좁은 막기공내에서의 확산이 자유로운 벌크에서의 확산보다 낮아지는 제한확산(hindered diffusion)현상은 용질입자와 기공의 크기는 물론이고 입자의 농도와 이온화 세기(ionic strength)에도 영향을 받는다. 씰린더형 막기공에서 진한 농도를 갖는 라텍스입자의 제한확산 현상에 대한 실험연구를 수행하였다. 확산쎌(diffusion cell)에서 시간이 지남에 따른 입자농도의 변화에 대한 물질수지 관계식과 물질전달 원리를 실험결과에 적용하여, 물질전달계수(mass transfer coefficient)와 제한확산계수(hindered diffusion coefficient)를 산출하였다. 일정한 이온화 세기에서의 입자농도의 영향을 살펴보기 위해 입자와 기공크기의 비(=λ)가 약 0.33인 범위에 걸쳐 라텍스 농도를 20 vol%까지 증가시켰다. 실험결과, λ가 작을수록 그리고 주어진 동일한 λ에서는 라텍스 농도가 증가할수록 제한확산계수는 증가하였다. 이것은 막기공을 통한 입사의 물질전달계수의 산출결과에서도 확인할 수 있듯이, 입자농도가 증가하면 라텍스입자와 기공 벽면간의 정전반발력(elec-trostatic repulsion)보다 라텍스입자들 상호간의 정전반발력이 우세하게 작용되어 벌크에서 막기공 내부로의 확산이 활발히 진행된 결과이다. 한편, 1 vol%라텍스 농도에 대해 KCI용액의 이온화 세기를 0.1,0.01,0.001 M로 변화시켜 얻은 확산실험의 결과는 이온화 세기가 감소할수록 제한확산계수도 감소하였다. 이 거동은 비교적 묽은 라텍스 농도에서 이온화 세기가 감소하면, 라텍스입자와 기공 벽면간의 정전반발력이 크게 증가된 영향으로 인하여 벌크에서 기긍으로의 확산이 억제되어 나타난 현상을 의미한다.

The diffusion coefficient of a solute particle within a membrane pore of comparable size is found to be less than its value in bulk solution. This hindered diffusion obviously depends on the sizes of solute and pore, and it is known both the solute concentration and the solution ionic strength are considerably influenced, although very little experimental data is available. In order to examine this fact, the diffusion coefficient of latex particle through the track-etched membranes with we11-defined cylindrical pore geometry has been measured by using diffusion cell apparatus. Note that both the relation of mass balance for the latex concentration and the principle of diffusional mass transfer across membranes are applied, which were provided in the previous studies, for the analysis of particle diffusion coefficient in the pore. Based on the Stokes-Einstein relation with virial type for the solute concentration, the bulk diffusion coefficient of latex for any KCl concentrations can be effectively estimated. The solute concentration dependence of hindered diffusion as a function of relative solute size has been observed, from which the hindered diffusion increases with increasing of solute concentration. This behavior suggests that, with increase of solute concentration, the repulsive interaction between a pore wall and a latex particle becomes strongly important than that of between pairs of latex particles. Therefore, as expected from the estimation of mass transfer coefficient, the particles are increasingly diffused firm bulk to pore region. Experimental results for latex concentration of 1 vol% showed that the hindered diffusion coefficient is decreased when the ionic strength of KCl is reduced ranging from 0.1 to 0.001 M. When the ionic strength decreases, the corresponding repulsion increment between a pore wall and a particle results in more restricted diffusion.

Hindered Diffusion Track-Etched Pores Polystyrene Latex Mass Transfer Coefficient Colloidal Interaction

Bohrer MP, Patterson GD, Carroll PJ, Macromolecules, 17, 1170 (1984) 
Deen WM, AIChE J., 33, 1409 (1987) 
Kim JT, Anderson JL, J. Membr. Sci., 47, 163 (1989) 
Phillips RJ, Deen WM, Brady JF, J. Colloid Interface Sci., 139, 369 (1990)
Zeman LJ, Zydney AL, "Microfiltration and Ultrafiltration: Principles and Application," Marcel Dekker, NY (1996)
Nitsche JM, Ind. Eng. Chem. Res., 34(10), 3606 (1995) 
Russel WB, Saville DA, Schowalter WR, "Colloidal Dispersions," Cambridge Univ. Press, NY (1989)
Malone DM, Anderson JL, Chem. Eng. Sci., 33, 1429 (1978) 
Baltus RE, Anderson JL, Chem. Eng. Sci., 38, 1959 (1983) 
Lin NP, Deen WM, J. Colloid Interface Sci., 153, 483 (1992) 
Mitchell BD, Deen WM, J. Membr. Sci., 19, 75 (1984) 
Chun MS, Phillips RJ, AIChE J., 43(5), 1194 (1997) 
Chun MS, HWAHAK KONGHAK, 36(2), 241 (1998)
Chun MS, Park OO, HWAHAK KONGHAK, 30(2), 200 (1992)
Imtiaz AK, Anderson JL, Ind. Eng. Chem. Res., 27, 866 (1988) 
Malone DM, Anderson JL, AIChE J., 23, 177 (1977) 
Deen WM, Bohrer MP, Epstein NB, AIChE J., 27, 952 (1981) 
Boher MP, Ind. Eng. Chem. Fundam., 22, 72 (1983) 
Batchelor GK, J. Fluid Mech., 74, 1 (1976) 
Anderson JL, Rauh F, Morales A, J. Phys. Chem., 82, 608 (1978)