Three dimensional simulation dynamics for the dilute colloidal suspensions of rod-like polymer particles flowing in the bulk and near solid boundaries

Ali Atwi; Antoine Khater; Abbas Hijazi

Macromolecular Research, Vol.21, No.11, 1171-1181, November, 2013

DOI10.1007/s13233-013-1158-7 Export Citation

Three dimensional simulation dynamics for the dilute colloidal suspensions of rod-like polymer particles flowing in the bulk and near solid boundaries

Ali Atwi^{1, 2, †}, Antoine Khater^{1, 3}, and Abbas Hijazi²

¹Institut des Molécules et Matériaux du Mans (IMMM, UMR6283), Université du Maine, F-72085, Le Mans, France
²Département de Physique, Faculté des Sciences I, Université Libanaise, Hadath-Beirut, Lebanon
³, France

E-mail:

Numerical simulations and algorithms are developed to analyze the dynamics of rigid rod-like polymer particles. We developed a theoretical model based on the equations of Jeffrey for the dynamics of rigid polymer particles in fluids and the molecular dynamics by mechanical restitution for the diffusive collisions of the particles at the solid boundaries. The simulations are developed to calculate the dynamic equilibrium probability distribution functions (PDF) distributions for rod-like polymer particles in colloidal suspensions in a fluid under hydrodynamic flow inside pores with solid boundaries. They are carried out for idealized atomically flat and the realistic rough surface boundaries. To accomplish this, we investigate the influence of the surface roughness on the choice of the hydrodynamic boundary conditions. The simulation results for the PDF distributions for the spatial positions and orientations of rod-like polymer particles are calculated, over several orders of magnitude of the rotational Peclet number. They demonstrate the importance and significance of modeling in a three-dimensional spatial frame as compared to the simulation results over a two-dimensional spatial frame. In particular we are able to produce a complete topography for the PDF distributions segmented as a hierarchy in the depletion layer by covering a complete range of orientations in 3D spatial frames. These simulations permit to calculate the nematic order parameter over its tensorial representation for the colloidal suspensions of rod-like polymer particles locally, and throughout the pore space including the depletion layer. Our results for the nematic order parameter are hence innovating and represent a new input for these systems.

Keywords:colloidal suspension;rod-like polymer;numerical simulation;three-dimensional spatial frame

[References]

Fuji M, Fujimori H, Takei T, Watanabe T, Chikazawa M, J. Phys. Chem. B, 102(51), 10498 (1998)
Binks BP, Curr. Opin. Colloid Interface Sci., 7, 21 (2002)
Jia HF, Zhu GY, Wang P, Biotechnol. Bioeng., 84(4), 406 (2003)
Sokolov A, Aranson IS, Kessler JO, Goldstein RE, Phys. Rev. Lett., 98, 158102 (2007)
Caro CG, Pedley TJ, Schroter RC, Seed WA, The Mechanics of the Circulation, Oxford University Press, Oxford, 1978.
Goldsmith HL, Prog. Hemost. Thromb., 1, 97 (1972)
Atwi A, Khater A, Hijazi A, Cent. Eur. J. Chem., 8, 1009 (2010)
Lee JS, Kim JM, Macromol. Res., 17(10), 807 (2009)
Pozrikidis C, J. Fluid Mech., 541, 105 (2005)
Sane J, Padding JT, Louis AA, Phys. Rev. E, 79, 051402 (2009)
Park J, Metzger B, Guazzelli E, Butler JE, J. Fluid Mech., 648, 351 (2010)
Rose KA, Hoffman B, Saintillan D, Shaqfeh ESG, Santiago JG, Phys. Rev. E, 79, 011402 (2009)
Subramanian G, Koch DL, J. Fluid Mech., 535, 383 (2005)
Zhang Y, Donev A, Weisgraber T, Alder BJ, Graham MD, Pablo JJD, J. Chem. Phys., 130, 13 (2009)
Adams WW, Eby RK, McLemore DE, The Materials Science and Engineering of Rigid-Rod Polymers, Materials Research Society symposia proceedings, Pittsburgh, 1989.
Gustin J, Joneson A, Mahinfalah M, Stone J, Compos. Struct., 69, 396 (2005)
Jeffery GB, Proc. R. Soc. A, 102, 161 (1922)
Moses KB, Advani SG, Reinhardt A, Rheol. Acta, 40(3), 296 (2001)
Hinch EJ, Leal LG, J. Fluid Mech., 92, 591 (1979)
Mason SG, Manley RSJ, Proc. R. Soc. London, 238, 117 (1956)
Taylor G, Proc. R. Soc. A, 103, 58 (1923)
Trevelyan BJ, Mason SG, J. Colloid Interface Sci., 6, 354 (1951)
Boeder P, Z. Phys. A, 75, 258 (1932)
Hijazi A, Khater A, Eur. Polym. J., 44, 3409 (2008)
Hijazi A, Khater A, Comput. Mater. Sci., 22, 279 (2001)
Hijazi A, Khater A, Comput. Mater. Sci., 20, 213 (2001)
KhaterA, Europhys. Lett., 2, 539 (1989)
Hijazi A, Yahia LB, Khater A, Zoaeter M, Eur. Polym. J., 39, 521 (2003)
Panzer P, Liu M, Einzel D, Int. J. Mod. Phys. B, 6, 3251 (1992)
Kunert C, Harting J, Phys. Rev. Lett., 99, 176001 (2007)
Harting J, Kunert C, John von Neumann Institute for Computing, 39, 221 (2008)
Oswald P, Pieranski P, Nematic and Cholesteric Liquid Crystals, Taylor & Francis Group, CRC Press, Boca Raton, 2005.
Hand GL, J. Fluid Mech., 13, 33 (1962)
Doi M, Edwards SF, J. Chem. Soc., 74, 560 (1978)
Advani S, J. Rheol., 31, 751 (1987)
Chun MS, Kim SI, Park OO, Colloids Surf. A: Physicochem. Eng. Asp., 205, 261 (2002)

[1] Fuji M, Fujimori H, Takei T, Watanabe T, Chikazawa M, J. Phys. Chem. B, 102(51), 10498 (1998)

[2] Binks BP, Curr. Opin. Colloid Interface Sci., 7, 21 (2002)

[3] Jia HF, Zhu GY, Wang P, Biotechnol. Bioeng., 84(4), 406 (2003)

[4] Sokolov A, Aranson IS, Kessler JO, Goldstein RE, Phys. Rev. Lett., 98, 158102 (2007)

[5] Caro CG, Pedley TJ, Schroter RC, Seed WA, The Mechanics of the Circulation, Oxford University Press, Oxford, 1978.

[6] Goldsmith HL, Prog. Hemost. Thromb., 1, 97 (1972)

[7] Atwi A, Khater A, Hijazi A, Cent. Eur. J. Chem., 8, 1009 (2010)

[8] Lee JS, Kim JM, Macromol. Res., 17(10), 807 (2009)

[9] Pozrikidis C, J. Fluid Mech., 541, 105 (2005)

[10] Sane J, Padding JT, Louis AA, Phys. Rev. E, 79, 051402 (2009)

[11] Park J, Metzger B, Guazzelli E, Butler JE, J. Fluid Mech., 648, 351 (2010)

[12] Rose KA, Hoffman B, Saintillan D, Shaqfeh ESG, Santiago JG, Phys. Rev. E, 79, 011402 (2009)

[13] Subramanian G, Koch DL, J. Fluid Mech., 535, 383 (2005)

[14] Zhang Y, Donev A, Weisgraber T, Alder BJ, Graham MD, Pablo JJD, J. Chem. Phys., 130, 13 (2009)

[15] Adams WW, Eby RK, McLemore DE, The Materials Science and Engineering of Rigid-Rod Polymers, Materials Research Society symposia proceedings, Pittsburgh, 1989.

[16] Gustin J, Joneson A, Mahinfalah M, Stone J, Compos. Struct., 69, 396 (2005)

[17] Jeffery GB, Proc. R. Soc. A, 102, 161 (1922)

[18] Moses KB, Advani SG, Reinhardt A, Rheol. Acta, 40(3), 296 (2001)

[19] Hinch EJ, Leal LG, J. Fluid Mech., 92, 591 (1979)

[20] Mason SG, Manley RSJ, Proc. R. Soc. London, 238, 117 (1956)

[21] Taylor G, Proc. R. Soc. A, 103, 58 (1923)

[22] Trevelyan BJ, Mason SG, J. Colloid Interface Sci., 6, 354 (1951)

[23] Boeder P, Z. Phys. A, 75, 258 (1932)

[24] Hijazi A, Khater A, Eur. Polym. J., 44, 3409 (2008)

[25] Hijazi A, Khater A, Comput. Mater. Sci., 22, 279 (2001)

[26] Hijazi A, Khater A, Comput. Mater. Sci., 20, 213 (2001)

[27] KhaterA, Europhys. Lett., 2, 539 (1989)

[28] Hijazi A, Yahia LB, Khater A, Zoaeter M, Eur. Polym. J., 39, 521 (2003)

[29] Panzer P, Liu M, Einzel D, Int. J. Mod. Phys. B, 6, 3251 (1992)

[30] Kunert C, Harting J, Phys. Rev. Lett., 99, 176001 (2007)

[31] Harting J, Kunert C, John von Neumann Institute for Computing, 39, 221 (2008)

[32] Oswald P, Pieranski P, Nematic and Cholesteric Liquid Crystals, Taylor & Francis Group, CRC Press, Boca Raton, 2005.

[33] Hand GL, J. Fluid Mech., 13, 33 (1962)

[34] Doi M, Edwards SF, J. Chem. Soc., 74, 560 (1978)

[35] Advani S, J. Rheol., 31, 751 (1987)

[36] Chun MS, Kim SI, Park OO, Colloids Surf. A: Physicochem. Eng. Asp., 205, 261 (2002)