Interfacial Energy Balances

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- 

LIQUID-SOLID AND SOLID-SOLID PHASE TRANSFORMATIONS 

Equilibrium occurs when a contact angle (0) is established that exactly balances the jc-direction components of the interfacial energy forces  

Depending on the relative magnitude of y j versus yjy, the water droplet can exhibit wetting (hydrophilic) or nonwetting (hydrophobic) behavior  

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In liquid-phase sintering, densification and microstmcture development can be assessed on the basis of the liquid contact or wetting angle, ( ), fonned as a result of the interfacial energy balance at the solid-liquid-vapour intersection as defined by the Young equation ... 

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. 

The function is the mass transfer rate equation for the vapor phase is the interfacial energy balance F3 is valid if the liquid phase may be assumed unmixed with... 

When the temperature is not constant, the bulk heat transfer equation complements the system and involves Equations 5.240, 5.241, and 5.276. The heat transfer equation is a special case of the energy balance equation. It should be noted that more than 20 various forms of the overall differential energy balance for multicomponent systems are available in the literature." " The corresponding boundary condition can be obtained as an interfacial energy balance." - Based on the derivation of the buUc and interfaciaT entropy inequalities (using the Onsager theory), various constitutive equations for the thermodynamic mass, heat, and stress fluxes have been obtained. 

The temperature sensitivity stays around 0.0028 fC for most cases. At elevated pressures, the heat feedback from the gas phase to the condensed phase is higher, and thus the effect of initial temperature on the interfacial energy balance becomes less important. A numerical analysis on the temperature sensitivity for low-pressure conditions was further performed by Beckstead and co-workers [35]. The predicted temperature sensitivity was determined to be too low compared to the measurements, mostly due to the uncertainties associated with the treatment of the condensed phase in the model. 

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