Contact angle force balance

The wettabiHty theory of adhesion is iaextricably related to the study of contact angles of Hquids on soHd surfaces. A force balance at the poiat of contact between the Hquid and the soHd can be written (3)... 

Fig. 1. Contact angles. The shapes of drops that are A, wetting and B, nonwetting with respect to the soHd (B), and C, penetration of a wetting Hquid into a pore to compress the gas (D) inside. The vector diagram shows the balance of forces at the perimeter of the Hquid drop on the soHd plate.

Fig. 4. Definition of contact angle showing the derivation of Young s equation, Eq.. 8, using a balance of horizontal forces at the three-phase interline.

Bubble size at departure. At departure from a heated surface, the bubble size may theoretically be obtained from a dynamic force balance on the bubble. This should include allowance for surface forces, buoyancy, liquid inertia due to bubble growth, viscous forces, and forces due to the liquid convection around the bubble. For a horizontally heated surface, the maximum static bubble size can be determined analytically as a function of contact angle, surface tension, and... 

Figure 2 is a representation of the force balance on a Wilhelmy plate that has gone through one phase and has been wetted by a second phase. The three interfacial tensions are related to the contact angle (measured through phase 2) by the familiar Young equation... 

If, when a liquid drop is placed on a smooth surface, the forces of adhesion between the solid and the liquid are greater than the forces of cohesion of the liquid, then the liquid will spread and will perfectly wet the surface spontaneously. If the forces reach an intermediate balance determined by the interfacial energies ylv, ysj and ysv, then the liquid drop will form a definite contact angle (0) with the solid surface (Figure 4.12). 

Fig. 1. The hypothetical balance of forces at the 3-phase line. The surface tension 7S of the solid (shaded) is supposed to be equal to the sum 7sj + 7 cos 0 7sj is the tension along the liquid - solid interface, 7 is surface tension of the liquid, and 0 is the contact angle...

The balance of forces as indicated, again, were analyzed very extensively in the last century by Young (1805), who related the different forces at the solid-liquid boundary and the contact angle, 9, as follows (Adamson and Gast, 1997 Chattoraj and Birdi, 1984 Birdi, 1997, 2002) ... 

The situation shown in Figure 6.2b is one in which surface tension and contact angle considerations pull a liquid upward in opposition to gravity. A mass of liquid is drawn up as if it were suspended by the surface from the supporting walls. At equilibrium the upward pull of the surface and the downward pull of gravity on the elevated mass must balance. This elementary statement of force balance applies to two techniques by which 7 can be measured if 6 is known the Wilhelmy plate and capillary rise. 

In Equations 21.9 and 21.10, the interfacial force 21.6 is used by employing a contact angle equal to rc/2. Generally in Equation 21.9 the droplet height is substituted by the droplet radius, Dd/2. These equations permit calculation of which diameter torques in clockwise and anticlockwise directions are balanced, beyond this value the droplet detaches. However, for a short period the droplet still maintains its... 

The surface free energy (s.f.e.) of a material is a measure for the work required to enlarge its surface (mJm-2). At constant pressure, constant temperature and if the surface composition remains constant, die s.f.e. equals the surface tension (ysv) of the material against its vapor [26], To determine the value of ysv and hence of the s.f.e. of a solid, contact angles with several liquids with known s.f.e. (yLv) are required. Thomas Young s equation relates the surface free energies and the contact angle (9) based on the force balance at the three-phase boundary [27] ... 

Since the fiber is heavier than the liquid, it would sink when placed on the liquid if it were not sustained by an upward force caused by the surface tension of the liquid. This force is exerted at the three-phase air-liquid-fiber boundary lines. If the contact angle 0 and the surface tension y are high enough, this upward force can become sufficient to balance the sinking force, and the fiber will come to rest when the two forces become equal, at an equilibrium depth corresponding to a definite value of < . In this situation, as shown in Figure 1, the force exerted vertically upward on a unit length (1 cm.) of fiber, measured in dynes, will be ... 

Contact angle measurement is probably the most common method for solid surface tension measurement in condensed state. Young [71] described the equilibrium at three-phase boundary in terms of the vectorial sum, as shown in Fig. 3, resulting in the following equation of equilibrium forces balance... 

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°)... 

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