유한 척력적 유체의 이동 특성에 관한 분자 동력학 연구: II. 전단 점도

김춘호; 하기룡; 서숭혁; Chun-Ho Kim; KiRyong Ha; Soong-Hyuck Suh

Polymer(Korea), Vol.41, No.1, 39-46, January, 2017

DOI10.7317/pk.2017.41.1.39 Export Citation

유한 척력적 유체의 이동 특성에 관한 분자 동력학 연구: II. 전단 점도

Molecular Dynamics Studies for the Transport Properties of Bounded Repulsive Fluids: II. Shear Viscosity

김춘호, 하기룡, 서숭혁^†

계명대학교 화학공학과

Chun-Ho Kim, KiRyong Ha, and Soong-Hyuck Suh^†

Department of Chemical Engineering, Keimyung University, 800 Dalgubeol-daero 2, Dalseo-ku, Daegu 42601, Korea

E-mail:

초록

상호 충첩이 가능한 유한 척력적 침투성 구형 유체의 전단 점도 특성을 고찰하고자 분자 동력학 방법을 이용한 전산 모사를 다양한 범위의 입자 충전 분율 φ 및 척력적 에너지 상수 ε* 조건에서 수행하였다. 외삽법에 의하여 전단 점도 계수를 φ→0의 희박 밀도의 조건으로 확장하는 경우, 전산 모사 결과는 모든 ε* 값에 대하여 침투성 유체에 관한 Boltzmann 확산식과 매우 좋은 일치도를 보여 주었다. 또한, 본 연구에서 제안한 Enskog 형태의 경험식에 전산 모사로부터 구현된 유효 충전 밀도와 상태 방정식의 압축 인자를 모두를 포함하는 경우, 제안된 경험식은 상호 일치되는 전단 점도 계수 예측값을 주었다. 높은 밀도 및 높은 척력적 에너지의 경우 정적 특성인 구조적 영향뿐만 아니라 연체형 또는 강체형 충돌 등 침투성 구형 입자의 자체 충돌 특성에 기인하는 서로 상관된 움직임 등 동적 특성이 전단 점도 특성에 매우 큰 영향을 나타내었다. 이와 동시에 기체 분자 운동론 및 관련 이론적 성과를 과학사적 배경과 함께 설명하였다.

Molecular dynamics simulations have been carried out over a wide range of the packing fraction φ and the repulsive energy parameter ε* to investigate the shear viscosity properties in the bounded repulsive molecular systems of penetrable-sphere fluids. By extrapolating simulation data to the zero-density limit (φ→0), an excellent agreement is found with the Boltzmann kinetic equation for all sets of ε*-values. A good agreement is found between simulation results and an empirical Enskog-like approximation proposed in this present work, in conjunction with both the effective packing fraction and the compressibility factor obtained from simulation results. In the range of higher densities with higher repulsive interactions, the shear viscosity process is greatly affected not only by static structural effects but also by the dynamic correlated motion involved in colliding particles, namely, soft-type and hard-type collisions. In addition, relevant historical background on viscosity is addressed to sketch the traditional gas kinetic theory and further developments.

Keywords:shear viscosity;molecular dynamics simulation;bounded repulsive fluid

[References]

Kim CH, Suh SH, Polym. Korea, 35(4), 325 (2011)
Kim CH, Suh SH, Polym. Korea, 35(6), 513 (2011)
Hansen JP, McDonald IR, Theory of Simple Liquids,Academic, Amsterdam, 2006.
Mayer C, Zaccarelli E, Stiakakis E, Likos CN, Sciortino F, Munam A, Gauthier M, Hadjichristidis N, Iatrou H, Tartaglia P, Lowen H, Vlassopoulos D, Nat. Mater., 7(10), 780 (2008)
Jusufi A, Likos CN, Rev. Mod. Phys., 81, 1753 (2009)
Likos CN, Phys. Rep., 348, 267 (2001)
Likos CN, Soft Matter, 2, 478 (2006)
Schmidt M, Fuchs M, J. Chem. Phys., 117(13), 6308 (2002)
Choudhury N, Ghosh SK, J. Chem. Phys., 119(9), 4827 (2003)
Acedo L, Santos A, Phys. Lett. A, 323, 427 (2004)
Malijevsky A, Santos A, J. Chem. Phys., 124, 074750 (2006)
Santos A, Malijevsky A, Phys. Rev. E, 75, 021201 (2007)
Malijevsky A, Yuste SB, Santos A, Phys. Rev. E, 76, 021504 (2007)
Zhang K, Charbonneau P, J. Chem. Phys., 136, 214106 (2012)
Qamhieh K, Khaleel AA, Colloids Surf. A: Physicochem. Eng. Asp., 442, 191 (2014)
Yuste SB, Santos A, de Haro ML, Mol. Phys., 109, 987 (2011)
Fantoni R, Malijevsky A, Santos A, Giacometti A, Mol. Phys., 109, 2723 (2011)
Suh SH, Kim CH, Kim SC, Santos A, Phys. Rev. E, 82, 051202 (2010)
Kim SC, Suh SH, J. Chem. Phys., 117(21), 9880 (2002)
Kim SC, Seong BS, Suh SH, J. Chem. Phys., 131, 134701 (2009)
Suh SH, Liu HL, Bull. Korean Chem. Soc., 32, 1336 (2011)
Chihaia V, Calderon-Moreno JM, Stanica N, Parvulescu V, Gartner M, Suh SH, Rev. Roum. Chim., 56, 1115 (2011)
Kim CH, Ha KR, Suh SH, Polym. Korea, 40(4), 594 (2016)
Viscardy S, arXiv:cond-mat/0601210v2 [cond-mat.stat-mech], 2010; Ph. D. thesis, Univ. Libre de Bruxelles, 2005.
Maxwell J, Philos. Trans. R. Soc. Lond. Ser. A-Math. Phys. Eng. Sci., 156, 249 (1866)
Boltzmann L, Lectures on Gas Theory, S. G. Brush, Editor, Dover, NY, 1995.
Chapman S, Cowling TG, The Mathematical Theory of Nonuniform Gases, Cambridge Univ. Press, Cambridge, 1970.
Santos A, in Rarefied Gas Dynamics, Capitelli M, Editor, AIP Conf. Proc. No. 762, NY, pp. 276-281 (2005).
Hirschfelder JO, Curtiss CF, Bird RB, Molecular Theory of Gases and Liquids, John Wiley & Sons Inc., NY, 1954.
Carnahan NF, Starling KE, J. Chem. Phys., 51, 635 (1969)
Sigurgeirsson H, Heyes DM, J. Molec. Phys., 101, 469 (2003)
Alder BJ, Wainwright TE, J. Chem. Phys., 31, 459 (1959)
Allen MP, Tildesley DJ, Computer Simulation of Liquids, Clarendon, Oxford, 1987.

[Referenced By]

[1] Kim CH, Suh SH, Polym. Korea, 35(4), 325 (2011)

[2] Kim CH, Suh SH, Polym. Korea, 35(6), 513 (2011)

[3] Hansen JP, McDonald IR, Theory of Simple Liquids,Academic, Amsterdam, 2006.

[4] Mayer C, Zaccarelli E, Stiakakis E, Likos CN, Sciortino F, Munam A, Gauthier M, Hadjichristidis N, Iatrou H, Tartaglia P, Lowen H, Vlassopoulos D, Nat. Mater., 7(10), 780 (2008)

[5] Jusufi A, Likos CN, Rev. Mod. Phys., 81, 1753 (2009)

[6] Likos CN, Phys. Rep., 348, 267 (2001)

[7] Likos CN, Soft Matter, 2, 478 (2006)

[8] Schmidt M, Fuchs M, J. Chem. Phys., 117(13), 6308 (2002)

[9] Choudhury N, Ghosh SK, J. Chem. Phys., 119(9), 4827 (2003)

[10] Acedo L, Santos A, Phys. Lett. A, 323, 427 (2004)

[11] Malijevsky A, Santos A, J. Chem. Phys., 124, 074750 (2006)

[12] Santos A, Malijevsky A, Phys. Rev. E, 75, 021201 (2007)

[13] Malijevsky A, Yuste SB, Santos A, Phys. Rev. E, 76, 021504 (2007)

[14] Zhang K, Charbonneau P, J. Chem. Phys., 136, 214106 (2012)

[15] Qamhieh K, Khaleel AA, Colloids Surf. A: Physicochem. Eng. Asp., 442, 191 (2014)

[16] Yuste SB, Santos A, de Haro ML, Mol. Phys., 109, 987 (2011)

[17] Fantoni R, Malijevsky A, Santos A, Giacometti A, Mol. Phys., 109, 2723 (2011)

[18] Suh SH, Kim CH, Kim SC, Santos A, Phys. Rev. E, 82, 051202 (2010)

[19] Kim SC, Suh SH, J. Chem. Phys., 117(21), 9880 (2002)

[20] Kim SC, Seong BS, Suh SH, J. Chem. Phys., 131, 134701 (2009)

[21] Suh SH, Liu HL, Bull. Korean Chem. Soc., 32, 1336 (2011)

[22] Chihaia V, Calderon-Moreno JM, Stanica N, Parvulescu V, Gartner M, Suh SH, Rev. Roum. Chim., 56, 1115 (2011)

[23] Kim CH, Ha KR, Suh SH, Polym. Korea, 40(4), 594 (2016)

[24] Viscardy S, arXiv:cond-mat/0601210v2 [cond-mat.stat-mech], 2010; Ph. D. thesis, Univ. Libre de Bruxelles, 2005.

[25] Maxwell J, Philos. Trans. R. Soc. Lond. Ser. A-Math. Phys. Eng. Sci., 156, 249 (1866)

[26] Boltzmann L, Lectures on Gas Theory, S. G. Brush, Editor, Dover, NY, 1995.

[27] Chapman S, Cowling TG, The Mathematical Theory of Nonuniform Gases, Cambridge Univ. Press, Cambridge, 1970.

[28] Santos A, in Rarefied Gas Dynamics, Capitelli M, Editor, AIP Conf. Proc. No. 762, NY, pp. 276-281 (2005).

[29] Hirschfelder JO, Curtiss CF, Bird RB, Molecular Theory of Gases and Liquids, John Wiley & Sons Inc., NY, 1954.

[30] Carnahan NF, Starling KE, J. Chem. Phys., 51, 635 (1969)

[31] Sigurgeirsson H, Heyes DM, J. Molec. Phys., 101, 469 (2003)

[32] Alder BJ, Wainwright TE, J. Chem. Phys., 31, 459 (1959)

[33] Allen MP, Tildesley DJ, Computer Simulation of Liquids, Clarendon, Oxford, 1987.