점탄성 용액의 비틀림 흐름에서의 입자의 이동

최형진

Korean Journal of Rheology, Vol.3, No.1, 13-21, April, 1991

Export Citation

점탄성 용액의 비틀림 흐름에서의 입자의 이동

Particle Migration in Torsional Flow of a Viscoelastic Solution

최형진

초록

본 연구에서는 단단한 구형 입자가 적은 변형속도에서 2차 유체로 간주될 수 있는 점탄성 용액의 disc-plate(비틀림)흐름에 놓였을 때의 측면 이동속도에 관하여 분석하였다. 이론적 계산을 통해 비틀림 유체 흐름에서 입자는 항상 중심쪽으로 이동하고 안쪽으로의 이동속도의 크기는 유체의 성질과 흐름의 형태의 함수라는 것을 발견하였으며, 이것은 2차 유체에서 입자는 높은 전단속도 영역에서 낮은 전단속도 영역으로 이동된다는 예측과 일치한다는 것을 알 수 있었다. 그러나 2차 유체 모델로부터의 이 결과는 이전 연구자들에 의해 관찰된 비틀림 유체 흐름에서의 바깥방향으로의 입자의 이동은 설명하지 못하였다.

The lateral migration velocity of a rigid single spherical particle is analyzed in this study, when placed in a disc-plate (torsional) flow of a viscoelastic solution which is regarded as a second-order fluid at low deformation rates. From theoretical calculation, it is found that the particle migrates always !toward the center and the magnitude of the inward migration velocity is a function of both fluid properties and flow geometry. The result corresponds with the prediction, i.e. the particle migrates from high shear rate region to low shear rate region in a second-order fluid. However, the result from this second-order fluid model does not show the outward migration of a rigid sphere in torsional flow which has been observed by previous investigators.

Keywords:Particle migration;Second-order fluid model;Torsional flow;Viscoelastic solution

[References]

Happel J, Brenner H, "Low Reynolds Number Hydrodynamics," Noordhoff, Leyden, The Netherlands (1973)
Ho BP, Leal LG, J. Fluid Mech., 65, 365 (1974)
Karnis A, Goldsmith HL, Mason SG, Nature, 200, 159 (1963)
Karnis A, Mason SG, Trans. Soc. Rheol., 10, 571 (1966)
Gauthier F, Goldsmith HL, Mason SG, Trans. Soc. Rheol., 15, 297 (1971)
Highgate DJ, Whorlow RW, Rheol. Acta, 8, 142 (1969)
Gauthier F, Goldsmith HL, Mason SG, Rheol. Acta, 10, 344 (1971)
Highgate DJ, Nature, 211, 1390 (1966)
Karis TE, Prieve DC, Rosen SL, J. Rheol., 28, 381 (1984)
Prieve DC, Jhon MS, Koenig TL, J. Rheol., 29, 639 (1985)
Choi HJ, Prieve DC, Jhon MS, J. Rheol., 31, 317 (1987)
Goddard JD, Trans. Soc. Rheol., 11, 381 (1967)
Brunn P, Rheol. Acta, 15, 104 (1976)
Brunn P, Rheol. Acta, 15, 163 (1976)
Brunn P, Rheol. Acta, 15, 589 (1976)
Brunn P, J. Fluid Mech., 82, 529 (1977)
Brunn P, J. Non-Newton. Fluid Mech., 7, 271 (1980)
Chan PCH, Leal LG, J. Fluid Mech., 82, 549 (1977)
Hess S, Z. Naturforschg., 23a, 1095 (1968)
Collyer AA, Clegg DW, "Rheological Measurement," Elsevier Applied Sci., New York, U.S.A. (1988)
Kaye A, Lodge AS, Vale DG, Rheol. Acta, 7, 368 (1968)
Gao HW, Ramachandran S, Christiansen EB, J. Rheol., 25, 213 (1981)
Olabisi D, Williams MC, Trans. Soc. Rheol., 16, 727 (1972)
Miller MJ, Christiansen EB, AIChE J., 18, 600 (1972)
Keentok M, Tanner RI, J. Rheol., 26, 301 (1982)
Choi HJ, Bull. Inst. Sci. Tech., (Inha Univ.), in press, 19 (1991)
Bird RB, Armstrong RC, Hassager O, "Dynamics of Polymeric Liquids," Vol. 1, Wiley, New York, U.S.A. (1987)
Boger DV, J. Non-Newton. Fluid Mech., 3, 87 (1977)
Boger DV, Proceeding 8th Int. Congress Rheol., 1, 195 (1980)
Prilutski G, Gupta RK, Sridhar T, Ryan ME, J. Non-Newton. Fluid Mech., 12, 233 (1983)
Mackay ME, Boger DV, J. Non-Newton. Fluid Mech., 22, 235 (1987)
Stratto RA, Butcher AF, J. Polym. Sci. A: Polym. Chem., 9, 1703 (1971)
Doi M, 4th Nisinomiya Symposium on "Dynamics and Patterns in Complex Fluids," Nisinomiya (1989)
Aubert JH, Tirrell M, J. Chem. Phys., 72, 2694 (1980)
Brunn P, J. Chem. Phys., 80, 3420 (1984)

[Referenced By]

[1] Happel J, Brenner H, "Low Reynolds Number Hydrodynamics," Noordhoff, Leyden, The Netherlands (1973)

[2] Ho BP, Leal LG, J. Fluid Mech., 65, 365 (1974)

[3] Karnis A, Goldsmith HL, Mason SG, Nature, 200, 159 (1963)

[4] Karnis A, Mason SG, Trans. Soc. Rheol., 10, 571 (1966)

[5] Gauthier F, Goldsmith HL, Mason SG, Trans. Soc. Rheol., 15, 297 (1971)

[6] Highgate DJ, Whorlow RW, Rheol. Acta, 8, 142 (1969)

[7] Gauthier F, Goldsmith HL, Mason SG, Rheol. Acta, 10, 344 (1971)

[8] Highgate DJ, Nature, 211, 1390 (1966)

[9] Karis TE, Prieve DC, Rosen SL, J. Rheol., 28, 381 (1984)

[10] Prieve DC, Jhon MS, Koenig TL, J. Rheol., 29, 639 (1985)

[11] Choi HJ, Prieve DC, Jhon MS, J. Rheol., 31, 317 (1987)

[12] Goddard JD, Trans. Soc. Rheol., 11, 381 (1967)

[13] Brunn P, Rheol. Acta, 15, 104 (1976)

[14] Brunn P, Rheol. Acta, 15, 163 (1976)

[15] Brunn P, Rheol. Acta, 15, 589 (1976)

[16] Brunn P, J. Fluid Mech., 82, 529 (1977)

[17] Brunn P, J. Non-Newton. Fluid Mech., 7, 271 (1980)

[18] Chan PCH, Leal LG, J. Fluid Mech., 82, 549 (1977)

[19] Hess S, Z. Naturforschg., 23a, 1095 (1968)

[20] Collyer AA, Clegg DW, "Rheological Measurement," Elsevier Applied Sci., New York, U.S.A. (1988)

[21] Kaye A, Lodge AS, Vale DG, Rheol. Acta, 7, 368 (1968)

[22] Gao HW, Ramachandran S, Christiansen EB, J. Rheol., 25, 213 (1981)

[23] Olabisi D, Williams MC, Trans. Soc. Rheol., 16, 727 (1972)

[24] Miller MJ, Christiansen EB, AIChE J., 18, 600 (1972)

[25] Keentok M, Tanner RI, J. Rheol., 26, 301 (1982)

[26] Choi HJ, Bull. Inst. Sci. Tech., (Inha Univ.), in press, 19 (1991)

[27] Bird RB, Armstrong RC, Hassager O, "Dynamics of Polymeric Liquids," Vol. 1, Wiley, New York, U.S.A. (1987)

[28] Boger DV, J. Non-Newton. Fluid Mech., 3, 87 (1977)

[29] Boger DV, Proceeding 8th Int. Congress Rheol., 1, 195 (1980)

[30] Prilutski G, Gupta RK, Sridhar T, Ryan ME, J. Non-Newton. Fluid Mech., 12, 233 (1983)

[31] Mackay ME, Boger DV, J. Non-Newton. Fluid Mech., 22, 235 (1987)

[32] Stratto RA, Butcher AF, J. Polym. Sci. A: Polym. Chem., 9, 1703 (1971)

[33] Doi M, 4th Nisinomiya Symposium on "Dynamics and Patterns in Complex Fluids," Nisinomiya (1989)

[34] Aubert JH, Tirrell M, J. Chem. Phys., 72, 2694 (1980)

[35] Brunn P, J. Chem. Phys., 80, 3420 (1984)