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In the case of incompressible fluids, the density of which is constant, as for common liquids, the continuity equation, Eq. 2 Diffusion Equation in Terms of Mass Fraction In contrast to the equation of motion and the energy equation, which are rigorously derived by application of the conservation laws, the derivation of the diffusion equation is insufficiently described in standard textbooks. Here, we present a rigorous derivation of the diffusion equation by applying the law of conservation of mass in fluid media.

4 Convective Mass Flux for Mass Transfer in a Mixture of Vapors In binary and multicomponent distillation, the condensation of mixed vapors and the evaporation of volatile solutions are always accompanied by an interfacial velocity, vs , caused by condensation of vapors or evaporation of liquids. Although mass transfer in such cases is considerably affected by convective mass flux, this effect has long been neglected by practical engineers. A. Ito and K. Asano [3] presented a theoretical approach to this important problem in binary distillation.

42) can be rewritten in dimensionless form by introducing the following dimensionless variables: Dimensionless velocity: Dimensionless pressure: Dimensionless axial distance: Dimensionless radial distance: u' ˆ u/Uav 2 p' ˆ p/rUav z' ˆ z/d r' ˆ r/d Substituting the above variables into Eq. 6 Dimensional Analysis This indicates that the relationship between dimensionless pressure and dimensionless velocity will be similar if Reynolds numbers in two flows, Re (: rUavd/m), are equal. Indeed, the criterion for similarity in two flows is equality of the Reynolds numbers.