Numerical Analysis of Electrical Interaction between two Axisymmetric Spheroids
The electrical interaction between two axisymmetric
spheroidal particles in an electrolyte solution is examined numerically.
A Galerkin finite element method combined with a Newton-Raphson
iteration scheme is proposed to evaluate the spatial variation in the
electrical potential, and the result obtained used to estimate the
interaction energy between two particles. We show that if the surface
charge density is fixed, the potential gradient is larger at a point, which
has a larger curvature, and if surface potential is fixed, surface charge
density is proportional to the curvature. Also, if the total interaction
energy against closest surface-to-surface curve exhibits a primary
maximum, the maximum follows the order (oblate-oblate) >
(sphere-sphere)>(oblate-prolate)>(prolate-prolate), and if the curve
has a secondary minimum, the absolute value of the minimum follows
the same order.
[1] R.J. Hunter, Foundations of Colloid Science, Vol. I, Oxford University Press,
London, 1992.
[2] B.V. Derjaguin and L.D. Landau, Acta Phys.-Chim. USSR, 14 (1941) 633.
[3] G.M. Bell, S. Levine, and L.N. McCartney, J. Colloid Interface Sci., 33
(1970) 335.
[4] H. Ohshima, D.Y.C. Chan, T.W. Healy and L.R. White, J. Colloid Interface
Sci., 92 (1983) 232.
[5] S.L. Carnie and D.Y.C. Chan, J. Colloid Interface Sci., 155 (1993) 297.
[6] J.E. Sader, S.L. Carnie and D.Y.C. Chan, J. Colloid Interface Sci., 171 (1995)
46.
[7] C.E. McNamee, Y. Tsujii, H. Ohshima, et al., Langmuir, 20 (2004) 1953
[8] H. Ohshima, Lngmuir, 23 (2007) IX.
[9] V Krautler and P.H. Hunenberger, Mol. Simul., 34 (2008) 491.
[10] H. Ohshima, J. Colloid Interface Sci., 328 (2008) 3.
[11] N.E. Hoskins and S. Levine, Philos. Trans. R. Soc. London A 248, (1956)
433.
[12] J.E. Ledbetter, T.L. Croxton and D.A. McQuarrie, Can. J. Chem., 59 (1981)
1860.
[13] S.L. Carnie, D.Y.C. Chan and J. Stankovich, J. Colloid Interface Sci., 165
(1994) 116.
[14] B.K.C. Chan and D.Y.C. Chan, J. Colloid Interface Sci., 92 (1983) 281.
[15] A.E. James and D.J.A. Williams, J. Colloid Interface Sci., 107 (1985) 44.
[16] Y.J. You and C. Harvey, J. Comput. Chem., 14 (1993) 484.
[17] F.R. Chou Chang and G. Sposito, J. Colloid Interface Sci., 163 (1994) 19.
[18] W.R. Bowen and A.O. Sharif, J. Colloid Interface Sci., 187 (1997) 363.
[19] B.T. Liu and J.P. Hsu, J. Chem. Phys., 128 (2008) 104509.
[20] J.J. Feng and W.Y. Wu, J. Fluid Mech., 264 (1994) 41.
[21] J.P. Hsu and B.T. Liu, J. Colloid Interface Sci., 178 (1996) 785.
[22] J.P. Hsu, C.C. Kuo and M.H. Ku, Electrophoresis, 29 (2008) 348.
[23] J.P. Hsu, C.Y. Chen and D.J. Lee, et al, J. Colloid Interface Sci., 325 (2008)
516.
[24] Y.C. Kuo and J.P. Hsu, J. Colloid Interface Sci., 156 (1993) 250.
[25] B.M. Irons, Int. J. Num. Methods Eng., 2 (1970) 5.
[26] P. Hood, Int. J. Num. Methods Eng., 10 (1976) 379.
[1] R.J. Hunter, Foundations of Colloid Science, Vol. I, Oxford University Press,
London, 1992.
[2] B.V. Derjaguin and L.D. Landau, Acta Phys.-Chim. USSR, 14 (1941) 633.
[3] G.M. Bell, S. Levine, and L.N. McCartney, J. Colloid Interface Sci., 33
(1970) 335.
[4] H. Ohshima, D.Y.C. Chan, T.W. Healy and L.R. White, J. Colloid Interface
Sci., 92 (1983) 232.
[5] S.L. Carnie and D.Y.C. Chan, J. Colloid Interface Sci., 155 (1993) 297.
[6] J.E. Sader, S.L. Carnie and D.Y.C. Chan, J. Colloid Interface Sci., 171 (1995)
46.
[7] C.E. McNamee, Y. Tsujii, H. Ohshima, et al., Langmuir, 20 (2004) 1953
[8] H. Ohshima, Lngmuir, 23 (2007) IX.
[9] V Krautler and P.H. Hunenberger, Mol. Simul., 34 (2008) 491.
[10] H. Ohshima, J. Colloid Interface Sci., 328 (2008) 3.
[11] N.E. Hoskins and S. Levine, Philos. Trans. R. Soc. London A 248, (1956)
433.
[12] J.E. Ledbetter, T.L. Croxton and D.A. McQuarrie, Can. J. Chem., 59 (1981)
1860.
[13] S.L. Carnie, D.Y.C. Chan and J. Stankovich, J. Colloid Interface Sci., 165
(1994) 116.
[14] B.K.C. Chan and D.Y.C. Chan, J. Colloid Interface Sci., 92 (1983) 281.
[15] A.E. James and D.J.A. Williams, J. Colloid Interface Sci., 107 (1985) 44.
[16] Y.J. You and C. Harvey, J. Comput. Chem., 14 (1993) 484.
[17] F.R. Chou Chang and G. Sposito, J. Colloid Interface Sci., 163 (1994) 19.
[18] W.R. Bowen and A.O. Sharif, J. Colloid Interface Sci., 187 (1997) 363.
[19] B.T. Liu and J.P. Hsu, J. Chem. Phys., 128 (2008) 104509.
[20] J.J. Feng and W.Y. Wu, J. Fluid Mech., 264 (1994) 41.
[21] J.P. Hsu and B.T. Liu, J. Colloid Interface Sci., 178 (1996) 785.
[22] J.P. Hsu, C.C. Kuo and M.H. Ku, Electrophoresis, 29 (2008) 348.
[23] J.P. Hsu, C.Y. Chen and D.J. Lee, et al, J. Colloid Interface Sci., 325 (2008)
516.
[24] Y.C. Kuo and J.P. Hsu, J. Colloid Interface Sci., 156 (1993) 250.
[25] B.M. Irons, Int. J. Num. Methods Eng., 2 (1970) 5.
[26] P. Hood, Int. J. Num. Methods Eng., 10 (1976) 379.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:62776", author = "Kuan-Liang Liu and Eric Lee and Jung-Jyh Lee and Jyh-Ping Hsu", title = "Numerical Analysis of Electrical Interaction between two Axisymmetric Spheroids", abstract = "The electrical interaction between two axisymmetric
spheroidal particles in an electrolyte solution is examined numerically.
A Galerkin finite element method combined with a Newton-Raphson
iteration scheme is proposed to evaluate the spatial variation in the
electrical potential, and the result obtained used to estimate the
interaction energy between two particles. We show that if the surface
charge density is fixed, the potential gradient is larger at a point, which
has a larger curvature, and if surface potential is fixed, surface charge
density is proportional to the curvature. Also, if the total interaction
energy against closest surface-to-surface curve exhibits a primary
maximum, the maximum follows the order (oblate-oblate) >
(sphere-sphere)>(oblate-prolate)>(prolate-prolate), and if the curve
has a secondary minimum, the absolute value of the minimum follows
the same order.", keywords = "interaction energy, interaction force,
Poisson-Boltzmann equation, spheroid.", volume = "3", number = "5", pages = "382-8", }