• Title/Summary/Keyword: Dispersion equation

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Dispersion Polymerization of Acrylamide in the Media of t-Butyl Alcohol/$H_2O$ Mixtures (t-Butyl Alcohol/$H_2O$ 혼합 용매에서 아크릴아미드의 분산중합)

  • 이기창;이성은;송봉근;이동주
    • Polymer(Korea)
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    • v.24 no.5
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    • pp.629-637
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    • 2000
  • Dispersion polymerization of acrylamide in the media of t-butyl alcoho1/$H_2O$ mixtures at 30~5$0^{\circ}C$ in the presence of hydroxypropyl cellulose and ammonium persulfate as steric stabilizer and initiator, respectively, was carried out. It was studied the effects of concentrations of initiator and steric stabilizer, amount of monomer, polymerization temperature, t-butyl alcohol/$H_2O$ ratio, concentration of crosslinker, purification of monomer and nitrogen purge on the particle size of the resulting acrylamide latices and molecular weight of the latex-poly(acrylamide). In this study, poly(acrylamide) latices of 0.1~0.5 ${\mu}{\textrm}{m}$ with 470000~2080000 in (equation omitted) were prepared and the resulting PAM latices were all dissolved in water in stantly.

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The Determination of Group Velocity of Lamb Wave So Mode in Composite Plates with Anisotropy (이방성 복합재료 판에서 램파 $S_0$ 모드의 군속도 결정)

  • Rhee, Sang-Ho;Lee, Jeong-Ki;Lee, Jung-Ju
    • Journal of the Korean Society for Nondestructive Testing
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    • v.26 no.4
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    • pp.239-245
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    • 2006
  • Experimentally measured Lamb wave group velocities in composite materials with anisotropic characteristics are not accorded with the theoretical group velocities as calculated with the Lamb wave dispersion equation. This discrepancy arises from the fact that the angle between the group velocity direction and the phase velocity direction in anisotropic materials exists. Wave propagation in a composite material with anisotropic characteristics should be considered with respect to magnitude in addition to direction. In this study, $S_0$ mode phase velocity dispersion corves are depicted with the variation of degree with respect to the fiber direction using a Lamb wave dispersion relation in the unidirectional, bidirectional, and quasi-isotropic composite plates. Slowness surface is sketched by the reciprocal value of the phase velocity curves. The magnitude and direction of the group velocity are calculated from the slowness surface. The theoretically determined group velocity, which is calculated from the slowness surface, Is compared with experimentally measured group velocities. The proposed method shows good agreements with theoretical and experimental results.

An experimental study on the correlation of hydraulic mean radius and hydrodispersive parameters in rockfill porous media (자갈 다공성매질에서 수리평균반경과 수리분산 매개변수의 상관성에 관한 실험적 연구)

  • Han, Ilyeong;Lee, Jaejoung;Kim, Gyoo Bum
    • Journal of Korea Water Resources Association
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    • v.54 no.11
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    • pp.863-873
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    • 2021
  • The mechanical dispersion which dominates solute transport in porous media is caused by the difference in flow velocity within pores. Longitudinal dispersion coefficient and longitudinal dispersivity that are hydro-dispersive parameters of advection-dispersion equation can only be obtained by experiment. Hydraulic mean radius that represents the amount and intensity of flowing water within pores can be obtained by the formula using the factors for physical properties. A slug injection test was conducted and a power type empirical formula for obtaining a longitudinal dispersivity using a hydraulic mean radius in rockfill porous media was derived. It is possible to obtain the longitudinal dispersivity depending on transport distance because it contains a formula for a scale constant, and expected to be applicable to waterways filled with homogeneous gravel and small flow rate.

The Group Velocity of Lamb Wave Generated by the one Source in Unidirectional Laminated Composite Plates (일방향 적층 복합재료 판에서 한 음원에서 발생된 램파의 군속도)

  • Lee Jeong-Ki;Rhee Sang-Ho
    • The Journal of the Acoustical Society of Korea
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    • v.25 no.3
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    • pp.107-112
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    • 2006
  • The elastic waves in a plate are dispersive waves due to the characteristics of Lamb waves. However, S0 symmetric mode is less dispersive in the frequency region below the first cut-off frequency. The wave Propagation velocities vary with the direction in anisotropic plates such as Carbon Fiber Reinforced Plastic (CFRP) Plates. The wave vector direction and energy flow vector direction are same in isotropic plates. However, the wave vector direction same as the phase velocity direction is not in accordance with the energy flow direction same as the group velocity direction in anisotropic plates. In this study. the dispersion curves or the phase velocity from anti-symmetric and symmetric Lamb wave dispersion equation are calculated for unidirectional laminated composite plate. Slowness surface is sketched using phase velocity under the first cut-off frequency. The direction and magnitude of group velocity are corrected with this slowness surface. The measured group velocities are in good agreement with the corrected group velocity curve except near the fiber direction zone which is called the cusp region.

Kinetic Behavior of Immobilized Tyrosinase on Carbon in a Simulated Packed-Bed Reactor (충전층에서 탄소에 고정시킨 Tyrosinase의 반응속도에 관한 연구)

  • Shin, Sun Kyoung;Kim, Kyeo-Keun
    • Analytical Science and Technology
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    • v.10 no.1
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    • pp.66-74
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    • 1997
  • Influence of the axial dispersion on immobilized enzyme catalytic bed was investigated in order to examine the kinetic behavior of the biocatalysis. The enzyme employed in this study was the tyrosinase(EC 1.14.18.1) immobilized on carbon support : this system requires two substrates of phenol and oxygen. This enzyme has potential application for phenol degradation in waste water. A simulated reactor was a packed-bed reactor of 2.54cm in diameter and 10cm long, loaded with the immobilized carbon particle with an average diameter of $550{\mu}m$. A phenol feed in the strength of 55.5mM(5220ppm) was used to observe the behavior of the immobilized enzyme column at three different dissolved oxygen levels of 0.08445mM(2.7ppm), 0.1689mM(5.4ppm) and 0.3378mM(9.5ppm) with the flow rates in the range of 60(1mL/s) to 180mL/min(3mL/s). Examination of the Biot number and Damkolher numbers of the immobilized system enables us to eliminate the contribution of external mass transfer to set of differential equations derived from the dispersion model. Solution of the equation was finally obtained numerically with the application of the Danckwert boundary conditions and the assumed zero-and first order rates on the non-linear two substrate enzyme kinetics. Higher conversion of phenol was observed at the low flow rates and at the higher oxygen concentration. Comparison of axial dispersion and plug flow model showed that no detectable difference was observed in the column outlet conversion between the axial and the plug flow models which was in complete agreement with the previous studies.

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A Study on the Flow and Dispersion in the Coastal Unconfined Aquifer (Development and Application of a Numerical Model) (해안지역 비피압 충적 대수층에서의 흐름 및 분산(수치모형의 개발 및 적용))

  • Kim, Sang Jun
    • Journal of Korea Water Resources Association
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    • v.49 no.1
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    • pp.61-72
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    • 2016
  • In Korea, the aquifers at the coastal areas are mostly shallow alluvial unconfined aquifers. To simulate the flow and dispersion in unconfined aquifer, a FDM model has been developed to solve the nonlinear Boussinesq equation. Related analysis and verification have been executed. The iteration method is used to solve the nonlinearity, and the model shows 3-D shape because it is a 2-D y model that consider the undulation of water table and bottom. For the verification of the model, the output of flow module is compared to the 1-D analytic solution of Lee (1989) which have the drawdown or uplift boundary condition, and the two results show almost the same value. and the mass balance of dispersion module shows about 10% error. The developed model can be used for the analysis and design of the flow and dispersion in the unconfined aquifers. The model has been applied to the estuary area of Ssangcheon watershed, and the parameters have been deduced as a result : hydraulic conductivity is 90 m/day, and longitudinal dispersivity is 15 m. And the analysis with these parameters shows that the wells are situated in the influence circle of each others except for No. 7 well. Groundwater discharge to sea is $3700m^3/day$. And the chlorine ion ($cl^-$) concentration at the pumping wells increase at least 1000 mg/L if groundwater dam is not exist, so the groundwater dam plays an important role for the prevention of sea water intrusion.

Prediction of Travel Time and Longitudinal Dispersion for Water Pollutant by Using Unit Concentration Response Function (단위오염도틀 이용한 하천 오염물질의 이동시간과 종확산 예측)

  • Kim, Soo-Jun;Kim, Hung-Soo;Kim, Byung-Sik;Seoh, Byung-Ha
    • Journal of Korea Water Resources Association
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    • v.39 no.5 s.166
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    • pp.395-403
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    • 2006
  • This study suggests the use of a simple method, called the unit concentration response function(UCRF) for predicting travel time and dispersion of pollutants with the minimum information of study area instead of numerical models which are widely used In the Previous studies. However, the numerical models require time-consuming, tedious effort, and many data sets. So we derive the UCRF using some components such as travel time, peak concentration, and passage time of pollutant etc. We use the regression equation for the estimations of components which were developed from the investigations of many river basins in USA. This study used the regression equaiton for the UCRF to the accident of Dichloromethane leak into the Nakdong River occurred on June 30, 1994 and applied the UCRF for the predictions of travel time and dispersion. The predictions were compared with the results by QUAL2E model. The results by the regression equaiton and QUAL2E model had a good agreement between observed and simulated concentrations. Therefore, the regression equation for the UCRF which can simply estimate travel time and concentration of pollutants showed its applicability for the ungaged basin.

Influence of impulsive line source and non-homogeneity on the propagation of SH-wave in an isotropic medium

  • Kakar, Rajneesh
    • Interaction and multiscale mechanics
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    • v.6 no.3
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    • pp.287-300
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    • 2013
  • In this paper, the effect of impulsive line on the propagation of shear waves in non-homogeneous elastic layer is investigated. The rigidity and density in the intermediate layer is assumed to vary quadratic as functions of depth. The dispersion equation is obtained by using the Fourier transform and Green's function technique. The study ends with the mathematical calculations for transmitted wave in the layer. These equations are in complete agreement with the classical results when the non-homogeneity parameters are neglected. Various curves are plotted to show the effects of non-homogeneities on shear waves in the intermediate layer.

Dispersion-Correction of ADCIRC Finite Element Model for the Simulation of Tsunami Propagation (지진해일 전파 모의를 위한 ADCIRC 유한요소모형의 분산보정)

  • 윤성범;임채호;윤기승;최병호
    • Proceedings of the Korean Society of Coastal and Ocean Engineers Conference
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    • 2002.08a
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    • pp.287-293
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    • 2002
  • 조석을 수치모의하기 위해 North carolina 대학의 R.A. Luettich와 Notre Dame 대학의 J.J. Westerink가 개발한 ADvanced CIRCulation model for oceanic, coastal and estuarine waters(ADCIRC) 유한요소모형 (Luettich, et al., 1992)은 수심 적분된 2 차원 모형(2DDI)과 3차원 모형(3DL)으로 구성되어 있는데, 그 중 2차원 ADCIRC 유한요소모형은 천수방정식에서 연속방정식과 운동방정식을 합성하여 수면변위에 대해 하나의 식으로 표현한 파동방정식(wave equation)을 지배방정식으로 사용하고 있다. (중략)

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Barotropic Shelf Waves Generated By Longshore Wind Stress

  • Lie, Heung-Jae
    • 한국해양학회지
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    • v.16 no.2
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    • pp.99-107
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    • 1981
  • A partial differential equation for the adjusted sea level, obtained from the long wave equations in shallow water, is reduced to a simpler one by the use of physically reasonable approximations based on the observations. The similar equation for the stream function indicates that shelf waves are generated by the longshore wind stress. This indication is in good agreement with the high correlation between the adjusted sea levels and the longshore wind stress. From the dispersion relationship and the boundary conditions, there exist a countable infinite number of modes which satisfy a first-order wave equations. The adjusted sea level for a given wind stress can easily be calculated by utilizing the convolution and the Fourier transformation. Some detailed solutions are presented here for sinusoidal and exponential wind stress.

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