Contact angle hysteresis of cylindrical drops on chemically heterogeneous striped surfaces

Contact angle hysteresis of a macroscopic droplet on a heterogeneous but flat substrate is studied using the interface displacement model. First, the apparent contact angle of a droplet on a heterogeneous surface under the condition of constant volume is considered. By assuming a cylindrical liquid-vapor surface (meniscus) and minimizing the total free energy, we derive an equation for the apparent contact angle, which is similar but different from the well-known Cassie's law. Next, using this modified Cassie's law as a guide to predict the behavior of a droplet on a heterogeneous striped surface, we examine several scenarios of contact angle hysteresis using a periodically striped surface model. By changing the volume of the droplet, we predict a sudden jump of the droplet edge, and a continuous change of the apparent contact angle at the edge of two stripes. Our results suggest that as drop volume is increased (advancing contact lines), the predominant drop configuration observed is the one whose contact angle is large; whereas, decreasing drop volume from a large value (receding contact lines) yields drop configuration that predominantly exhibit the smaller contact angle.     

Wetting of nanopatterned surfaces: the hexagonal disk surface

Metropolis Monte Carlo simulations are used to investigate the wetting of chemically nanopatterned surfaces, for the case of hexagonal disk patterns where liquid wishes to wet high-energy circular patches but not wet the background surface. We calculate the density profiles of saturated liquid adsorbed on a variety of such substrates, spanning the nanoscale to atomic scale patterns. In addition, statistical mechanical sum rules are used to obtain interfacial order parameters and interfacial free energies. We observe that Cassie's law is typically obeyed, together with an associated breakdown of the mechanical interpretation of Young's equation, for pattern wavelengths greater than 15 molecular diameters. Here, the adsorbed fluid exists as an array of hemi-drops. At about half this wavelength, the breakdown of Cassie's law lies within realistic energy scales and is associated with the unbending of the outer surface of adsorbed films. For atomic scale patterns, the usual interpretation of Young's equation is restored for films thicker than one monolayer. At high chemical contrast, when the monolayer in contact with high-energy regions would prefer to be crystalline, we observe a variety of exotic interfacial phenomena that may have technological significance.     

Dynamics of imbibition into a pore with a heterogeneous surface

We use large-scale molecular dynamics simulations to study the dynamics of liquid penetration into a cylindrical pore having a randomly heterogeneous surface comprising areas of differing wettability. Our results confirm that the equilibrium contact angle in the heterogeneous pore is well described by Cassie's law. As in the case of the uniform pore studied previously, the dynamics of penetration can be described by the Lucas-Washburn equation corrected to include the effect of a dynamic contact angle. The dissipation at the three-phase line, which gives rise to the dynamic contact angle, may be characterized in terms of a friction coefficient. Interestingly, the wetting-line friction on the heterogeneous surface also turns out to be a linear function of the fractional concentration of the areas of different wettability, analogous to Cassie's law. These results can be interpreted in terms of an independent random walk mechanism.     

A modified Poisson-Boltzmann model including charge regulation for the adsorption of ionizable polyelectrolytes to charged interfaces, applied to lysozyme adsorption on silica

The equilibrium adsorption of polyelectrolytes with multiple types of ionizable groups is described using a modified Poisson-Boltzmann equation including charge regulation of both the polymer and the interface. A one-dimensional mean-field model is used in which the electrostatic potential is assumed constant in the lateral direction parallel to the surface. The electrostatic potential and ionization degrees of the different ionizable groups are calculated as function of the distance from the surface after which the electric and chemical contributions to the free energy are obtained. The various interactions between small ions, surface and polyelectrolyte are self-consistently considered in the model, such as the increase in charge of polyelectrolyte and surface upon adsorption as well as the displacement of small ions and the decrease of permittivity. These interactions may lead to complex dependencies of the adsorbed amount of polyelectrolyte on pH, ionic strength, and properties of the polymer (volume, permittivity, number, and type of ionizable groups) and of the surface (number of ionizable groups, pK, Stern capacity). For the adsorption of lysozyme on silica, the model qualitatively describes the gradual increase of adsorbed amount with pH up to a maximum value at pHc, which is below the iso-electric point, as well as the sharp decrease of adsorbed amount beyond pHc. With increasing ionic strength the adsorbed amount decreases (for pH > pHc), and pHc shifts to lower values.     

Viscoelastic Effects on the Dynamics of Spinodal Decomposition in Binary Polymer Mixtures

Numerical simulations based on the modified time‐dependent Ginzburg‐Landau (TDGL) equation have been performed on the domain growth dynamics of binary polymer mixtures. An elastic relaxation term was introduced into the equation to take the entanglement effects of the polymer chains into account. A cell dynamical scheme (CDS) is employed in this paper to improve the computing efficiency. The dynamics of the phase separation in polymer blends was investigated through to a very late stage. In the system without viscoelastic effects, there exists an apparent early stage, and in the late stage the modified Lifshitz‐Slyozov law and dynamical scaling law are satisfied very well. In the system with viscoelastic effects, there are some unique characteristics. A morphology with a rough interface between the domains is obtained and suppression of order‐parameter fluctuations is observed. The growth behavior of domains was altered, and there exits an intermediate stage between the early and late stage, in which the growth rate of domains slows down drastically. The intermediate stage was prolonged with enhanced entanglement effects. Entanglement effects also enhance the quench‐depth effects on the correlation and diminish the discrimination of correlation induced by criticality. After the relaxation of entanglements, the growth exponents with the model employed in this paper are independent of entanglements and are essentially consistent with the modified Lifshitz‐Slyozov law. In addition, the pair correlation function and the structure function are shown to exhibit the dynamical scaling law at the late stage.     

Experimental and theoretical study of the displacement process between two electrolyte solutions in a microchannel

Displacement of one electrolyte solution by another in a microchannel is required in many biolab chip devices. The objective of this paper is to develop a better understanding of the displacement process between two electrolyte solutions under an applied electric field in a cylindrical microchannel in terms of the traveling distance of the interface between these two electrolyte solutions. In order to develop a general model to predict the location of the interface, two different situations are considered; one model assumes the presence of a sharp interface between the two solutions and the other model considers a mixing zone between the two solutions. Carefully conducted experiments were carried out to obtain the current-time relationship, which is used in the model to predict the location of the interface. In these experiments, deionized ultrafiltered water (DIUF water), 10 mM KCl, 0.1 mM KCl, and 0.1 mM LaCl3 solutions were used as the testing liquids. Polyamide-coated silica capillary tubes of internal diameter 100 mum and length 10 cm were employed in this study. The relationship between traveled distance of the interface and time was predicted by a developed model based on the measured current-time relationship for such a displacement process under a constant applied electric field. The characteristics of the nonlinear change of the traveling distance with the time were also discussed in this paper.     

Adsorption of cetyltrimethylammonium bromide and propanol mixtures with regard to wettability of polytetrafluoroethylene. I. Adsorption at aqueous solution-air interface

Measurements of surface tension of aqueous solutions of cetyltrimethylammonium bromide (CTAB) and propanol mixtures (gamma(L)) for 1 x1 0(-5), 1 x 10(-4), 6 x 10(-4), and 1 x 10(-3) M concentrations of CTAB as a function of propanol concentration in the range from 0 to 6.67 M at 293 K were carried out. The obtained results indicate that there is first-order exponential relationship between the surface tension and propanol concentration in the solution at constant CTAB concentration. These results were compared with those calculated from the equations derived by von Szyszkowski, Joos, Miller et al. From the comparison it resulted that the values of gamma(L) determined by the Szyszkowski equation are correlated with those measured only in a limited propanol concentration range because of changes of the constant related to the specific capillary activity in this equation as a function of propanol concentration, particularly in the range of its high concentration. In the case of the modified Joos equation there is a correlation between the calculated and measured values of gamma(L) only at a very low concentration of propanol. The values of the surface tension of aqueous solutions of CTAB and propanol mixtures determined by the relationships of Miller et al. at CTAB concentration, corresponding to unsaturated surface layer in the absence of propanol, are close to those measured, but there are bigger differences between the calculated and measured values of the surface tension for solutions at a constant value of CTAB concentration close to CMC. However, the values of the surface tension of aqueous solution of CTAB and propanol mixtures calculated from the modified Miller et al. equation, in which the aggregation process of alcohol molecules at water-air interface was taken into account, are in excellent agreement with those measured. The measured values of the surface tension and the Gibbs equations were used for determination of the surface excess of CTAB and propanol concentration at solution-air interface. The obtained results indicate that at the constant concentration of CTAB equal to 1 x 10(-5) and 1 x 10(-4) M there is a maximum of excess concentration of propanol in the surface region at its bulk concentration close to 1 M. Using the calculated values of the surface excess concentration of propanol and CTAB at solution-air interface and assuming the proper thickness of the interface region, the total values of their concentration in this region were evaluated. Next, the standard surface free energy of CTAB and propanol mixtures adsorption was calculated. The calculated values of this energy indicate that the tendency to adsorb molecules of CTAB and propanol decreases with increasing propanol concentration probably because of entropy of adsorption decrease resulting from water structure destruction by propanol molecules.     

Load-displacement behavior for double-edge cracked plate of polytetrafluoroethylene

Polytetrafluoroethylene (PTFE) has been employed in many engineering applications, mainly due to its special properties such as high electrical resistivity, high melting temperature, chemical inertness, corrosion resistance and very low friction. Although there are many works on PTFE, very few attempts have been made to understand the fracture behavior of this material. For this reason, the load-displacement behavior of double-edge cracked specimens of PTFE was examined and modeled and is reported in this paper. Specimens were tested under monotonic tensile load in quasi-static conditions at constant temperature. Images of the region around the crack were captured with a high-resolution camera and then processed by digital image correlation to obtain the displacement fields. Using these data, values of crack tip opening displacement and crack extension were estimated. To model the behavior of PTFE, a constitutive phenomenological model based on saturation and power law expressions combined with a damage evolution equation is proposed. The predictions are in good agreement with the experimental data.     

Quasistatic detachment of a sphere from a liquid interface

In this paper the problem of removing a spherical particle initially attached to a liquid-gas interface is analytically treated. In particular, the Derjaguin equation for small radii is used to derive a closed-form approximate expression for the work of detachment of the sphere from the interface. Expressions corresponding to the prescribed displacement condition and the applied force condition, which seems to be the relevant condition for the flotation separation process, are presented. A special effort has been made to closely compare analytical results with data obtained through the exact numerical treatment of the detachment process. Results show that proposed expressions are sufficiently accurate to calculate the energy required to detach the sphere from the interface as soon as the sphere radius is small compared to the capillary length. Validity limits are specified.     

Determination of Henry’s law constant of light hydrocarbon gases at low temperatures

The solubility of i-butane in water at the low temperatures was measured (274 K to 293 K). Additionally, Henry’s law constants of light hydrocarbons (methane, ethane, propane, i-butane, and n-butane) in water at the low temperatures are reported. A modified equation based on Krichevsky–Kasarnovsky equation is proposed to consider the effect of pressure and temperature on the equation parameters. Results show that Henry’s law constant of the selected components depends on temperature. It is deduced that pressure has a considerable effect on Henry’s law constant for methane, ethane, and propane, whereas this dependency for butanes is negligible.     

Simulation of Non-Linear Flow Density in Transition State from the Mathematical Model of the Diffusion of Metal Anions Through a Flat Sheet Supported Liquid Membrane

A mathematical model is developed for the carrier facilitated transport of metal ions through a flat sheet support liquid membrane (FSSLM) in transition state from Fick's second law. From this model, and from Fick's first law, the flow density is derived as a non-linear concentration gradient. Both expressions, concentration and flow density, depend on the thickness of the membrane and on time. Since the rate constant plays an important role in the model, it is considered as the parameter that controls the system and an equation for it is obtained. This equation explains the velocity of the co-transport process. The proposed model takes into account the species co-transported together with the metal ions. An equation for the number of moles of this species is obtained as a function of the metal species. The concentration gradient of this species explains the behaviour of pH in the feed phase during the process. The model is tested against experimental data corresponding to the transport of metal anions in acidic solution and it is shown that the co-transport process is reproduced with high accuracy.     

Application of a single model to study the adsorption equilibrium of prednisolone on six carbonaceous materials

The knowledge of sorption processes of nonelectrolytes in solution by solid adsorbents implies the study of kinetics, equilibrium, and thermodynamic functions. However, quite frequently the equilibrium isotherms are studied by comparing them with those corresponding to the Giles et al. classification (1); these isotherms are also analyzed by fitting them to equations based on thermodynamic or kinetic criteria, and even to empirical equations. Nevertheless, information obtained is more coherent and satisfactory if the adsorption isotherms are fitted by using an equation describing the equilibrium isotherms according to the kinetic laws. These mentioned laws would determine each one of the unitary processes (one or more) which condition the global process. In this paper, an adsorption process of prednisolone in solution by six carbonaceous materials is explained according to a previously proposed single model, which allows to establish a kinetic law which fits satisfactorily most of C vs t isotherms (2). According to the above-mentioned kinetic law, equations describing sorption equilibrium processes have been deducted, and experimental data points have been fitted to these equations; such a fitting yields to different values of adsorption capacity and kinetic equilibrium constants for the different processes at several temperatures. However, in spite of their practical interest, these constants have no thermodynamic signification. Thus, the thermodynamic equilibrium constant (K) has been calculated by using a modified expression of the Gaines et al. equation (3). Global average values of the thermodynamic functions have also been calculated from the K values. Information related to variations of DeltaH and DeltaS with the surface coverage fraction was obtained by using the corresponding Clausius-Clapeyron equations.     

用计量置换吸附模型研究液-固色谱中的溶质保留机理

本文以表面物理化学吸附模式为基础, 推导出液-固色谱中溶质计量置换保留模型. 与其他模型进行比较的结果证明本模型为最佳. 提出用参数j作为区别反相色谱和液-固色谱的判据.     

Revision of a multiparameter equation of state to improve the representation in the critical region: application to water

We have developed a crossover formalism for the thermodynamic surface of pure fluids, which can be applied to any multiparameter equation of state. This procedure has been used to incorporate scaling law behavior into a representation of the thermodynamic properties of water and steam developed by Pruss and Wagner (PW EOS) and adopted recently by the International Association for the Properties of Water and Steam. Our revision to this equation retains most of the functional form and coefficients of the PW EOS, but replaces two of the terms with a crossover representation of scaling law behavior. In order to develop this model, we first developed a new crossover formulation for steam in the critical region, and second, we have incorporated universal crossover functions into the original PW EOS. In the modified form, the PW equation of state reproduces the scaling laws down to dimensionless temperatures τ=10⁻⁷. Far from the critical point the equations practically coincide.     

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.     

Molecular simulation of adsorption and intrusion in nanopores

This paper reports Monte Carlo simulations of the adsorption or intrusion in cylindrical silica nanopores. All the pores are opened at both ends towards an external bulk reservoir, so that they mimic real materials for which the confined fluid is always in contact with the external phase. This realistic model allows us to discuss the nature of the filling and emptying mechanisms. The adsorption corresponds to the metastable nucleation of the liquid phase, starting from a partially filled pore (a molecular thick film adsorbed at the pore surface). On the other hand, the desorption occurs through the displacement at equilibrium of a gas/liquid hemispherical interface (concave meniscus) along the pore axis. The intrusion of the non-wetting fluid proceeds through the invasion in the pore of the liquid/gas interface (convex meniscus), while the extrusion consists of the nucleation of the gas phase within the pore. In the case of adsorption, our simulation data are used to discuss the validity of the modified Kelvin equation (which is corrected for both the film adsorbed at the pore surface and the curvature effect on the gas/liquid surface tension).     

Thermodynamic analysis of the cation binding to a phosphatidylcholine monolayer at a polarised interface between two immiscible electrolyte solutions

Thermodynamic analysis of the polarised interface between two immiscible electrolyte solutions (ITIES) was outlined, which accounts for the adsorption of phosphatidylcholine (PC) both as a zwitterion and a cation formed by the aqueous cation association with the zwitterionic PC form, as well as for the aqueous cation transfer facilitated by PC leading to its depletion from the interface. Electrocapillary equation was derived clarifying the physical significance of the surface charge density; the differential capacity and the PC surface excess concentration. The potential dependence of the interfacial tension calculated using the Damaskin’s adsorption model of a compound adsorbed in two different forms was found to agree well with that measured for the polarised water|1,2-dichloroethane interface in the presence of dl-α-dipalmitoylphosphatidylcholine. Experimentally observed effect of the nature of the aqueous cation on the interfacial tension was ascribed to the difference in the PC association constant.