Interfaces interfacial energy balances

The discrepancy functions F -F are zero at the solution. We have ignored the Ag term in the interfacial energy balance F2. The temperature of the two bulk phases will, therefore, be assumed to be equal to the (as yet unknown) interface temperature. 

When the nucleus is formed on a solid substrate by heterogeneous nucleation the above equations must be modified because of the nucleus-substrate interactions. These are reflected in the balance of the interfacial energies between the substrate and the environment, usually a vacuum, and the nucleus-vacuum and the nucleus-substrate interface energies. The effect of these terms is usually to reduce the critical size of the nucleus, to an extent dependent on... 

Sometimes the failure occurs by propagation of a crack that starts at the top and travels downward until the interface is completely debonded. In this case, the fracture mechanics analysis using the energy balance approach has been applied [92] in which P, relates to specimen dimensions, elastic constants of fiber and matrix, initial crack length, and interfacial work of fracture (W,). 

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. ... 

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... 

Manipulate the multicomponent thermal energy balance in the gas-phase boundary layer that surrounds each catalytic pellet. Estimate the external resistance to heat transfer by evaluating all fluxes at the gas/porous-solid interface, invoking continuity of the normal component of intrapellet mass flux for each component at the interface, and introducing mass and heat transfer coefficients to calculate interfacial fluxes. 

The capillary pressure of water is determined by a balance of the interfacial energies among the three phases solid, liquid, and vapor, the wetting angle of liquid-solid, and the radii of the pores, which are dependent on the pore structure in the medium and the amount of water existing in the pores. The osmotic pressure is dependent on the pore structure and the liquid-solid interface. Therefore, one must predict the pressure p statistically from the pore structure distribution model. 

Note that the third term in this expression, which is associated with the wall/liquid interfacial energy, is subtracted from the other two terms because this interface is replaced by the solid/wall interface upon nucleation of the particle. From the interfacial energy force balance derived in Equation 6.17, we can relate the interfacial energy terms to the contact angle 9 via... 

Surfactants are molecules that consist of a non-polar hydrophobic (e.g. alkyl-chains) and a polar hydrophilic part, which can be cationic, anionic, zwitter-ionic, or non-ionic. The relevance of the polar part for the molecule behaviour is quantified in form of the hydrophilic-lipophihc balance (HLB), for which values above 7 indicate dominance of the hydrophilic groups (Myers 1999, pp. 270-273). The heterogeneous composition leads to amphiphilic properties and interfacial activity. That means surfactants accumulate on interfaces and, thus, reduce the interfacial energy (cf. Sect. 3.1.3). Surfactant molecules associate to nanosized aggregates, so-caUed micelles, above a critical concentration (the critical micelle concentration—CMC). Such molecule associations do not only exist in the bulk solution but can also be formed by adsorbed siufactant molecules (Holmberg et al. 2002, pp. 39-66). 

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