model has been formulated for the prediction of average saturation and the saturation profile through a fibrous bed during coalescence of secondary dispersion. The approach utilizes the Blake-Kozeny equation to relate experimental pressure drop data to saturation in the bed. Reasonable agreement was obtained between predicted saturations and those measured experimentally. The predicted saturation profiles could be used to determine other coalescer design parameters.     

Dynamics of Drop Formation in an Electric Field

The effect of an electric field on the formation of a drop of an inviscid, perfectly conducting liquid from a capillary which protrudes from the top plate of a parallel-plate capacitor into a surrounding dynamically inactive, insulating gas is studied computationally. This free boundary problem which is comprised of the surface Bernoulli equation for the transient drop shape and the Laplace equation for the velocity potential inside the drop and the electrostatic potential outside the drop is solved by a method of lines incorporating the finite element method for spatial discretization. The finite element algorithm employed relies on judicious use of remeshing and element addition to a two-region adaptive mesh to accommodate large domain deformations, and allows the computations to proceed until the thickness of the neck connecting an about to form drop to the rest of the liquid in the capillary is less than 0.1% of the capillary radius. The accuracy of the computations is demonstrated by showing that in the absence of an electric field predictions made with the new algorithm are in excellent agreement with boundary integral calculations (Schulkes, R. M. S. M. J. Fluid Mech. 278, 83 (1994)) and experimental measurements on water drops (Zhang, X., and Basaran, O. A. Phys. Fluids 7(6), 1184 (1995)). In the presence of an electric field, the algorithm predicts that as the strength of the applied field increases, the mode of drop formation changes from simple dripping to jetting to so-called microdripping, in accordance with experimental observations (Cloupeau, M., and Prunet-Foch, B. J. Aerosol Sci. 25(6), 1021 (1994); Zhang, X., and Basaran, O. A. J. Fluid Mech. 326, 239 (1996)). Computational predictions of the primary drop volume and drop length at breakup are reported over a wide range of values of the ratios of electrical, gravitational, and inertial forces to surface tension force. In contrast to previously mentioned cases where both the flow rate in the tube and the electric field strength are nonzero, situations are also considered in which the flow rate is zero and the dynamics are initiated by impulsively changing the field strength from a certain value to a larger value. When the magnitude of the step change in field strength is small, the results of the new transient calculations accord well with those of an earlier stability analysis (Basaran, O. A., and Scriven, L. E. J. Colloid Interface Sci. 140(1), 10 (1990)) and thereby provide yet another testament to the accuracy of the new algorithm. Copyright 1999 Academic Press.     

Atomic oxygen recombination on quartz at high temperature: experiments and molecular dynamics simulation

A joint experimental and theoretical approach has been developed to study oxygen atom recombination on a beta-quartz surface. The experimental MESOX setup has been applied for the direct measurement of the atomic oxygen recombination coefficient gamma at T(S) = 1000 K. The time evolution of the relative atomic oxygen concentration in the cell is described by the diffusion equation because the mean free path of the atoms is less than the characteristic dimension of the reactor. The recombination coefficient gamma is then calculated from the concentration profile obtained by visible spectroscopy. We get an experimental value of gamma = 0.008, which is a factor of about 3 less than the gamma value reported for O recombination over beta-cristobalite. The experimental results are discussed and compared with the semiclassical collision dynamics calculations performed on the same catalytic system aimed at determining the basic features of the surface catalytic activity. Agreement, both qualitative and quantitative, between the experimental and the theoretical recombination coefficients has been found that supports the Eley-Rideal recombination mechanism and gives more evidence of the impact that surface crystallographic variation has on catalytic activity. Also, several interesting aspects concerning the energetics and the mechanism of the surface processes involving the oxygen atoms are pointed out and discussed.     

Injection profiles in liquid chromatography. I. A fundamental investigation

This is a fundamental experimental and theoretical investigation on how the injection profile depends on important experimental parameters. The experiments revealed that the injection profile becomes more eroded with increased (i) flow rate, (ii) viscosity of the eluent, (iii) size of the solute, (iv) injection volume and (v) inner diameter of the injection loop capillary. These observations cannot be explained by a 1D-convection-diffusion equation, since it does not account for the effect of the parabolic flow and the radial diffusion on the elution profile. Therefore, the 1D model was expanded into a 2D-convection-diffusion equation with cylindrical coordinates, a model that showed a good agreement with the experimental injection profiles dependence on the experimental parameters. For a deeper understanding of the appearance of the injection profile the 2D model is excellent, but to account for injection profiles of various injection volumes and flow rates in preparative and process-chromatography using computer-optimizations, a more pragmatic approach must be developed. The result will give guidelines about how to reduce the extra-column variance caused by the injection profile. This is important both for preparative and analytical chromatography; in particular for modern analytical systems using short and narrow columns.     

Simultaneous measurement of contact angle and surface tension using axisymmetric drop-shape analysis-no apex (ADSA-NA)

Axisymmetric drop-shape analysis-no apex (ADSA-NA) is a recent drop-shape method that allows the simultaneous measurement of contact angles and surface tensions of drop configurations without an apex (i.e., a sessile drop with a capillary protruding into the drop). Although ADSA-NA significantly enhanced the accuracy of contact angle and surface tension measurements compared to that of original ADSA using a drop with an apex, it is still not as accurate as a surface tension measurement using a pendant drop suspended from a holder. In this article, the computational and experimental aspects of ADSA-NA were scrutinized to improve the accuracy of the simultaneous measurement of surface tensions and contact angles. It was found that the results are relatively insensitive to different optimization methods and edge detectors. The precision of contact angle measurement was enhanced by improving the location of the contact points of the liquid meniscus with the solid substrate to subpixel resolution. To optimize the experimental design, the capillary was replaced with an inverted sharp-edged pedestal, or holder, to control the drop height and to ensure the axisymmetry of the drops. It was shown that the drop height is the most important experimental parameter affecting the accuracy of the surface tension measurement, and larger drop heights yield lower surface tension errors. It is suggested that a minimum nondimensional drop height (drop height divided by capillary length) of 1.7 is required to reach an error of less than 0.2 mJ/m(2) for the measured surface tension. As an example, the surface tension of water was measured to be 72.46 ± 0.04 at 24 °C by ADSA-NA, compared to 72.39 ± 0.01 mJ/m(2) obtained with pendant drop experiments.     

A method for correcting the contact angle from the θ/2 method

The θ/2 method, a widely used technique on measuring the contact angle of a sessile drop, assumes that the drop profile is part of a sphere. However, the shape profile of a sessile drop is governed by the Young–Laplace equation and is different from a sphere, especially for drops with a large bound number (e.g. large volume or small surface tension). The spherical assumption, therefore, causes errors on evaluating the contact angles. The deviation of contact angle from the θ/2 method is evaluated from a theoretical calculation in this work. A simple means is given for correcting the measurement error. The corrected angle results from the drop volume, surface tension, liquid density and the contact angle from θ/2 method. An algorithm for finding the correct contact angle without knowing the density and surface tension is also given. At the end, two examples of pendant drops are given for the illustration.     

Modeling of the adsorption kinetics of surfactants at the liquid-fluid interface of a pendant drop

This paper presents a theoretical model for simulating the adsorption kinetics of a surfactant at the liquid-fluid interface of a pendant drop. The diffusion equation is solved numerically by applying the semidiscrete Galerkin finite element method to obtain the time-dependent surfactant concentration distributions inside the pendant drop and inside the syringe needle that is used to form the pendant drop. With the obtained bulk surfactant concentration distributions, the adsorption at the interface is determined by using the conservation law of mass. It should be noted that the theoretical model developed in this study considers the actual geometry of the pendant drop, the depletion process of the surfactant inside the pendant drop, and the mass transfer of the surfactant from the syringe needle to the pendant drop. The present pendant-drop model is applied to study the adsorption kinetics of surfactant C10E8 (octaethylene glycol mono n-decyl ether) at the water-air interface of a pendant drop. The numerical results show that the Ward and Tordai equation, which was derived for adsorption from a semi-infinite surfactant solution to a planar interface, is unsuitable for interpreting the dynamic surface or interfacial tension data measured by using the pendant-drop-shape techniques, especially at low initial surfactant concentrations. The spherical-drop model, which assumes the pendant drop to be a perfectly spherical drop with the same drop volume, can be used to interpret the dynamic surface or interfacial tension data for pendant drops either with high initial surfactant concentrations or with low initial surfactant concentrations in short adsorption durations only. For pendant drops with low initial surfactant concentrations in long adsorption durations, the theoretical model developed in this study is strongly recommended.     

A new theoretical-experimental model deriving from the contactless measurement of the thickness of bulge-tested elastomeric samples

In this paper, an ultrasound measurement method was applied to bulge test on carbon black-filled SBR specimens, in order to determine their thickness at the top of the dome. This method consists in measuring first the variation in the ultrasonic velocity as a function of the deformation in the uniaxial state and subsequently obtaining the thickness value in the equibiaxial state, assuming the congruence of velocity in uniaxial and equibiaxial stress states, respectively.The comparison between experimental data and the thickness values deriving from the most reliable theoretical criteria for both metallic and rubbers-like materials was shown.A new theoretical approach taking into account the slight compressibility of elastomers to estimate the thickness at the dome apex was proposed. Such an approach provided a general equation to define the thickness of the dome in bulge-tested SBR+20%CB as a function of the Poisson ratio.     

Spreading of liquid drops over saturated porous layers

Spreading of small liquid drops over thin porous layers saturated with the same liquid is investigated from both theoretical and experimental points of view. A theory is presented that shows that spreading is governed by the same power law as in the case of spreading over a dry solid substrate. The Brinkman's equations are used to model the liquid flow inside the porous substrate. An equation of the drop spreading is deduced, which shows that both an effective lubrication and the liquid exchange between the drop and the porous substrates are equally important. The presence of these two phenomena removes the well-known singularity at the moving three-phase contact line. Matching of the drop profile in the vicinity of the three-phase contact line with the main spherical part of the drop gives the possibility to calculate the pre-exponential factor in the spreading law via permeability and effective viscosity of the liquid in the porous layer. Unfortunately, the latter dependency turns out to be very weak. Spreading of silicone oils over different microfiltration membranes is carried out. Radii of spreading on time experimental dependencies confirm the theory predictions. Experimentally found coefficients agree with theoretical estimations.     

Development of a constant surface pressure penetration langmuir balance based on axisymmetric drop shape analysis

A new constant pressure pendant-drop penetration surface balance has been developed combining a pendant-drop surface balance, a rapid-subphase-exchange technique, and a fuzzy logic control algorithm. Beside the determination of insoluble monolayer compression-expansion isotherms, it allows performance of noninvasive kinetic studies of the adsorption of surfactants added to the new subphase onto the free surface and of the adsorption/penetration/reaction of the former onto/into/with surface layers, respectively. The interfacial pressure pi is a fundamental parameter in these studies: by working at constant pi one controls the height of the energy barrier to adsorption/penetration and can select different regimes and steps of the adsorption/penetration process. In our device a solution drop is formed at the tip of a coaxial double capillary, connected to a double microinjector. Drop profiles are extracted from digital drop micrographs and fitted to the equation of capillarity, yielding pi, the drop volume V, and the interfacial area A. pi is varied changing V (and hence A) with the microinjector. Control is based on a case-adaptable modulated fuzzy-logic PID algorithm able to maintain constant pi (or A) under a wide range of experimental conditions. The drop subphase liquid can be exchanged quantitatively by the coaxial capillaries. The adsorption/penetration/reaction kinetics at constant pi are then studied monitoring A(t), i.e., determining the relative area change necessary at each instant to compensate the pressure variation due to the interaction of the surfactant in the subsurface with the surface layer. A fully Windows-integrated program manages the whole setup. Examples of experimental protein adsorption and monolayer penetration kinetics are presented.     

Optical determination of the pitch-dependent diffusion constant in a cholesteric liquid crystal

The concentration profile of a cholesteric compound diffusing into a nematic liquid crystal is observed with optical methods. We propose new experimental initial and boundary conditions which allow a more accurate mathematical solution of the differential equation involved. A numerical approach is applied to compute the concentration profiles with a concentration dependent diffusion constant. Diffusion is found to decrease with the shorter pitch length.     

Determination of indomethacin polymorphic contents by chemometric near-infrared spectroscopy and conventional powder X-ray diffractometry

A chemoinfometric method for the quantitative determination of the crystal content of indomethacin (IMC) polymorphs, based on Fourier-transform near-infrared (FT-NIR) spectroscopy, was established. A direct comparison of the data with those collected using the conventional powder X-ray diffraction method was performed. Pure alpha and gamma forms of IMC were prepared using published methods. Powder X-ray diffraction profiles and NIR spectra were recorded for six kinds of standard material with various contents of the gamma form of IMC. Principal component regression (PCR) analyses were performed on the basis of the normalized NIR spectral sets of standard samples with known contents of the gamma form of IMC. A calibration equation was determined to minimize the root mean square error of the prediction. The predicted gamma form contents were reproducible and had a relatively small standard deviation. The values of the gamma form contents predicted by the two methods were in close agreement. The results indicated that NIR spectroscopy provides an accurate quantitative analysis of crystallinity in polymorphs compared with the results obtained by conventional powder X-ray diffractometry.     

Microscopic treatment of a barrel drop on fibers and nanofibers

The microscopic approach of Berim and Ruckenstein (J. Phys. Chem. B 108 (2004) 19330, 19339) regarding the shape and stability of a liquid drop on a planar bare solid surface is extended to a liquid barrel drop on the bare surface of a solid cylinder (fiber) of arbitrary radius. Assuming the interaction potentials of the liquid molecules between themselves and with the molecules of the solid of the London-van der Waals form, the potential energy of a liquid molecule with an infinitely long fiber was calculated analytically. A differential equation for the drop profile was derived by the variational minimization of the total potential energy of the drop by taking into account the structuring of the liquid near the fiber. This equation was solved in quadrature and the shape and stability of the barrel drop were analyzed as functions of the radius of the fiber and the microscopic contact angle theta(0) which the drop profile makes with the surface of the fiber. The latter angle is dependent on the fiber radius and on the microscopic parameters of the model (strength of the intermolecular interactions, densities of the liquid and solid phases, hard core radii, etc.). Expressions for the evaluation of the microcontact angle from experimentally measurable characteristics of the drop profile (height, length, volume, location of inflection point) are obtained. All drop characteristics, such as stability, shape, are functions of theta(0) and a certain parameter a which depends on the model parameters. In particular, the range of drop stability consists of three domains in the plane theta(0)-a, separated by two critical curves a=a(c)(theta(0)) and a=a(c1)(theta(0)) [a(c)(theta(0))h(m1) cannot exist, whereas in the third domain (between those curves) the drop can have values of h(m) either smaller than h(m1) or larger than h(m2), where h(m2)>h(m1) is a second critical height. For sufficiently large fiber radii, R(f)1 >/= microm, the critical curves almost coincide and only two domains, the first and the second, remain. The smaller the radius, the larger is the difference between the critical curves and the larger is the second domain of drop stability. The shape of the drop depends on whether the point (theta(0),a) on the theta(0)-a plane is far from the critical curve or near it. In the first case the drop profile has generally a large circular part, while in the second case the shape is either almost planar or contains a long manchon that is similar to a film on the fiber.     

Using (18)O/(16)O exchange to probe an equilibrium space-charge layer at the surface of a crystalline oxide: method and application

The use of an (18)O/(16)O exchange experiment as a means for probing surface space-charge layers in oxides is examined theoretically and experimentally. On the basis of a theoretical treatment, isotope penetration profiles are calculated for (18)O/(16)O exchange across a gas-solid interface and subsequent diffusion of the labelled isotope through an equilibrium space-charge layer depleted of mobile oxygen vacancies and into a homogeneous bulk phase. Profiles calculated for a range of conditions all have a characteristic shape: a sharp drop in isotope fraction close to the surface followed by a normal bulk diffusion profile. Experimental (18)O profiles in an exchanged (001) oriented single crystal of Fe-doped SrTiO(3) were measured by time-of-flight secondary ion mass spectrometry (ToF-SIMS). By extracting the space-charge potential from such profiles, we demonstrate that this method allows the spatially resolved characterization of space-charge layers at the surfaces of crystalline oxides under thermodynamically well-defined conditions.     

Structure of star-burst dendrimers: a comparison between small angle x-ray scattering and computer simulation results

We investigated the generation dependent shape and internal structure of star-burst dendrimers under good solvent conditions using small angle x-ray scattering and molecular modeling. Measurements have been performed on poly(amidoamine) dendrimers with generations ranging from g=0 up to g=8 at low concentrations in methanol. We described the static form factor P(q) by a model taking into account the compact, globular shape as well as the loose, polymeric character of dendrimers. Monomer distributions within dendrimers are of special interest for potential applications and have been characterized by the pair correlation function gamma(r), as well as by the monomer and end-group density profile, rho(r) and rho(e)(r), respectively. Monomer density profiles and gamma(r) can be derived from P(q) by modeling and via a model independent approach using the inverse Fourier transformation algorithm first introduced by Glatter. Experimental results are compared with computer simulations performed for single dendrimers of various generations using the cooperative motion algorithm. The simulation gives direct access to gamma(r) and rho(r), allows an independent determination of P(q), and yields in addition to the scattering experiment information about the distribution of the end groups. Excellent qualitative agreement between experiment and simulation has been found.     

Optical determination of the pitch-dependent diffusion constant in a cholesteric liquid crystal

Abstract

The concentration profile of a cholesteric compound diffusing into a nematic liquid crystal is observed with optical methods. We propose new experimental initial and boundary conditions which allow a more accurate mathematical solution of the differential equation involved. A numerical approach is applied to compute the concentration profiles with a concentration dependent diffusion constant. Diffusion is found to decrease with the shorter pitch length.     

Transient molecular dynamics simulations of liquid viscosity for nonpolar and polar fluids

A transient molecular dynamics (TMD) method for obtaining fluid viscosity is extended to multisite, force-field models of both nonpolar and polar liquids. The method overlays a sinusoidal velocity profile over the peculiar particle velocities and then records the transient decay of the velocity profile. The viscosity is obtained by regression of the solution of the momentum equation with an appropriate constitutive equation and initial and boundary conditions corresponding to those used in the simulation. The transient velocity decays observed appeared to include both relaxation and retardation effects. The Jeffreys viscoelastic model was found to model accurately the transient responses obtained for multisite models for n-butane, isobutane, n-hexane, water, methanol, and 1-hexanol. TMD viscosities obtained for saturated liquids over a wide range of densities agreed well for the polar fluids, both with nonequilibrium molecular dynamics (NEMD) results using the same force-field models and with correlations based on experimental data. Viscosities obtained for the nonpolar fluids agreed well with the experimental and NEMD results at low to moderate densities, but underpredicted experimental values at higher densities where shear-thinning effects and viscous heating may impact the TMD simulations.