Journal of the Korea Academia-Industrial cooperation Society (한국산학기술학회논문지)

The Korea Academia-Industrial cooperation Society (한국산학기술학회)
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First-Order Mass Transfer in a Diffusion-Dominated (Immobile) Zone of an Axisymmetric Pore: Semi-Analytic Solution and Its Limitations

대칭형 다공성 매질의 확산주도 영역에 관한 1차 물질이동 방정식

  • Kim, Young-Woo (Department of Automotive Engineering, Hoseo University) ;
  • Kang, Ki-jun (Department of Automotive Engineering, Hoseo University) ;
  • Cho, Jung-ho (Department of Chemical Engineering, Kongju National University) ;
  • Kabala, Zbigniew (Department of Civil and Environmental Engineering, Duke University)
  • 김영우 (호서대학교 자동차공학과) ;
  • 강기준 (호서대학교 자동차공학과) ;
  • 조정호 (공주대학교 화학공학부) ;
  • Received : 2010.09.03
  • Accepted : 2010.11.19
  • Published : 2010.11.30
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Abstract

Comparison of the classical mobile-immobile zone (MIM) model to the derived model led to several conclusions. If the MIM model is to be applied, the initial concentration in the immobile zone has to be down-scaled by a correction factor that is a function of pore geometry. The MIM model was valid only after sufficiently long time has passed, i.e., only after the diffusion front reaches the deepest pore wall in the immobile zone. The MIM mass-transfer coefficient $\alpha$, was inversely proportional to the square of the pore depth. Also it did not depend on the mobile-zone flow velocity, contrary to the number of laboratory and field observations. The classical MIM model displayed a rapid exponential decay of immobile-zone concentration. Meanwhile at large times, the newly derived model displayed similar exponential decay. This was contrary to the mounting evidence of power-law BTC tails observed in laboratory and field settings.

본 연구에서는 기존 MIM Zone model과 새로이 유도한 모델과 비교를 통해 몇가지 결론을 도출하였다. MIM model 이 적용되면 immobile 영역에서의 초기농도는 기공의 형태에 의해 달라지는 보정계수에 의해 실제농도보다 저평가되었으며 이는 오직 확산이 기공의 가장 깊은 부분까지 시행된 이후에 유효함을 확인하였다. 물질이동계수, $\alpha$는 기공의 깊이에 따라 반비례하며, 유동 구역의 유속에는 종속되어지지 않는다. 기존의 MIM model 은 확산주도영역의 농도가 급속하게 감소하는 현상을 보여주는데 새로이 유도된 모델의 경우도 충분한 시간이 경과한후 비슷한 현상을 보였으며 이는 기존의 여러 실험에서 관찰된 power-law BTC 의 상반되는 결과를 보여준다.

Keywords

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