Interphase transport flux expressions

A review of the literature and thermodynamic calculation procedures for such systems are available in McHugh and Krukonis (1986). The same reference may he studied for thermodynamic equilibrium calculations for the solute distribution between a liquid and a supercritical fluid solvent. 

So far, we have been concerned with the distribution of molecules, ions or macromolecules between two immiscible phases. The molecules may have been solutes present in small quantities or major constituents of either or both phases. Classical principles of thermodynamics were used to develop estimates of such solute distributions. When it comes to large particles, such as ore fines, cells or other particulate matter, classical thermodynamics may not appear to he of any use. However, using the phenomenon of wetting based on interfecial thermodynamics, particle separation from one phase is achieved by introducing a second immiscible phase. 

There are two types of systems here depending on whether the two immiscible phases are gas-liquid or liquid-liquid. Particle separation in a gas-liquid system is much more common and is called flotation. The following three paragraphs will focus on the basic thermodynamic principles in such a system. 

Consider two types of mineral particles in an aqueous suspension. If air bubbles can be attached to one type of particle only, the latter will float to the surface of the suspension, due to reduced density, and can be separated from the other type of particles. Normally, mineral particles are wetted completely by water so that air bubbles cannot attach to them. However, if the particle surface can be made sufficiently hydrophobic to prevent wetting, air bubble attachment is possible. 

The criterion for air bubble attachment is that the free energy change should be negative  

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Appropriate boundary conditions arise from the actual process or the problem statement. They essentially are given, or, more often, must be deduced from, physical principles associated with the problem. These physical principles are usually mathematical statements that show that the dependent variable at the boundary is at equilibrium, or, if some transport is taking place, that the flux is conserved at the boimdary. Another type of boundary condition uses interfacial transport coefficients (e g. heat Iransfer or mass transfer coefficients) that express the flux as the product of the interphase transport coefficient and some kind of driving force. 

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