Interfaces contact angles

Very finely disperse solids, which are adsorbed at the liquid/liquid interfaces, forming films of particles around the disperse globules. Certain powders can very effectively stabilize against coalescence. The solid s particle size must be very small compared with the emulsion droplet size and must exhibit an appropriate angle of contact at the three-phase (oil/water/solid) boundary [141]. 

FIGURE 5.5 Liquid-solid interface contact showing advancing and retreating contact angle. 

During the rarefaction cycle of the acoustic wave, as the pressure in the liquid decreases the liquid gas interface becomes increasingly more convex, its angle of contact decreases, until, at sufficiently low pressure it breaks away from the surface to produce a bubble of radius, Rj. 

Carroll, B.J, (1976). The accurate measurement of contact angle, phase contact areas, drop volume, and Laplace excess pressure in drop-on-fiber system. J. Colloid. Interface Sci. 57, 488-495. 

Let A represent the solid, B, G the two fluids, EG, GD, GF the two solid-fluid and the fluid-fluid interfaces respectively, the line GF forming an angle a with EB. This angle is called the angle of contact of the system. Then since FG represents an equilibrium configuration the potential energy of the system in this position must be a minimum, so that an infinitesimal displacement of GF to G F will not cause an alteration in the energy of the system. 

Hence the difference between the tensions at the two solid-fluid interfaces which is the quantity always involved in equations of equilibrium can be expressed in terms of the fluid-fluid tension and an angle, called the angle of contact which is plainly susceptible of direct measurement. 

Now Antonow s rule appears to be valid for two liquids provided that saturation be carefully defined and it is true for solid and liquid interfaces provided that the angle of contact be zero. 

When a liquid is placed in contact with a surface of a porous solid the question arises as to whether it will penetrate into the pores. The answer must be pursued in the realm of capillarity which deals with the equilibrium geometries of liquid-solid interfaces and the angle of contact between the liquid and the pore wall. 

A quantity that is closely related to surface tension is the contact angle. The contact angle 0 is defined as the angle (measured in the liquid) that is formed at the junction of three phases, for example, at the solid-liquid-gas junction as shown in Figure 6.2b. Although the surface tension is a property of the two phases that form the interface, 0 requires that three phases be specified for its characterization, as mentioned above. The above definition of contact angle is, however, highly simplified, and we take a more in-depth look at the concept later in this chapter. 

Wilhelmy (1863) suggested that the interfacial tension of liquids could be determined by measuring the maximum force required to pull a glass plate vertically from the interface. In his experiment, he was careful to ensure that the glass plate was extremely clean so that the angle of contact ((p) was relatively small or close to zero. The force, F, exerted on the plate raises the meniscus of the fluid above the level of the flat surface as shown in Figure D3.6.7. The mass of the liquid that is elevated above the fluid interface increases to some maximum value as F increases. Once the meniscus is fully formed, the force acting on the plate is equal to... 

It is well known that under certain conditions one liquid will displace another from a particulate mass (in a tube, for example). This will occur when the contact angle made by the liquid-liquid interface with the solid is acute, the direction of displacement being toward the concavity. This is shown in Figure 63, illustrating a capillary formed of particles. The direction of movement will be as indicated as long as the angle of contact is small. The conditions for this situation are set forth by Eq (11-5), and dAB is acute as long as... 

Contact angle — The contact angle is the angle of contact between a droplet of liquid and a flat rigid solid, measured within the liquid and perpendicular to the contact line where three phases (liquid, solid, vapor) meet. The simplest theoretical model of contact angle assumes thermodynamic equilibrium between three pure phases at constant temperature and pressure [i, ii]. Also, the droplet is assumed to be so small that the force of gravity does not distort its shape. If we denote the - interfacial tension of the solid-vapor interface as ysv. the interfacial tension of the solid-liquid interface as ySL and the interfacial tension of the liquid-vapor interface as yLV, then by a horizontal balance of mechanical forces (9 < 90°)... 

The capillary pressure equation (Berg, 1975) predicts that capillary leakage will occur when the upward pressure of the hydrocarbon column is greater than the capillary resistance of the seal. The magnitude of upward reservoir pressure is determined by hydrocarbon buoyancy pressure plus any overpressure in the reservoir relative to the seal. The capillary resistance of the seal is determined by the size of interconnected pore throats and the interfacial tension between hydrocarbon (gas or oil) and formation water. The relationship between these factors can be expressed as follows if the angle of contact of the hydrocabon-water interface is assumed to be 0° (Clayton and Hay, 1994) ... 

Spreading of drops on powder surface spreading Contact angle goniometer Contact angle Drop height or volume Spreading velocity References Kossen and Heertjes, Chem. Eng. Sd, 20, 593 (1965). Pan et al., Dynamic Properties of Interfaces and Association Structure, American Oil Chemists Society Press, 1995. 

Fig. 10.1.4. The liquid may spread freely over the surface, or it may remain as a drop with a specific angle of contact with the solid surface. Denote this static contact angle by 6. There must be a force component associated with the liquid-gas surface tension (t that acts parallel to the surface and whose magnitude is a cos 0. If the drop is to remain in static equilibrium without moving along the surface, it has to be balanced by other forces that act at the contact line, which is the line delimiting the portion of the surface wetted by the liquid, for example, a circle. It is assumed that the surface forces can be represented by surface tensions associated with the solid-gas and solid-liquid interfaces that act along the surface, and tr i, respectively. Setting the sum of the forces in the plane of the surface equal to zero, we have...

Interactions of Proteins at Solid-Liquid Interfaces Contact Angle, Adsorption, and Sedimentation Volume Measurements... 

Volyak LD, Stepanov VG, Tarlakov YV (1975) Temperature dependence of the angle of contact of water and water-d2 on quartz and sapphire. Zh Fiz Khim 49 2931-3133 Walker DS, Moore FG, Richmond GL (2007) Vibrational sum frequency spectroscopy and molecular dynamics simulations of the carbon tetrachloride-water and 1,2-dichloromethane-water interfaces. J Phys Chem C 111 6103-6112... 

Zhang J, Kwok DY (2004) Lattice Boltzmann study on the contact angle and contact line dynamics of liquid-vapor interfaces. Langmuir 20 8137-8141... 

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