• Applied Chemistry for Engineering
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• v.7 no.6
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• pp.1043-1052
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• 1996

Supercritical fluid chromatographic method was recommended as an alternative separation method of fatty acids of the conventional method such as distillation or extraction. Although diffusion characteristics are varied by the carbon numbers and the degree of unsaturation of fatty acids, the quantitative data were so rare that the commercialization of supercritical fluid chromatographic method has been hindered. In this study, diffusion coefficients of fatty acids which are differently unsaturated are measured by CPB method in the range of 308.15K to 328.15K and 13MPa to 17MPa in supercritical carbon dioxide. A decrease in the binary diffusion coefficient was observed with an increase in temperature and pressure. Also, the decrease in the binary diffusion coefficient with increasing fluid density and viscosity. Wilke-Chang equation, Funazukuri empirical equation, and Matthews-Akgerman equation are used to correlate the experimental diffusion coefficients of fatty acids in supercritical carbon dioxide. Among the various theoretical equations, Matthews-Akgerman equation based on RHS theory was suggested as a more successful correlation model with experimental data.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.3
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• pp.197-207
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• 2013

The Cahn-Hilliard equation was proposed as a phenomenological model for describing the process of phase separation of a binary alloy. The equation has been applied to many physical applications such as amorphological instability caused by elastic non-equilibrium, image inpainting, two- and three-phase fluid flow, phase separation, flow visualization and the formation of the quantum dots. To solve the Cahn-Hillard equation, many numerical methods have been proposed such as the explicit Euler's, the implicit Euler's, the Crank-Nicolson, the semi-implicit Euler's, the linearly stabilized splitting and the non-linearly stabilized splitting schemes. In this paper, we investigate each scheme in finite-difference schemes by comparing their performances, especially stability and efficiency. Except the explicit Euler's method, we use the fast solver which is called a multigrid method. Our numerical investigation shows that the linearly stabilized stabilized splitting scheme is not unconditionally gradient stable in time unlike the known result. And the Crank-Nicolson scheme is accurate but unstable in time, whereas the non-linearly stabilized splitting scheme has advantage over other schemes on the time step restriction.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.18 no.10
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• pp.136-152
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• 2017

The thermodynamic models, PC-SAFT (Perturbed-Chain Statistical Associated Fluid Theory) state equation and the Two-model approach liquid activity coefficient model NRTL (Non Random Two Liquid) + Henry + Peng-Robinson, for modeling the Rectisol process using methanol aqueous solution as the $CO_2$ removal solvent were compared. In addition, to determine the new binary interaction parameters of the PC-SAFT state equations and the Henry's constant of the two-model approach, absorption equilibrium experiments between carbon dioxide and methanol at 273.25K and 262.35K were carried out and regression analysis was performed. The accuracy of the newly determined parameters was verified through the regression results of the experimental data. These model equations and validated parameters were used to model the carbon dioxide removal process. In the case of using the two-model approach, the methanol solvent flow rate required to remove 99.00% of $CO_2$ was estimated to be approximately 43.72% higher, the cooling water consumption in the distillation tower was 39.22% higher, and the steam consumption was 43.09% higher than that using PC-SAFT EOS. In conclusion, the Rectisol process operating under high pressure was designed to be larger than that using the PC-SAFT state equation when modeled using the liquid activity coefficient model equation with Henry's relation. For this reason, if the quantity of low-solubility gas components dissolved in a liquid at a constant temperature is proportional to the partial pressure of the gas phase, the carbon dioxide with high solubility in methanol does not predict the absorption characteristics between methanol and carbon dioxide.