• Proceedings of the Membrane Society of Korea Conference
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• 1995.10a
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• pp.43-44
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• 1995

The diffusion behavior of liquid into polymer has been described by Fick's law, but the departure from Fickian diffusion is frequently found. In this study, 'noble' expressions for the rates of relaxation and sorption are introduced to eliminate these limitations. The ralaxation-sorption coupled mechanism model are based on the possibility of contacting liquid molecule and the active site which has the numerical concept of free volume. The concept has an analogy of reaction rate expressed by the possibility of collision with molecules and used in adsorption and reactive extraction etc. The new model simulated by Rungc-Kutta method for initial-value problem and Fickian diffusion is caompared with experimental data. The results show that the ralaxation-sorption coupled mechanism is able to account well for Fickian and non-Fickian sorption behavior including sigmoid and two-stage. In addition, this model has a chance of expansion to multi-component sorption with ease.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.36 no.11
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• pp.1297-1303
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• 2012

In this paper, the standard procedures for measuring the moisture sorption properties of thin polymeric materials such as polyethylene terephthalate (PET) by using the thermo-gravimetric method to characterize the moisture diffusion in the polymer are presented, and the sorption properties are quantified. The moisture diffusivity and solubility are characterized to investigate the effect of temperature and humidity on the moisture sorption properties according to the Arrhenius equation. The validation of the obtained sorption properties using thermogravimetry is discussed with the measured permeability based on Fickian diffusion. The nonlinear behavior of the concentration dependent moisture diffusion is investigated experimentally, and the nonlinearity is characterized numerically for the case of having an interface with an inorganic material such as a metal. The Fickian/Non-Fickian model based on the obtained moisture sorption properties is compared and discussed.

• Proceedings of the Membrane Society of Korea Conference
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• 1996.04a
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• pp.34-35
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• 1996

The diffusional behavior of many non-solvents in glassy or semicrystalline polymers cannot be adequately described by a concentration-dependent form of Fick's law, especially when mass transfer is coupled with structural changes. Many mathematical models have been devised to interprete non-Fickian diffusion dominated by relaxation kinetics. In formulation of non-Fickian diffusion mathematics, therefore, the most important factor to consider is how relaxation effects can influence the governing constitutive equation and boundary conditions. That is, relaxation parameters can be accommodated by variable boundary conditions or a modified continuity equation, or both, depending on specific systems and conditions (Frish, 1980). Accoring to Astarita and Nicolais (1983), the model equations can be broadly categorized as continuous or discontinuous. Continuous model equations encompass phenomena where the structural change takes place gradually over the whole volume of the polymer sample (Crank, 1953; Long and Richman, 1961; Berens and Hopfenberg, 1978). On the other hand, discontinuous model equations deal with the phenomena where the morphological change appears to be abrupt (Li, 1984). Four mathematical models with different relaxation parameters were applied to fit the anomalous sorption data observed in fluoropolymers (PVDF, ECTFE). The fitted result for PVDF-benzene sorption data is shown in Fig. 1.

• Journal of Korea Water Resources Association
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• v.30 no.6
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• pp.621-628
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• 1997

Excavation works on stream beds have been done for various reasons including aggregate collection, sediment dredging, bridge constructions, or laying pipes under the ground. These activities may cause significant loadings of SS (suspended solids) resulting in water pollution and other detrimental effects to the surrounding environment. This research investigates application potential of a fickian diffustion model, derived from two dimensional advection-diffusion equation through some simplifying assumptions, as a planning tool for the estimation of SS loadings from excavation works and evaluation fo pollution prevention measures in case that sophisticated numerical simulation models are not applicable due to various practical reasons. Through a case study of the Juncheon stream in the Donghae City on the Kangwondo Province, this study demonstrates applicability of the fickian diffustion model as a practical method for the preliminary estimation of Ss loadings from excavation works and evaluation of performance of fabrics made of synthetic fiber for the reduction of downstream SS concentration with deficient field data.

• Membrane Journal
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• v.10 no.3
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• pp.139-147
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• 2000

Non-Fickian (or anomalous) diffusion was observed in transient sorption of aromatic solvents(such as benzene, toluene, and chlorobenzene) in fluoropolymers (such as ETFE, ECTFE and PVDF). In this study, five other transient sorption models (Crank, Long ＆ Richman, Berens ＆ Hopfenberg, Neogi, Li) based on Fick's law were employed to fit the anomalous sorption data for aromatic solvents. The adjustable parameters were determined by least square analysis of the measured and predicted fractional uptake. For ETFE sorption data slightly deviating from Fickian behavior, all the models exhibited satisfactory results in fitting the anomalous sorption data. In particular, Neogj model predicted intrinsic diffusivity (0.4～0.8$\times$10$^{-5}$ $\textrm{cm}^2$/day) and equilibrium diffusivity (0.13～0.31$\times$10$^{-4}$ $\textrm{cm}^2$/day) as well as relaxation kinetics related to non-Fickain diffusion. For a typical sigmoidal sorption behavior in PVDF, only Crank's model could give the reasonable evaluation on transport properties. The ratio of intial diffusivity (D$_{i}$) to final equilibrium diffusivity (D$_{\infty}$) was ranged from 80 to 200. For the final stage of uptake In ECTFE with drastic acceleration, all the models exhibited significant deviations from the sorption data. New diffusion models based on thermodynamics and continuum mechanics should be employed to get valuable information on transport properties as well as relaxation kinetics coupled with non-Fickian diffusion.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.69-78
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• 2004

This paper treats the conditions for the existence of rotating wave solutions of a system modelling the behavior of students in graduate programs at neighbouring universities near each other which is a modified form of the model proposed by Scheurle and Seydel. We assume that both types of individuals are continuously distributed throughout a bounded two-dimension spatial domain of two types (circle and annulus), across whose boundaries there is no migration, and which simultaneously undergo simple (Fickian) diffusion. We will show that at a critical value of a system-parameter bifurcation takes place: a rotating wave solution arises.

• Fisheries and Aquatic Sciences
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• v.7 no.2
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• pp.90-95
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• 2004

An analytical model for predicting the convection-diffusion of solute dumped in a homogeneous open sea of constant water depth has been developed in a time-integral form. The model incorporates spatially uniform, uni-directional, mean and oscillatory currents for horizontal convection, the settling velocity for the vertical convection, and the anisotropic turbulent diffusion. Two transformations were introduced to reduce the convection-diffusion equation to the Fickian type diffusion equation, and then the Galerkin method was then applied via the expansion of eigenfunctions over the water column derived from the Sturm-Liouville problem. A series of calculations has been performed to demonstrate the applicability of the model.

• KOREAN JOURNAL OF PACKAGING SCIENCE & TECHNOLOGY
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• v.4 no.1
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• pp.11-16
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• 1997

Sorption studies involving the sorption of n-propanol by an Amorphous Nylon(Nylon 6I/6T) were carried out as a function of sorbate vapor activity at $23^{\circ}C$. Vapor activity levels from 0.035 to 0.91 were investigated to evaluate the concentration dependency of sorption mechanism. Sorption behavior of propanol by Nylon 6I/6T showed distinctive two mode sorption phenomena as a function of Vapor activity. At Vapor activity levels below a=0.11, equilibrium sorption was achieved within a short period of time(less than 20hrs), which can be interpreted as following a Fickian diffusion model. A Langmuir-Flory-Muggins Dual Mode Sorption model can also be applied at these concentration levels. However, for Vapor activities above a=0.11, the sorption process appeared to be non-Fickian and resulted in a lack of equilibrium being attained.

• Journal of Korea Soil Environment Society
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• v.4 no.2
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• pp.137-147
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• 1999

Fluidized-bed thermal desorber coupled with a heat pipe was investigated for the remediation of soil contaminated with diesel oils. Thermal gravimetric analysis by Cahn-balance indicated that the desorption of diesel oils from the soil particles was mainly governed by the internal diffusion at low concentration of less than 0.5 wt. % of oils in the soil particles. In fluidized-bed experiments. increase of fluidizing gas velocity reduced the residual oils of the contaminated soils, the increase of soil feed rate decreased efficiency of fluidized-bed desorber. A mathematical model was developed by incorporating Fickian diffusion kinetics into the Kunii-Levenspiel model Simulation results showed reasonable agreement for the performance of fluidized-bed thermal desorber.

• Applied Chemistry for Engineering
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• v.24 no.6
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• pp.621-627
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• 2013

In order to apply eco-friendly poly(propylene carbonate) (PPC) into barrier packaging materials, six different PPC/exfoliated graphite (EFG) nanocomposite films with different EFG were successfully prepared by a solution blending method. Their water sorption behavior was gravimetrically investigated as a function of the EFG content and interpreted with respect to their chemical structure and morphology. The water sorption isotherms were reasonably well fitted by Fickian diffusion model, regardless of morphological heterogeneities. With increasing the EFG content, the diffusion coefficient and water uptake decreased from $12.5{\times}10^{-10}cm^2sec^{-1}$ to $7.2{\times}10^{-10}cm^2sec^{-1}$ and from 8.9 wt% to 4.2 wt%, respectively, which indicates that the moisture resistance capacity of PPC was greatly enhanced by incorporating EFG into PPC. The enhanced water barrier property of the PPC/EFG nanocomposite films with the high aspect ratio EFG makes them potential candidates for versatile packaging applications. However, to maximize the performance of the nanocomposite films, further researches are required to increase the compatibility of EFG in the PPC matrix.