Hysteresis of the contact angle

Contact angle hysteresis has been extensively studied for the last two decades due to the technological interest in super-hydrophobic systems. Classical approaches, experimental evidence, and understandings of the topic will be presented in the following sections. Much more will be discussed on this subject in Chap. 3 where the Lotus 

The phenomenon of the hysteresis of the contact angle has been mosdy associated with physical or chemical heterogeneities on the sohd surface or with impurities in any of the components of the system. It was thought that Young s equation was stiU applicable locally this statement was only proved for particular situations, for example choosing the shape of the liquid-fluid interface as a spherical cup, but not in general due to the mathematical difficulty to describe all the possible states of the system. 

Wemel extended Young s equation to describe rough surfaces when the area covered by liquid is much larger than the roughness scale and if the liquid completely penetrates into the roughness grooves, obtaining 

On the other hand, Cassie and Baxter considered a heterogeneous surface made up of two species with area fractions and ( 2 = 1 — / i and contact angles 9 and 02- When the individual areas are much smaller than the droplet size, they found that the apparent contact angle (9c-b) is given by 

Equation (21) can be also appHed to a homogeneous and rough solid surface when the liquid of the droplet does not penetrate into the grooves and the base of the droplet is in contact with the solid (with contact angle 9 ) and with the air trapped in the grooves (with contact angle 9j = 180°). The transition between this and Wenzels cases is discussed by Lafuma and Quere. These approaches are discussed in Chap. 3. 

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H, particularly when contact angles are in the range of intermediate wettability. Consequently, each mechanism should be expected to play a role in GDM capillary behavior. For instance, the attribution of capillary pressure hysteresis entirely to hysteresis of the contact angle in the sense of Eq. (3)59 can be correct only if GDMs are composed of bundles of tubes of cylindrical cross section.60... 

As far as the available evidence goes, it appears that the cleaner the surface, the smaller is the hysteresis of the contact angle. It seems possible that the large advancing contact angle (small adhesion between liquid and solid) is due to the presence of some film which prevents the liquid adhering closely to the solid after contact with the liquid, this film is wholly or... 

Drops Deposited on Dirty Surfaces. We have implicitly assumed an ideal surface. On a real surface, the contact angle of a drop is often slightly dependent on the preparation conditions. Its value lies between two limits (larger) and 6 (smaller). The hysteresis of the contact angle, determined via the force 5 = 7 cos Or cos a), will be discussed in chapter 3. The difference 0a. is a measure of the state of cleanliness and roughness of a surface. It is used as a test in the automobile industry to ensure that surfaces are perfectly clean before applying paint. Oa Or must be sufficiently small for good adhesion. 

The modification of the fluid interfaces due to surfactant adsorption strongly influences the interactions between fluid particles (droplets, bubbles) in dispersions. Frequently a thin liquid film is formed in the zone of contact of two fluid particles. The contact angle at the periphery of such a film is a measure for the interaction of the two opposite surfactant adsorption monolayers. When the latter adhere to each other, a hysteresis of the contact angle is observed, irrespective of the fact that the fluid interfaces are molecularly smooth. The properties of the thin liquid films are important for the flocculation in dispersions and the deposition (attachment-detachment) of particles at surfaces see Sec. V. 

There is no doubt that heterogeneity affects the wetting process. However, heterogeneity of the surface is apparently not the sole reason for hysteresis of the contact angle. This follows from the fact that not all predictions made on the... 

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... 

The hydrodynamic receding contact angle in the case of the porous substrates has nothing to do with the hysteresis of the contact angle and is completely detemuned by the hydrodynamic interactions in a way similar to the complete wetting case in Section 4.3. 

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