한외여과에서 농도분극층의 물질전달 특성 해석[I]-삼투압 모델과 경계층저항 모델의 비교-

염경호; 김우식

HWAHAK KONGHAK, Vol.31, No.6, 813-823, December, 1993

Analysis of Mass Transfer Characteristics in Concentration Polarization Layer of Ultrafiltration[I]-Comparison of Osmotic Pressure Model and Boundary Layer Resistance Model-

염경호, 김우식

초록

막표면에 형성된 농도분극층내 거대분자 용액의 거동 상태를 중심으로 삼투압 모델과 경계층저항 모델을 비교ㆍ고찰하여, 두 모델의 적용 가능한 한외여과 영역을 제시하였다. 모델의 비교를 위해 polysulfone 막(분획분자량:3,000)을 이용해 막의 분획분자량과 유사한 분자량을 갖는 PEG(M_w=4,010) 용액과 큰 분자량을 갖는 dextran(M_W=70,000) 용액의 한외여과 실험을 수행하여 막투과량과 용질 배제도를 측정하였다. 이 결과 삼투압 모델은 막의 분획분자량과 유사한 분자량을 갖는 거대분자로부터 큰 분자량을 갖는 거대분자에 이르기까지 한외여과의 전체 영역에 대해 적용이 가능하였다. 그러나 경계층저항 모델은 농도분극율과 용질 배제도가 높아 농도분극층내 거대분자 용액이 semi-dilute 한 상태의 거동을 나타내는, 막의 분획분자량 보다 큰 분자량을 갖는 거대분자의 경우에만 적용이 가능하였다.

On the basis of the macromolecular solution behavior in the concentration polarization layer formed on the membrane surface, the comparison of the osmotic pressure model and the boundary layer resistance model was investigated. The applicable ultrafiltration range was suggested to these two models respectively. The permeate flux and solute rejection during the ultrafiltration of macromolecular solutions such as PEG(M_w=4,010, similar to the cut-off of membrane) and dextran(M_w=70,000, higher than the cut-off of membrane) solutions were measured with polysulfone membranes(MWCO : 3,000). The osmotic pres-sure model was capable of predicting the complete ultrafiltration range obtained using low molecular weight (similar to the cut-off of membrane) and high molecular weight macromolecular solutions. Whereas the boun-dary layer resistance model was only capable of analyzing the ultrafiltration of high molecular weight macro-molecular solution, i.e., dextran which represented high concentration polarization modulus and solute rejec-tion, and formated the semi-dilute solution behavior in the concentration polarization layer.

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[2] Michaels AS, Chem. Eng. Prog., 64, 31 (1968)

[3] Porter MC, Ind. Eng. Chem. Prod. Res. Dev., 11, 234 (1972)

[4] Gekas V, Hallstrom B, J. Membr. Sci., 30, 153 (1987)

[5] Gekas V, Olund K, J. Membr. Sci., 37, 145 (1988)

[6] Blatt WF, Dravid A, Michales AS, Nelson L, Membrane Science and Technology, Flinn, J.E., Ed., Plenum Press, New York, 47 (1970)

[7] Nakao SI, Nomura T, Kimura S, AIChE J., 25, 615 (1979)

[8] Wijmans JG, Nakao S, Smolders CA, J. Membr. Sci., 20, 115 (1984)

[9] Vilker VL, Colton CK, Smith KA, Green DL, J. Membr. Sci., 20, 63 (1984)

[10] Goldsmith RL, Ind. Eng. Chem. Fundam., 10, 113 (1971)

[11] Kozinski AA, Lightfoot EN, AIChE J., 18, 1030 (1972)

[12] Wijmans JG, Nakao SI, VanDenBerg JWA, Troelstra FR, Smolders CA, J. Membr. Sci., 22, 117 (1985)

[13] Nakao SI, Wijmans JG, Smolders CA, J. Membr. Sci., 26, 165 (1986)

[14] Colton CK, Friedman S, Wilson DE, Lees RS, J. Clin. Invest., 51, 2472 (1972)

[15] DeGennes PG, "Scaling Concepts in Polymer Physics," Cornell Univ. Press, Ithaca, New York, 69 (1979)

[16] Roots J,Nystrom B, J. Polym. Sci. B: Polym. Phys., 19, 479 (1981)

[17] Flory PJ, "Principles of Polymer Chemistry," Cornell Univ. Press, Ithaca, New York, 347 (1971)

[18] Wales M, Synthetic Membranes, Vol. II, Turbak, A.F., ed., ACS Symp., Ser, No. 154, Amer. Chem. Soc., Washington, D.C., 159 (1981)

[19] Mijnlieff PF, Jaspers WJ, Trans. Faraday Soc., 67, 1837 (1971)

[20] Ring W, Cantow HJ, Holtrup H, Eur. Polym. J., 2, 151 (1966)

[21] Senti FR, Hellman NN, Ludwig NH, Babcock GE, Tobin R, Glass CA, Lamberts BI, J. Polym. Sci., 17, 527 (1955)

[22] Granath KA, J. Colloid Sci., 13, 308 (1958)

[23] Hsieh FH, Matsuura T, Sourirajan S, J. Appl. Polym. Sci., 23, 561 (1979)

[24] Frigon RP, Leypoidt JK, Uyeji S, Handerson LW, Anal. Chem., 55, 1349 (1983)

[25] Jonsson G, Desalination, 51, 61 (1984)

[26] Lance-Gomez FT, J. Appl. Polym. Sci., 31, 333 (1986)

[27] Youm KH, Kim WS, J. Chem. Eng. Jpn., 24, 1 (1991)

[28] Mystrom B, Roots J, J. Macromol. Sci.-Rev. Macromol. Chem. Phys., C19, 35 (1980)

[29] Long TD, Anderson JL, J. Polym. Sci. B: Polym. Phys., 22, 1261 (1984)

[30] Nguyen QT, Neel J, J. Membr. Sci., 14, 111 (1983)

[31] Spiegler KS, Kedem O, Desalination, 1, 311 (1966)

[32] Marquardt DW, J. Soc. Ind. Appl. Math., 11, 431 (1963)