Surfaces interfacial energy balances

For a liquid that rests on a smooth surface with a finite contact angle, one can determine the relationship between the interfacial tensions at the different interfaces from consideration of the balance of surface forces at the line of contact of the three phases (solid, liquid, and gas). Remembering that the interfacial tension always exerts a pressure tangentially along the surface, the surface free-energy balance (a... 

FIGURE 6.11 Interfacial energy balances determine the wetting behavior of a liquid droplet in contact with a sohd surface, (a) The balance of the -direction components of the interfacial energy forces determines the contact angle 0. (b) If y,s y, 0 -> 0° and completely hydrophilic (spreading) behavior occurs, (c) If yis y v- nd completely hydropho-... 

Figure C2.11.8. An illustration of the equilibrium contact (i.e. wetting) angle, ( ), fonned by the balance of interfacial energies for or a liquid (sessile) drop on a flat solid surface.

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). 

The value of the equilibrium contact angle (9) at the three-phase line (TPL) produced by a liquid droplet placed on a flat, solid substrate is determined by the balance of interfacial energies at each surface. Thomas Young derived an equation describing this situation in 1804 ... 

The three interfacial surface energies, as shown at the three-phase junction in Figure 2.29, can be used to perform a simple force balance. The liquid-solid interfacial energy plus the component of the liquid-vapor interfacial energy that lies in the same direction must exactly balance the solid-vapor interfacial energy at equilibrium ... 

Kitamori s group has proposed selective chemical surface modification utilizing capillarity (called the capillarity restricted modification or CARM method) (Hibara et al., 2005). In the CARM method, a microchannel structure combining shallow and deep microchannels and the principle of capillarity are utilized. The procedures are shown in Figure 19. A portion of an ODS/toluene solution (lwt%) is dropped onto the inlet hole of the shallow channel, and the solution is spontaneously drawn into this channel by capillary action. The solution is stopped at the boundary between the shallow and deep channels by the balance between the solid-liquid and gas-liquid interfacial energies. Therefore, the solution does not enter the deep channel. It remains at the boundary for several minutes and is then pushed from the deep channel side by air pressure. 

Surfactants assist wetting because they lower surface and interfacial tension. The energy balance that determines spreading is expressed by the spreading coefficient, S, and is illustrated in Figure 6.21. 

The balance of forces between surface tensions at the contact line results either in the Neumann triangle for a liquid/liquid/liquid or liquid/liquid/gas system or in the Young-Dupre equation on a liquid/liquid/solid or a liquid/gas/solid system (Fig. 1). While the Neumann triangle represents a true balance of forces, the Young-Dupre equation is little more than a definition of the (o As ctbs) term, a difference between the respective solid/fluid surface free energies and not truly solid/fluid interfacial tensions. 

Since our concern is primarily with interface energy transfer rather than with the energy associated with the dividing surface, we normally neglect all interfacial effects and write the jump internal energy balance (3.99) as ... 

The contribution to the energy from the surface is usually written as a A, where a is the surface tension for the liquid-vapor interface (or the interfacial tension for a liquid-liquid interface) and A is the surface area. The a A contribution is the two-dimensional analogue of the P V term For bulk fluids. Including the effect of changing surface area in the energy balance, just as we have included the effect of changing volume, gives for a closed system without shaft work. ... 

The power supplied to the vessel contents, which is responsible for the agitation and creation of large interfacial area, is derived from the gas flow. Bernoulli s equation, a mechanical energy balance written for the gas between location o (just above the sparger orifices) and location 5 (at the liquid surface), is... 

All IMDSs can be approximated by constant mean curvature (CMC) surfaces that minimize interfacial area subject to a volume (or volume fraction) constraint. This fact is not surprising, since the microdomain structure is the result of the balance between chain-stretching and the interfacial energies, where the latter term seeks to minimize surface area and thus favors CMC surfaces. 

The simplest heterogeneous model considers only the interfacial gradients between sohd and fluid phases, imposing mass and energy balances for all phases involved and introdueing mass and heat transport from the gas bulk to catalyst surface and vice versa. Typical mass and energy balances equations are ... 

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