A comprehensive mathematical model of mass diffusion has been developed for binary fluids at high pressures, including critical and supercritical pressures. Heretofore, diverse expressions, valid for limited parameter ranges, have been used to correlate high-pressure binary mass-diffusion-coefficient data. This model will likely be especially useful in the computational simulation and analysis of combustion phenomena in diesel engines, gas turbines, and liquid rocket engines, wherein mass diffusion at high pressure plays a major role.
The model recasts the kinetic theory (i.e. low-pressure) expressions into forms consistent with the principle of corresponding states. Also presented are corresponding states forms for the Stokes-Einstein hydrodynamic model for diffusion in liquids, which are used for purposes of comparison. By ansatz, the model includes an expression that reflects departures from the kinetic-theory diffusion-coefficient relationship by means of a division factor that is partly a function of the reduced species density, becomes unity in the limit of low-pressure gases, and includes parameters to be determined empirically for higher pressures. The final model equation is
Dij0 = (Dij)KT / wD,j
where Dij0 is the high-pressure infinite dilution diffusivity of species i in j, (Dij)KT is the binary diffusivity calculated according to kinetic theory, and wD,j = 1 + δD,j is the division factor. As the reduced density of species j approaches zero, so does δD,j . Empirical parameters have been determined and the model evaluated by means of correlations with experimental data from the literature (see figure). Typical uncertainties in the correlations have been estimated to lie between 10 and 15 percent and to reach a maximum of about 30 percent at high density.
Simulations of heptane drops in nitrogen under zero gravity and at high pressure were performed using the model in order to investigate the sensitivities of predicted drop diameters to uncertainties in diffusivity values. The results of the simulations showed that the root-mean-square deviations of relative drop diameters were approximately one-fourth of the corresponding imposed relative changes in diffusivities.
This work was done by Josette Bellan and Kenneth Harstad of Caltech for NASA's Jet Propulsion Laboratory. For further information, access the Technical Support Package (TSP) free on-line at www.techbriefs.com/tsp under the Physical Sciences category. NPO-30409
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Calculating Mass Diffusion in High-Pressure Binary Fluids
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