Contact angle at equilibrium

Using the Young-Dupre equation, W = y(l + cos 0), and introducing the boundary condition of 0 = 0o for t = 0 (no swelling) and 0o , (contact angle at equilibrium with swelling), we obtain ... 

Equation (52) allows us to estimate the impact of viscoelastic braking on the capillary flow rate. As an example, we will consider that the liquid is tricresyl phosphate (TCP, 7 = 50 mN-m t = 0.07 Pa-s). The viscoelastic material is assumed to have elastic and viscoelastic properties similar to RTV 615 (General Electric, silicone rubber), i.e., a shear modulus of 0.7 MPa (E = 2.1 MPa), a cutoff length of 20 nm, and a characteristic speed, Uo, of 0.8 mm-s [30]. TCP has a contact angle at equilibrium of 47° on this rubber. 

A simple experimental evidence of surface modification, for instance concerning the hydrophilic/hydrophobic balance of the surface, can be searched for. To do this, the simplest and oldest method measures the contact angle at equilibrium between the clean surface of a material, a liquid and its vapour. This method permits evaluation of the surface tension of material surfaces, which can be related to the hydrophilic/hydrophobic balance. Several experimental processes have been described, but the simplest is deposition of a droplet of liquid on the surface, as shown in Eigure 2.18. 

Figure 2.18 Measuring the contact angle at equilibrium. A droplet of liquid is deposited on the horizontal clean surface of the material. The size of the droplet should be small enough to decrease the effects of gravity. When apparent equilibrium has been reached, the contact angle is measured.

E. Assume that the water in the cell walls is in equilibrium with the internal cellular water. What are cos a and the contact angle at the ail-water interface for cylindrical cell wall pores 20 nm in diameter Assume that... 

In the further elaboration a general phenomenological framework for wetting can be developed. Because of its thermodynamic nature, this framework is macroscopic and static it refers to equilibrium or to reversible processes. So, the kinetics of wetting cannot be analyzed in this way and only one contact angle, the equilibrium angle, can be considered. It remains an issue how this thermodynamic contact angle relates to the one that is physically measurable. Another typical feature is that interfaces are always taken to be at equilibrium with the adjacent... 

The shape of the curved surface, in turn, allows one to determine the surface tension of the liquid when it is in equilibrium with its own vapor or to determine the interfacial tension if the droplet is in contact with a different substance (gas, liquid, or solid). The interfacial tension is determined by measuring the contact angles at the liquid-solid and solid-vapor interfaces. The contact angle is defined in Figure 3.11, which shows a typical liquid-solid interface. 

The relation between equilibrium contact angles at a solid surface, and the adhesion between solid and liquid, is reviewed. The information deducible as to the chemical nature of the groups exposed at the surface is summarized. 

Equilibrium contact angles are functions of the surface free energies of the solid substrate and the liquid in contact with it and of the free energy of the interface between the two phases. Much useful information can be obtained through studies of contact angles. This equilibrium, however, represents the extent to which a liquid spreads over the substrate and not the extent of wetting at the interface. 

This report is concerned with contact angle hysteresis and with a closely related quantity referred to as "critical line force (CLF)." More particularly, it is concerned with the relationship between contact angle hysteresis and the magnitude of the contact angle itself. Two sets of liquid-solid-vapor systems have been investigated to provide the experimental data. One set consists of Teflon [poly(tetrafluoroethylene), Du Pont] and a series of liquids forming various contact angles at the Teflon-air interface. The second set consists of polyethylene and a similar series of liquids. In neither case was the ratio of air to test liquid vapor at the boundary line controlled, but it can be assumed that the ambient vapor phase operative in all the systems was close to an equilibrium mixture. 

By equating the expressions for Laplace pressures of the front and side (Eqs. 3 and 4), the equations for the radius of curvature of the sides and bottom contact angle at the side can be obtained for equilibrium conditions as... 

The density profile at a vapor-liquid interface was considered briefly in Chapter 1 (Section 5). Prominent in that discussion was the positive contribution to the local free energy density produced by sharp gradients in density (cf. Equation 1.41). The buildup of a thin film on a solid surface is also influenced by this gradient energy (Cahn, 1977 Teletzke et al., 1982). As we shall see, gradient effects sometimes prevent the continuous film buildup predicted by conventional adsorption isotherms as the bulk density of the vapor approaches its samration value. Moreover, when both liquid and vapor are present, the liquid spreads spontaneously on the solid for temperatures sirfficiendy near the eritical temperature, but has a finite equilibrium contact angle at lower temperatures. 

A thin liquid film lies on the solid surface which forms the floor of a narrow horizontal slit. Through the slit, air is blown at a steady rate. The air is seen to exert a constant shear stress on the liquid surface, thus the film thickness varies linearly with the distance from the leading edge, which is also the contact line (Derjaguin et al., 1944 Levich, 1962). Very close to the contact line the profile changes to retain the equilibrium contact angle at the contact line. The equations of motion and continuity under the lubrication theory approximation reduce to (Neogi, 1982) (see Problem 7.13)... 

Here yig is the interfacial tension at the liquid-gas interface and Xsg and /si are the interfacial tensions between the solid-gas and the solid-liquid interfaces, respectively. Knowing yig and the contact angle in equilibrium at the solid-liquid-gas interface, we can determine the difference Xsg — Ys but not their absolute values. Since the wet-... 

Fig. 1.3. Equilibrium contact angles at a triple line at rest, (a) Solid substrate Young s construction. (b) Liquid substrate Neumann s triangle. If the line moves, the dynamical contact angle is 9d-If 6d < E, the line recedes in the B direction and if > fe, the line advances in the A direction.

Thus, the value of the contact angle at time t, being greater than the equilibrium value, 600, leads to a lower extent of penetration than if the equilibrium value had been relevant from the onset of the wetting process. This equation also reveals that a higher temperature, which will lead to the equilibrium value being attained in a shorter time, will therefore aid penetration, as indeed intuitively expected. 

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