A Numerical Analysis for Estimations of Osmotic Pressure of Colloidal Suspension and Gradient Diffusion Coefficient of Particles from Permeate Flux Experiments

투과플럭스 실험으로부터 콜로이드 서스펜션의 삼투압과 입자의 구배확산계수 산출을 위한 수치적 해석

  • 전명석 (한국과학기술원 Complex Fluids and Membrane 연구팀)
  • Published : 2002.06.01

Abstract

A novel methodology on the calculations of osmotic pressure and gradient diffusion coefficient has been provided ill the present study, by applying a succinct numerical analysis on the experimental results. Although both the osmotic pressure and the gradient diffusion coefficient represent a fundamental characteristic in related membrane filtrations such as microfiltration and ultrafiltration, neither theoretical analysis nor experiments can readily determine them. The osmotic pressure of colloidal suspension has been successfully determined from a relationship between the data of the time-dependent permeate flux, their numerical accumulations, and their numerical derivatives. It is obvious that the osmotic pressure is gradually increased, as the particle concentration increases. The thermodynamic coefficient was calculated from the numerical differentiation of the correlation equation of osmotic pressure, and the hydrodynamic coefficient was evaluated from the previously developed relation for an ordered system. Finally, the estimated gradient diffusion coefficient, which entirely depends on the particle concentration, was compared to the previous results obtained from the statistical mechanical simulations.

멤브레인 여과 실험에서 얻어진 데이터 처리에 간단한 수치해석을 적용하여 삼투압(osmotic pressure) 과 구배확산계수(gradient diffusion coefficient)를 도출하는 새로운 방법론을 제시하였다. 삼투압과 구배확산계수는 이론 및 실험적으로 쉽게 구할 수 없는 물리적 특성치로서 멤브레인 여과의 특성 규명에 중요하다. 모델 라텍스 콜로이드의 여과시간에 따른 투과플럭스(permeate flux) 값과 이에 대한 수치적분과 수치미분 데이터로부터 분산된 입자농도의 함수인 삼투압 관계식을 구했다. 이로부터 계산된 열역학적 계수(thermodynamic coefficient)는 입자농도가 증가할수록 감소하는 거동을 보였고, 여기에 기존에 제시되어 있는 수력학적 계수(hydrodynamic coefficient)를 도입하여 구배확산계수를 산출하였다. 아울러, 본 연구에서 계산된 입자농도에 따른 구배확산계수의 결과와 동일한 멤브레인과 라텍스 콜로이드의 여과에 대해서 기존에 통계역학적 시뮬레이션으로 예측한 결과를 비교하였다.

Keywords

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