Static Hysteresis of Contact Angle

The previous consideration shows that the situation with Young s equation (Equation 1.1) is far more difficult than it is usually assumed. This equation is supposed to describe the equilibrium contact angle. We explained in Section 1.1 that the latter equation does not comply with any of the three requirements of the equilibrium liquid-vapor equilibrium, liquid-solid equilibrium, and vapor-solid equilibrium. 

However, there is a phenomenon that is far more important than the previous ones from a practical point of view. It is called the static hysteresis of contact angle. 

The derivation of Equation 1.1 and further considerations show that the given equation (or its modifications) determines only one unique equilibrium contact 

FIGURE 1.13 Calculated and experimentally-measured isotherms of disjoining pressure, n(h), of the films of water on a quartz surface at concentration of KCl C = 10 mol/l, pH = 7, and dimensionless potential of the quartz surface equals to 6 [1]. (a) Within the region of large thicknesses dimensionless q potential of the film—air interface equals to 2.2 (curve 1), 1 (curve 2), and 0 (curve 3) (b) within the region of small thicknesses dimensionless q potential of the film-air interface equals to 2.2 (curve 1). The structural component, Ilj(/j), of the disjoining pressure isotherm and electrostatic component, n/h), are indicated by curves 2 and 3, respectively. Curves 4 in both part (a) and (b) are calculated according to Equation 1.13. 

FIGURE 1.14 Schematic presentation of a liquid droplet on a horizontal solid substrate, which is slowly pumped through the liquid source in the drop center. R is the radius of the drop base 0 is the contact angle (1) liquid drop, (2) solid substrate with a small orifice in the center, (3) liquid source (syringe). 

---

It is usnally believed that the static hysteresis of contact angle is determined by the surface roughness and/or heterogeneity (Figure 1.15). 

Figure 1.15b presents the magnified vicinity of the three-phase contact line of the same droplet as in Figure 1.15a. This picture gives a qualitative explanation of the phenomenon of the static hysteresis of contact angle, which is widely adopted in the literature. The static hysteresis of contact angle is connected with multiple equilibrium positions on the drop edge on a rough surface. No doubt...

Static Hysteresis of Contact Angles from Microscopic Point of View Surface Forces... 

In the case of equilibrium liquid drops and menisci (see Section 2.3), they are supposed to be always at equilibrium with flat films with which they are in contact with in the front. Only the capillary pressure acts inside the spherical parts of drops or menisci, and only the disjoining pressure acts inside thin flat films. However, there is a transition zone between the bnlk liquid (drops or menisci) and the thin flat film in front of them. In this transition zone, both the capillary pressure and the disjoining pressure act simultaneously (see Section 2.3 for more details). A profile of the transition zone between a meniscus in a flat capillary and a thin a-fllm in front of it, in the case of partial wetting, is presented in Figure 2.5. It shows that the liquid profile is not always concave but changes its curvature inside the transition zone. Just this peculiar liquid shape in the transition zone determines the static hysteresis of contact angle (see Chapter 3)... 

According to the definition of line tension (2.222), it is determined by the equilibrium liquid profile in the transition region from the thin flat liquid interlayer to the bulk surface of bubbles. Note that in the case of partial wetting, which is under consideration, the static hysteresis of contact angle (see Chapter 3, Section 3.10) is unavoidable. The latter phenomenon can substantially influence the comparison. 

Further consideration shows that the initial state as well as the presence or absence of the film in front (zone 3 in Figure 3.28b) does not influence our consideration. That is, the same consideration as below can be applied to the static hysteresis of contact angle on initially dry surface. 

The fundamental conclusion of this section is the relation of the mechanism of static hysteresis of contact angle of smooth homogeneous surfaces to the form of the disjoining pressure isotherm. It should be noted that static hysteresis of the nature considered appears not only on smooth homogeneous surfaces but also on heterogeneous ones. Thus, in actual cases, the possibility of the simultaneous appearance of static hysteresis phenomena of different natures must be taken into consideration. 

Regions of practically immobile states of a meniscus are shown in Fig. 25 by arrows on the pressure axis for solution concentration Co = 5 x 10 (curves 3) and 5 x 10 M (curves 4). This makes it possible to assess static values of contact angles. Because of small hysteresis (the regions shown by arrows are short) the mean value of static contact angle is equal to 40° for C = 5 X 10 M and 36° at 5 x 10 M. The calculated values are close to those measured using captive bubbles [45] and differential ellipsometry method [46] on quartz surface for the same solutions. 

Next, results are presented on measurements of static advancing and static receding contact angles on smooth nonporous nitrocellulose substrate for different SDS concentrations. The idea is to compare hysteresis of contact angles on the smooth nonporous nitrocellulose substrate with the hysteresis contact angles obtained earlier on porous nitrocellulose substrates at corresponding SDS concentrations. 

There is no doubt that heterogeneity affects the wetting properties of any solid substrate. However, heterogeneity of the surface is apparently not the sole reason for static hysteresis of the contact angle. This follows from the fact that not all the predictions made on the basis of this theory have turned out to be true [39,40]. Besides that, static hysteresis of the contact angle has been observed in cases of quite smooth and uniform surfaces [41 5]. Further, it is present even on surfaces that are definitely molecularly smooth free liquid films [60,61]. 

A theory of static hysteresis of the contact angle has been developed on the basis of the analysis of conditions of quasi-equihbrium of the system and their violation. The suggested theory agrees quahtatively with known experimental data. For more rigorous quantitative calculations, a theory of disjoining pressure should be developed, which is apphcable to profiles of drops or menisci having sufficiently steep part of the profiles. It is also necessary to determine the thickness of the film thickness, h, that corresponds to the beginning of the flow zone. 

In the case of partial wetting, the static hysteresis of the contact angle determines the spreading behavior at low capillary numbers, Ca 1, where U = R(t) is the rate of spreading. This condition was always satisfied under our experimental conditions. 

Static Hysteresis of the Contact Angle of SDS Solution Drops on Smooth Nonporous Nitrocellulose Substrate... 

To sum up, the effects on static contact angles of the departures from ideality of solid surfaces are qualitatively well understood and some of these effects are used in practice to improve or reduce wettability. Moreover, for simple geometries, a semi-quantitative agreement is obtained between experimental results and theoretical predictions. For surfaces with random roughness, predictions of wetting hysteresis present a great difficulty because the relevant size of defects is not yet well-established. 

---