Models of adsorption at a line of three-phase contact

Two model density distributions at a line of three-phase contact for which the adsorptions are readily calculated are analyzed. One of them provides a numerical illustration of a recently found surprising fact about the thermodynamics of adsorption at such contact lines. A form of the line analogue of the Gibbs adsorption equation is conjectured, and it is noted that the conjecture is in principle testable by computer simulation and by experiment.     

The shape of a flexible polymer in a cylindrical pore

We calculate the mean end-to-end distance R of a self-avoiding polymer encapsulated in an infinitely long cylinder with radius D. A self-consistent perturbation theory is used to calculate R as a function of D for impenetrable hard walls and soft walls. In both cases, R obeys the predicted scaling behavior in the limit of large and small D. The crossover from the three-dimensional behavior (D --> infinity) to the fully stretched one-dimensional case (D --> 0) is nonmonotonic. The minimum value of R is found at D approximately 0.46R(F), where R(F) is the Flory radius of R at D --> infinity. The results for soft walls map onto the hard wall case with a larger cylinder radius.     

Electrophoresis of a toroid along the axis of a cylindrical pore

The electrophoresis of a toroid (doughnut-shaped entity) along the axis of a long cylindrical pore is analyzed under the conditions of low surface potential and weak applied electric field. The system under consideration is capable of modeling the electrophoretic behavior of various types of biocolloid such as bacterial DNA, plasmid DNA, and anabaenopsis, in a confined space. The influences of the key parameters of the problem, including the sizes of a toroid, the radius of a pore, and the thickness of the double layer, on the electrophoretic mobility of a toroid are discussed. We show that the electrophoretic behavior of a toroid under typical conditions can be different from that of an integrated entity. For instance, although the presence of the pore wall has the effect of retarding the movement of a particle, it becomes advantageous if a toroid is sufficiently close to the boundary. Several interesting behaviors are also observed, for example, the mobility of a toroid when the boundary effect is significant can be larger than that when it is insignificant.     

Stability considerations of the capillary condensation within a cylindrical pore

A proof of the stability of the unduloid configuration within a cylindrical pore is given. The proof involves calculus of variation techniques and in particular the theory of the problem of Bolza is used. It is shown that the unduloid configuration is stable to small disturbances provided dV/dκ < 0, where V represents the volume of the configuration and κ is the curvature of the configuration. If this condition is not satisfied the unduloid configuration is unstable.     

Geometric view of the thermodynamics of adsorption at a line of three-phase contact

We consider three fluid phases meeting at a line of common contact and study the linear excesses per unit length of the contact line (the linear adsorptions Lambda(i)) of the fluid's components. In any plane perpendicular to the contact line, the locus of choices for the otherwise arbitrary location of that line that makes one of the linear adsorptions, say Lambda(2), vanish, is a rectangular hyperbola. Two of the adsorptions Lambda(2) and Lambda(3) then both vanish when the contact line is chosen to pass through any of the intersections of the two corresponding hyperbolas Lambda(2)=0 and Lambda(3)=0. There may be two or four such real intersections. It is found most surprisingly, and confirmed in a numerical example, that Lambda(1(2,3)), the adsorption of component 1 in a frame of reference in which the adsorptions Lambda(2) and Lambda(3) are both 0, depends on which intersection of the hyperbolas Lambda(2)=0 and Lambda(3)=0 is chosen for the location of the contact line. This implies that what had long been taken to be the line analog of the Gibbs adsorption equation is incomplete; there must be additional, previously unanticipated terms in the relation, consistent with the invariance of the line tension to choice of location of the contact line. It is then not Lambda(1(2,3)) by itself but a related expression containing it that must be invariant, and this invariance is also confirmed in the numerical example. The presence of the additional terms in the adsorption equation is further confirmed and their origin clarified in a mean-field density-functional model. The supplemental terms vanish at a wetting transition, where one of the contact angles goes to 0.     

Finite-size effects in the microscopic structure of a hard-sphere fluid in a narrow cylindrical pore

We examine the microscopic structure of a hard-sphere fluid confined to a small cylindrical pore by means of Monte Carlo simulation. In order to analyze finite-size effects, the simulations are carried out in the framework of different statistical mechanics ensembles. We find that the size effects are specially relevant in the canonical ensemble where noticeable differences are found with the results in the grand canonical ensemble (GCE) and the isothermal isobaric ensemble (IIE) which, in most situations, remain very close to the infinite system results. A customary series expansion in terms of fluctuations of either the number of particles (GCE) or the inverse volume (IIE) allows us to connect with the results of the canonical ensemble.     

Electrophoresis of two identical rigid spheres in a charged cylindrical pore

The electrophoresis of two identical spheres moving along the axis of a long cylindrical pore under the conditions of low surface potential and weak applied electric field is investigated. The geometry considered allows us to examine simultaneously the effects of boundary and the presence of a nearby entity on the behavior of a particle. The influences of the separation distance between two spheres, the thickness of a double layer, the ratio (radius of sphere/radius of pore), and the charged conditions on the surfaces of the spheres and the pore on the mobility of a particle are investigated. Several interesting results that are not reported in the literature are observed. For instance, although for the case of two positively charged spheres in an uncharged pore the qualitative behavior of a sphere depends largely on its size relative to that of a pore and the thickness of the double layer, this might not be the case when two uncharged spheres are in a positively charged pore. In addition, in the latter, the mobility of a sphere increases with the increases in the separation distance between two spheres, and this effect is pronounced when the ratio (radius of sphere/radius of pore) takes a medium value or the thickness of the double layer is either sufficiently thin or sufficiently thick.     

Boundary effect on electrophoresis: finite cylinder in a cylindrical pore

The boundary effect on electrophoresis is investigated by considering a finite cylindrical particle moving along the axis of a long cylindrical pore under conditions of low surface potential and weak applied electric field. The influence of the thickness of the double layer, the aspect ratio of a particle, the ratio particle radius/pore radius, and the charged conditions of the surfaces of the particle and pore on the electrophoretic behavior of a particle are investigated. We show that the effect of the aspect ratio of a particle on its electrophoretic behavior for the case where the particle is charged and the pore is uncharged is larger than that for the case where the particle is uncharged and the pore is charged. Also, depending on the parameters chosen, increasing the aspect ratio of a particle can either promote or hinder its movement, which is not reported in previous studies, and can play a role in electrophoresis measurements. Because both the electric and the flow fields in the gap between the particle and the pore are mediated by those near the top and the end of the particle, the end effect is large when the double layer is thick.     

Truncated versus extended microfilms at a vapor-liquid contact line on a heated substrate

The microstructure of a contact line formed by a liquid and its pure vapor on a perfectly wetted superheated smooth substrate, with the disjoining pressure most often in the form of a positive inverse cubic law (nonpolar case), is routinely considered to end up in a microfilm extended over adjacent "dry" parts of the solid surface. Invoking the spreading coefficient as an additional independent parameter within this framework, we argue however that a regime with a truncated microfilm is chosen instead if the spreading coefficient is decreased below a positive (still perfect wetting) critical value dependent upon the superheat, in which case the extended-microfilm thickness is surpassed by that of the "pancake" introduced by de Gennes and co-workers. Conversely, for a given positive spreading coefficient, there is a critical superheat above which the microfilm gets truncated, whereas for a negative one (partial wetting) the truncated regime should be preferred at any superheat. A parametric study of the apparent contact angle (a nonlinear eigenvalue of the steady microstructure problem) versus the spreading coefficient is carried out. When the latter is negative, Young's law is asymptotically recovered. Microfilm fronts on a bare surface are shown to be advancing or receding in accordance with the selected regime. A slightly more general class of disjoining pressures is also touched upon. The analysis is based in part upon thermodynamic considerations and in part upon a standard one-sided model of an evaporating liquid layer in the lubrication approximation.     

Probing with a laser sheet the contact angle distribution along a contact line

An optical method for probing contact angle distribution along contact lines of any shape using a laser sheet is proposed. This method is applied to a dry patch formed inside a film flowing along an inclined plane, both liquid and solid being transparent. Falling normally to the plane, a laser sheet cuts the contact line and is moved along this line. Distortions of the sheet trace observed on a screen put below the plane allow us to extract the contact angle distribution and the local line inclination along the line. Our results show that the contact angle around a dry patch is nearly constant and equal to the static advancing angle, at least when the evolution of its shape is followed for increasing flow rates. This supports a model of dry patch shape recently proposed by Podgorski and co-workers. Preliminary results obtained for decreasing flow are also qualitatively observed.     

Monte Carlo simulations of conformations of chain molecules in a cylindrical pore

Off-lattice Monte Carlo simulations are employed to study the behavior of chain molecules confined in a long cylindrical pore under the condition of hard-body interaction. The emphasis is placed on the chain and bead distributions as well as the location dependence of the chain conformation and anisotropy. The simulation results show that the chains very near the pore surface tend to wrap around the surface in various configurations. This behavior is qualitatively similar to that of the chains near but outside a cylindrical rod. Moreover, the bead concentration near the pore surface increases with increasing surface curvature.     

Electrophoresis of a charge-regulated spheroid along the axis of an uncharged cylindrical pore

Boundary effects can have a profound influence on the electrophoretic behavior of a charged entity, in particular, when the entity is nonspherical and its surface conditions are dependent upon the nearby environment. In this study, the electrophoresis of a spheroid along the axis of an uncharged cylindrical pore is analyzed for the case where the electrical potential is low and the applied electric field is weak. We consider the case where the surface of a particle contains dissociable acidic and basic functional groups, which simulate biological colloids and entities covered by an artificial membrane. This leads to a mixed-type boundary value problem, which extends the conventional constant-surface-potential and constant-surface-charge-density models to a more general case. The effects of the particle aspect ratio, the relative magnitudes of particle and pore, the thickness of the double layer surrounding a particle, and the pH of the liquid phase on the electrophoretic mobility of a particle are investigated. Several interesting results are observed; for example, if the volume of a particle is fixed, its mobility may have a local maximum as the relative magnitudes of its two axes vary.     

Electrophoresis of a finite cylinder positioned eccentrically along the axis of a long cylindrical pore

The electrophoresis of a finite cylindrical particle positioned eccentrically along the axis of a long cylindrical pore is modeled under the conditions of low surface potential and weak applied electric field. The influences of the eccentricity of a particle and its linear size, the radius of the pore, and the thickness of the electrical double layer on the electrophoretic mobility of the particle are investigated. Some interesting results are observed. For instance, for the case of a positively charged particle placed in an uncharged pore, if the double layer is thin and the particle is short, the mobility has a local minimum as the eccentricity varies. Also, for a short particle the mobility at a thinner double layer can be smaller than that at a thicker double layer, which has never been reported for the case of constant surface potential. In general, the mobility increases with the increase in the eccentricity, and this effect is pronounced when the size of a particle is large and/or the radius of a pore is small.     

Assembly of nanoparticles at the contact line of a drying droplet under the influence of a dipped tip

The manipulation of colloidal nanoparticles (NPs) in a drying droplet has critical importance not only for several industrial applications but also their assembly into patterns on surfaces. The influence of a tip with hydrophilic or hydrophobic surfaces dipped into a drying droplet on hydrophilic or hydrophobic surfaces on the behavior of 98 nm latex NPs was investigated. The formation of concentric rings on hydrophilic glass surfaces regardless of the surface chemistry of the dipped tip was observed. On the other hand, no pattern formation on hydrophobic surfaces was observed with the insertion of the tip. With a hydrophilic tip, the concentric rings were formed due to stick-slip motion of the solvent contact line resulting from competition between pinning and capillary forces while the capillary effect was not effective until the surface of the tip was changed by adherent NPs making the tip surface available for water adherence with a hydrophobic tip, which results in the pulling of droplet towards the tip. It is also found that the tip thickness and suspension concentration significantly influences the formation of concentric rings on surfaces. This simple procedure can be used to influence the distribution or assembly of NPs in the droplet area.     

Structure and rheological behavior of highly charged colloidal particles in a cylindrical pore I. Effect of pore size

In this work we performed nonequilibrium Brownian dynamics (NEBD) computer simulations of highly charged colloidal particles in diluted suspension under a parabolic flow in cylindrical pores. The influence of charged and neutral cylindrical pores on the structure and rheology of suspensions is analyzed. A shear-induced disorder-order-disorder-like transition was monitored for low shear rates and small pore diameters. We calculate the concentration profiles, axial distribution functions, and axial-angular pair correlation functions to determine the structural properties at steady state for a constant shear flow for different pore sizes and flow strengths. Similar behavior has been observed in a planar narrow channel in the case of charged interacting colloidal particles (M.A. Valdez, O. Manero, J. Colloid Interface Sci. 190 (1997) 81). The mobility of the particles in the radial direction decreases rapidly with the flow and becomes practically frozen. The flow exhibits non-Newtonian shear thinning behavior due to interparticle interactions and particle-wall interaction; the apparent viscosity is lower as the pore diameter decreases, giving rise to an apparent slip in the colloidal suspension. The calculated slip velocity was higher than that obtained in a rectangular slit under shear flow.     

Electrophoresis of a spherical particle along the axis of a cylindrical pore filled with a Carreau fluid

The electrophoresis of a spherical particle along the axis of a cylindrical pore filled with a Carreau fluid is investigated theoretically. In addition to the boundary effect due to the presence of the pore, the influences of the thickness of double layer surrounding a particle and the properties of the fluid on the electrophoretic behavior of the particle are also examined. We show that, in general, the presence of the pore has the effect of retarding the movement of a particle. On the other hand, the shear-thinning nature of the liquid phase is advantageous to its movement. For both Newtonian and Carreau fluids, the mobility of a particle increases monotonically with the decrease in the thickness of double layer, but the mobility is more sensitive to the variation of the thickness of double layer in the latter. The mobility of a particle in a Carreau fluid is larger than that in the corresponding Newtonian fluid, and the difference between the two increases with the decrease in double-layer thickness; in addition, depending upon the values of the parameters assumed, the percentage difference can be in the order of 50%.     

Determining the contact angle between liquids and cylindrical surfaces

One of the simplest methods of measuring the quantities for estimating the adhesion properties of materials (i.e., the adhesion work, the surface energy, and the interfacial tension between certain liquids and a surface) requires the determination of the contact angle between the liquid and the surface. In the case of plane surfaces the determination of the drop dimensions makes it possible to calculate the contact angle by the sessile drop method, but in the case of cylindrical surfaces (such as the monofilaments), several methods were developed to improve the accuracy of the contact angle measurements. This paper presents a comprehensive method for precise evaluation of the contact angle between liquid drops and monofilaments by establishing a differential equation describing the drop contour. This equation makes it possible to accurately compute the contact angle using the dimensions of the drop. A comparison of the values of the contact angle calculated by our method and those obtained by other approaches is made. We applied our method in the case of polyamide-6 monofilaments treated using dielectric barrier discharge, knowing their medical applications in surgical sutures.     

Electrophoresis of a spherical particle along the axis of a cylindrical pore: effect of electroosmotic flow

The electrophoresis of a spherical particle along the axis of a cylindrical pore is investigated under conditions of low surface potential and thick double layer. In particular, the effect of electroosmotic flow is taken into account. The results of numerical simulation reveal that if both particle and pore are positively charged, the variation of the mobility of a particle may have a local minimum as the thickness of the double layer varies, which is not reported in the literature. This is mainly due to the charge induced on the particle surface, which arises from the presence of the charged boundary. Depending upon the level of the surface potential of the pore, the presence of the local minima may lead to a reversal in the direction of particle movement as the thickness of the double layer surrounding it varies: if the surface potential is either too low or too high, reversal does not occur; if it has a medium level, reversal occurs twice. This interesting observation can play a role in electrophoresis measurements. Previous analysis predicts that reversal always occurs once, regardless of the level of the surface potential of the pore.     

Electrophoresis of an ellipsoid along the axis of a cylindrical pore: effect of a charged boundary

The influence of a charged boundary on the electrophoretic behavior of a particle is investigated by considering the electrophoresis of a nonconducting ellipsoid along the axis of a cylindrical pore at the level of the linear Poisson-Boltzmann equation ignoring the polarization effect. The problem considered simulates the electrophoresis conducted in a narrow space such as capillary electrophoresis and electrophoresis through a porous medium. Here, because the effect of electroosmotic flow can be important the electrophoretic behavior is much more complicated than that for the case where a boundary is uncharged. The influences of the thickness of double layer, the aspect ratio of an ellipsoid, the relative radius of a pore, and the charge conditions on the ellipsoid and pore surfaces on the mobility of the ellipsoid are discussed. Several interesting but nonintuitive electrophoretic behaviors are observed.