Transactions of the Korean Society of Mechanical Engineers B (대한기계학회논문집B)

The Korean Society of Mechanical Engineers (대한기계학회)
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Derivation of the First-Order Mass-Transfer Equation for a Diffusion-Dominated Zone of a 2-D Pore

2차원으로 구현한 다공성 매질의 확산주도영역에 관한 1차 물질이동 방정식의 유도

  • Kim, Young-Woo (Department of Automotive Engineering, Hoseo University) ;
  • Seo, Byong-Min (Department of Environmental Engineering, Hoseo University) ;
  • Hwang, Seung-Min (Graduate School of Venture, Department of Health Environment, Hoseo University) ;
  • Park, Cha-Sik (Department of Automotive Engineering, Hoseo University)
  • 김영우 (호서대학교 자동차공학과) ;
  • 서병민 (호서대학교 환경공학과) ;
  • 황승민 (호서대학교 벤처전문대학원) ;
  • 박차식 (호서대학교 자동차공학과)
  • Published : 2010.02.01
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Abstract

A new analytic solution was derived for the diffusion into or from an immobile zone of a rectangular 2-D pore. For a long time, the new solution converges to a traditional mobile-immobile zone (MIM) model, but only if the latter is used with an apparent initial concentration that is smaller by almost 20% than the true one. This is the tradeoff for using a simple MIM model instead of an exact model based on the diffusion equation. The mass-transfer coefficient was found to be constant for a sufficiently long time; it was proportional to the molecular diffusion and inversely proportional to the square of the pore depth. The mass-transfer coefficient was time-dependent for a sufficiently short time and may be significantly larger than its asymptotic value.

다공성 매질상에서 유체와 용질의 이동은 Mobile zone과 Immobile zone으로 분리해서 분석하는 Mobile-Immobile Zone Model을 이용하여 쉽게 현상을 구현할 수 있었으나 본 연구에서는 2차원 4각형태의 pore 상에서 확산주도영역(Immobile zone)으로 들어가고 나오는 용질의 확산에 관한 새로운 Analytic solution을 유도하여 기존 MIM Zone model과 비교 분석하였다. 새롭게 유도된 Analytic solution은 기존의 MIM model 과 비교했을때 충분히 오랜시간이 경과한 후에는 해의 일치를 보이지만 MIM model의 경우 초기 농도값이 주입된 실제 농도보다 약 20 % 낮게 나타난다. Mass-transfer 계수, $\alpha$는 일반적으로 시간의 흐름에 따라 감소하게 되는데 일정 시간이 경과하게 되면 안정화 되고 일정함을 유지하며 그 시간은 무차원으로 약 ${\tau}_0=0.15$이다. 또한 $\alpha$는 분자확산과 비례하며 Immobile 영역의 깊이와 반비례하는 반면 작은 시간이 경과한 후에는 시간에 종속되어진다.

Keywords

References

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  1. First-Order Mass Transfer in a Diffusion-Dominated (Immobile) Zone of an Axisymmetric Pore: Semi-Analytic Solution and Its Limitations vol.11, pp.11, 2010, https://doi.org/10.5762/KAIS.2010.11.11.4664