용질입자들의 임의적인 자리바꿈과 상호교환의 추계적 섭동에 기초한 깁스 앙상블 몬테카를로(Gibbs ensemble Monte Carlo) 수치모사를 수행하여 슬릿(slit)형 기공과 벌크용액에서의 농도분포를 구하였다. 기본적으로 용질입자들의 한정된 공간에서의 운동은 브라운 운동과 주위의 유체의 움직임에 따른 결과인데, 점근조화(asymptotic matching)법에 기초하여 최근에 새로이 제시된 확산제한인자(diffusive hindrance factor)를 적용하였다. 장거리(long-range) 정전기적 상호작용 에너지는 선형 포아슨-볼쯔만식의 해를 정확히 제공할 수 있는 특이점 방법에 의해 산출하였다. 용질입자들과 기공벽면의 하전여부에 상관없이 입자농도의 증가에 따른 입자-입자간의 상호작용이 기공벽면부근에서의 농도 상승을 가져옴을 확인하였다. 주어진 기공과 입자크기에서의 제한적 확산계수(hindered diffusion coefficient)값은, 입자농도와 용액 중의 이온농도가 증가함에 따라 입자-벽면과 입자-입자간 상호작용의 복합적인 영향으로 증가하였다

Concentration profiles of spherical solutes both in a slit pore and in a bulk are obtained for a wide range of solute concentrations by employing the Gibbs ensemble Monte Carlo scheme, in which two kinds of stochastic perturbations are performed with a random displacement of solutes and random interchanges of solutes. In principle, the solute particle is in motion due to a combination of Brownian movement and convective displacement by the surrounding fluid. The hydrodynamic coefficient for diffusive hindrance factor applied in this study is the recently provided result using an asymptotic matching technique. The long-range electrostatic interactions between the particle and the adjacent wall and between the particles are determined by solving with the singularity method, which provides accurate solutions to the linearized Poisson-Boltzmann equation. The obtained concentration profiles indicate that, whether both solutes and pores are uncharged or of like charge, solute-solute interactions promote concentration buildup near the pore wall. Due to the interplay of solute-solute and solute-wall interactions associated with repulsive energy, the hindered diffusion coefficient of charged system is predicted to increase with increasing solute concentration or ionic strength of solution, for a given relative pore size. Present investigation with the Gibbs ensemble Monte Carlo has made it possible to provide a proper estimation for the charged systems at non-dilute concentrations.

Hindered Diffusion Monte Carlo Simulation Slit Pore Electrostatic Interaction Asymptotic Matching

Davidson MG, Deen WM, Macromolecules, 21, 3474 (1988) 
Opong WS, Zydney AL, AIChE J., 37, 1497 (1991) 
Pujar NS, Zydney AL, Ind. Eng. Chem. Res., 33(10), 2473 (1994) 
Schnabel R, Langer P, J. Chromatogr., 544, 137 (1991) 
Renkin EM, J. Gen. Physiol., 38, 225 (1954)
Deen WM, AIChE J., 33, 1409 (1987) 
Brenner H, Gaydos LJ, J. Colloid Interface Sci., 58, 312 (1977) 
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) 
Nitsche JM, Balgi G, Ind. Eng. Chem. Res., 33(9), 2242 (1994) 
Nitsche JM, Ind. Eng. Chem. Res., 34(10), 3606 (1995) 
Pawar Y, Anderson JL, Ind. Eng. Chem. Res., 32, 743 (1993) 
vande Ven TGM, "Colloidal Hydrohynamics," Academic Press, London (1989)
Chun MS, Phillips RJ, AIChE J., 43(5), 1194 (1997) 
Glandt ED, AIChE J., 27, 51 (1981) 
Post AJ, J. Colloid Interface Sci., 129, 451 (1989) 
Panagiotopoulos AZ, Quirke N, Stapleton M, Tildesley DJ, Mol. Phys., 63, 527 (1988) 
de Pablo JJ, Prausnitz JM, Fluid Phase Equilib., 53, 177 (1989) 
Green DG, Jackson G, Demiguel E, Rull LF, J. Chem. Phys., 101(4), 3190 (1994) 
McQuarrie DA, "Statistical Mechanics," Happer & Row, New York (1976)
Suh SH, Park HK, Korean J. Chem. Eng., 11(3), 198 (1994)
Allen MP, Tildesley DJ, "Computer Simulation of Liquids," Oxford Univ. Press, New York (1987)
Chun MS, Park OO, HWAHAK KONGHAK, 30(2), 200 (1992)
Won YS, Yoon BJ, HWAHAK KONGHAK, 34(1), 1 (1996)
Phillips RJ, J. Colloid Interface Sci., 175(2), 386 (1995) 
Dabros T, J. Fluid Mech., 156, 1 (1985) 
Smith FG, Deen WM, J. Colloid Interface Sci., 91, 571 (1983) 
Happel J, Brenner H, "Low Reynolds Number Hydrodynamics: with Special Applications to Particulate Media," Martinus Nijhoff, The Hague (1983)
Weinbaum S, Lect. Math. Life Sci., 14, 119 (1981)