Contact line position

The effect of the nanoparticle volume fraction on the displacement of the contact line becomes pronounced only at higher volume fractions. For example, the displacement of the contact line is 10 times the nanoparticle diameter or approximately 0.2 im for a nanoparticle volume fraction of 0.25, while there is no appreciable change in the contact line position when the volume fraction is 0.2. This non-linear dependence of contact line position on nanoparticle volume fraction is consistent with the form of Eq. 10, where the film energy contribution due to structural disjoining pressure is subtracted from the surface energy contribution. The extent of displacement of the con-... 

Now that we have minimized to find the liquid-vapor interface shape at fixed contact line position, X(y), we evaluate the free energy for this shape (Eq. (4.37)) and minimize to find the optimal value of X(y). We therefore put Eq. (4.37) in Eq. (4.34) for the capillary energy and integrate over the x-coordinate from a = X(y) 0 (since there is already a term proportional to X(y) in the expression for /i(a , y)) to find the change in the interface free energy, AFv, as... 

Case (I) fixed contact angle 6 i) = Bo = const, R(t) variable. On smooth, ideal surfaces in the absence of any contact angle hysteresis and dynamic effects, the contact angle remains constant independent of the contact line radius, i.e., independent of the contact line position, and the radius of curvature of the interface (Fig. lb). In this case Eq. 2 can readily be integrated, thus yielding the explicit volume decrease... 

In analogy to the complete wetting (see Eq. 5.13), for the movement of the contact line (position F) in the partial wetting case (with dewetting velocity V), the following relation may be obtained ... 

Contacts with other pipelines or grounds can be localized to within a few hundred meters by pipe current measurements. Contacts with foreign pipelines or cables can also be found by measuring potential at the fittings of the other line while the protection current of the cathodically protected pipeline is switched on and off. While the potential of unconnected pipelines will assume more positive values when the protection current is switched on, the cathodic current may also enter any line in contact with the cathodically protected pipeline and thus shift its potential to more negative values. Should the contacting line not be located by this method, fault location can be attempted with direct or alternating current. 

It has been shown that contact angle hysteresis might arise as a result of inhomogeneities of the surface wetted by the liquid phase or surface roughness [70]. When surface roughness plays a considerable role, the observed contact angle may depend on the exact position of the contact line with respect to the microscopic or... 

The suitable system for studying linear energy K is the small circular black film (separating two gas phases) in contact with the bulk phase of the solution from which the film is formed. The presence of linear energy of this contact line can be expected on the basis of the experimental observations leading back to Boys [316]. He estimated its values to be less than 5.25-10 4 dyn (positive) for an aqueous solution of sodium oleate and glycerol. 

A general conclusion could be drawn on the basis of the results obtained from the above three experiments the linear energy at the contact line NBF/bulk solution can be either positive or negative, depending on the solution composition. 

Another theory of the linear energy of the contact line wetting film/bulk liquid drop on a solid surface has been developed by Churaev at al. [478]. These authors also considered both cases of negative and positive line tension. In their interpretation the transition region film/bulk can be presented [478] schematically as shown in Fig. 3.103. The dashed line 1 represents the idealised surface. The real surface is shown for two different cases in case 2 the... 

In conclusion it may be noted that both experimental and theoretical results, obtained so far, point out that the linear energy of the contact line free liquid film/bulk liquid phase can be either negative or positive. The sign of the K value is determined by the interaction forces acting in the film and in the transition region film/bulk. Thus, the sign and the value of the linear energy susceptibly reflect all interactions due to surface forces in the system. 

The linear energy of the contact line in three-phase equilibrium system could have either positive or negative values. This does not violate the mechanical equilibrium stability condition in such systems. This is proved experimentally by determining k in the case of liquid black films in equilibrium with bulk solutions. The absolute values of k obtained are less than about 10 9 J m 1 (10 4 dyn) they are positive at lower and negative at higher electrolyte (NaCl) concentrations. 

The linear energy of the contact line between two-dimensional phases is only positive. Otherwise the mechanical equilibrium stability condition will be violated. This case is illustrated by examining the fluctuation formation of holes in bilayers. The linear energy of holes in between +6-10 12 J m 1 and +4.5-10 11 J m 1 (+6-10 7 dyn and +4.5-10 6 dyn). 

Figure 26.10 A schematic representation of the meniscus shape and position of the three-phase contact line (solid/liquid/air) during immersion and emersion of a hydrophobic surface (e.g., TMS treated polymers) the dual arrows indicate which direction the beaker is moving, the small arrow on the plate indicates the direction the three-phase contact line is moving.

Figure 5.36. Molecular dynamics pictures of liquid motion near the contact line. Partial wetting. Given is the height as a function of horizontal position, both In reduced units. Panel (a) initial stage of spontaneous wetting, (c) intermediate stage, (d) fined stage. Panel (b) corresponds to panel (a), but is taken with respect to the position of the contact line. The solid is at h = 0.55. (Courtesy of M. de Ruijter and J. De Coninck.)...

A force of capillary attraction appears also when the particles (instead of being freely floating) are partially immersed in a liquid layer on a substrate - " (Figure 5.17b). The deformation of the liquid surface in this case is related to the wetting properties of the particle surface, i.e., to the position of the contact line and the magnitude of the contact angle, rather than to gravity. 

Wenzel s relation has been confirmed in terms of the first two laws of thermodynamics. Huh and Mason, in 1976, used a perturbation method for solving the Young-Laplace equation while applying Wenzel s equation to the surface texture. Their results can be reduced to Wenzel s equation for random roughness of small amplitude. They assume that hysteresis was caused by nonisotropic equilibrium positions of the three-phase contact line, and its movement was predicted to occur in jumps. On the other hand, in 1966, Timmons and Zisman attributed hysteresis to microporosity of solids, because they found that hysteresis was dependent on the size of the liquid molecules or associated cluster of molecules (like water behaves as an associated cluster of six molecules). 

In the absence of gravity a spherical particle of radius r will be oriented in such a way that the energy of the system is minimized. This means that the change (first variation) in the interfacial free energy when the contact line is shifted by a small distance, 5h, is zero. It follows from geometry that a shift in the position of the contact line by 5 h downward from its initial position (bold line in Fig. HI-20) results in changes in the interfacial areas of the solid-gas (SSG), solid-liquid (SSL), and liquid-gas (SLB) interfaces equal to... 

It is usually pointed out in most texts on the subject of surface tension that no equilibrium position of the contact line exists when... 

One of the most important interactions of the electron spin of the paramagnetic molecule, which influences its line position, is that with the nearby nuclear spins. These are the nuclei of the molecule itself and nuclei in the local surrounding upto a distance of ca. 0.6 nm. There are two different contributions to this interaction an isotropic part (fcrmi-contact interaction), which arises from electron spin density of the unpaired electron at the nucleus, and an anisotropic part, which arises from through-space magnetic dipole-dipole interaction between the electron and nuclear magnetic moments. Whereas for intramolecular nuclei, the isotropic part can be very large, interactions with intermolecular nuclei further apart are mainly anisotropic. This offers the possibility to measure directly the distance to the nucleus by the... 

We must minimize this energy with respect to the two degrees of freedom, h(x, y) and X(y), which determine the shape and position of the fluctuating interface respectively. We first minimize AF with respect to the shape of the fluid-vapor interface, h(x,y) for a fixed but spatially varying contact line, X(y). Thus, 8AF/Sh(x, y) = 0 implies... 

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