臺灣博碩士論文加值系統

An analysis is presented for the electrophoresis and electric conduction in a dilute suspension of charged spherical porous shells or permeable microcapsules with electric double layers of arbitrary thickness in an electrolyte solution. With the assumption that the system is slightly perturbed from equilibrium, the linearized electrokinetic equations governing the ionic electrochemical potential energy and fluid velocity distributions are solved as series expansions in the small fixed charge density of the porous shells. Explicit formulas for the electrophoretic mobility of the porous shells and effective electric conductivity of the suspension are derived. Both the electrophoretic mobility and the effective conductivity decrease monotonically with a decrease in the relative thickness of the porous shells, but these decreases are not conspicuous until the porous shells are quite thin. When the fluid permeability of the porous shells is smaller or the electric double layers are thicker, the effect of this relative thickness on the electrophoretic mobility and effective conductivity becomes more significant. In the limiting case of zero inner radius of the porous shells, our formulas reduce to the corresponding results obtained for the electrophoresis and electric conduction in a suspension of charged porous spheres.

Abstract I

摘要 III

List of Figures VII

Chapter 1 Introduction 1

Chapter 2 Electrokinetic Equations 3
2.1 Governing Equations 3
2.2 Boundary Conditions 5

Chapter 3 Solution of the Electrophoretic Velocity and Electric Conductivity 7
3.1 Equilibrium Electrostatic Potential 7
3.2 Solution to the Electrokinetic Equations 8
3.3 Electrophoretic Mobility 9
3.4 Electric Conductivity 10

Chapter 4 Results and Discussion 13
4.1 Electrophoretic Mobility of the Porous Spherical Shell
13
4.2 Effective Electric Conductivity of the Suspension
21

Chapter 5 Conclusions 31

List of Symbols 33

References 36

Appendix Dimensionless functions and coefficients in Eqs. (16), (17), and (20)
39

Biographical Sketch 48

(1)S.S. Dukhin, B.V. Derjaguin, in: E. Matijevic (Ed.), Surface and Colloid Science, vol. 7, Wiley, New York, 1974.
(2)R.W. O’Brien, The electric conductivity of a dilute suspension of charged particles, J. Colloid Interface Sci. 81 (1981) 234–248.
(3)H. Ohshima, T.W. Healy, L.R. White, Approximate analytic expressions for the electrophoretic mobility of spherical colloidal particles and the conductivity of theirdilute suspensions, J. Chem. Soc. Faraday Trans. 2 (79) (1983) 1613–1628.
(4)S.B. Chen, H.J. Keh, Axisymmetric electrophoresis of multiple colloidal spheres, J. Fluid Mech. 238 (1992) 251–276.
(5)A.S. Dukhin, V. Shilov, Yu. Borkovskaya, Dynamic electrophoretic mobility in concentrated dispersed systems. Cell model, Langmuir 15 (1999) 3452–3457.
(6)H. Ohshima, Electrical conductivity of a concentrated suspension of spherical colloidal particles, J. Colloid Interface Sci. 212 (1999) 443–448.
(7)J.M. Ding, H.J. Keh, The electrophoretic mobility and electric conductivity of a concentrated suspension of colloidal spheres with arbitrary double-layer thickness, J.Colloid Interface Sci. 236 (2001) 180–193.
(8)F. Carrique, F.J. Arroyo, M.L. Jimenez, A.V. Delgado, Influence of double-layer overlap on the electrophoretic mobility and DC conductivity of a concentrated suspension of spherical particles, J. Phys. Chem. B 107 (2003) 3199–3206.
(9)J.J. Hermans, H. Fujita, Electrophoresis of charged polymer molecules with partial free drainage, K. Ned. Akad. Wetenschap. Proc. Ser. B 58 (1955) 182–187.
(10)Y.C. Liu, H.J. Keh, The electric conductivity of dilute suspensions of charged porous spheres, J. Colloid Interface Sci. 192 (1997) 375–385.
(11)H.J. Keh, C.P. Liu, Electric conductivity and electrophoretic mobility in suspensions of charged porous spheres, J. Phys. Chem. C 114 (2010) 22044–22054.
(12)H.Y. Huang, H.J. Keh, Electrophoretic mobility and electric conductivity in suspensions of charge-regulating porous particles, Colloid Polym. Sci. 293 (2015) 1903–1914.
(13)H. Ohshima, Electrophoretic mobility of soft particles, J. Colloid Interface Sci. 163 (1994) 474–483.
(14)Y.C. Liu, H.J. Keh, Electric conductivity of a dilute suspension of charged composite spheres, Langmuir 14 (1998) 1560–1574.
(15)J.J. Lopez-Garcia, C. Grosse, J. Horno, Numerical calculation of the electrophoretic mobility of concentrated suspensions of soft particles, J. Colloid Interface Sci. 301(2006) 651–659.
(16)S. Ahualli, M.L. Jimenez, F. Carrique, A.V. Delgado, AC electrokinetics of concentrated suspensions of soft particles, Langmuir 25 (2009) 1986–1997.
(17)I.P. Jones, Low Reynolds number flow past a porous spherical shell, Proc. Camb. Philos. Soc. 73 (1973) 231–238.
(18)B.S. Bhatt, N.C. Sacheti, Flow past a porous spherical shell using the Brinkman model, J. Phys. D: Appl. Phys. 27 (1994) 37–41.
(19)M.P. Keh, H.J. Keh, Slow motion of an assemblage of porous spherical shells relative to a fluid, Transp. Porous Media 81 (2010) 261–275.
(20)J. Fransaer, J.-P. Celis, J.R. Roos, Electro-osmophoresis of a charged permeable microcapsule with thin double layer, J. Colloid Interface Sci. 151 (1992) 26–40.
(21)A. Tateno, M. Shiba, T. Kondo, Emulsions, Latices, and Dispersions, in: P. Becher, M.N. Yudenfreund (Eds.), Dekker, New York, 1978, p. p. 279.
(22)T.G.M. van de Ven, Colloidal Hydrodynamics, Academic Press, London, 1989.