Abstract.
We use a hydrodynamic reciprocal approach to phoretic motion to derive general expressions for the electrophoretic and thermophoretic mobility of weakly charged colloids in aqueous electrolyte solutions. Our approach shows that phoretic motion can be understood in terms of the interfacial transport of thermodynamic excess quantities that arises when a colloid is kept stationary inside a bulk fluid flow. The obtained expressions for the mobilities are extensions of previously known results as they can account for different hydrodynamic boundary conditions at the colloidal surface, irrespective of how the colloid-fluid interaction range compares to the colloidal radius.
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References
M.v. Smoluchowski, Bull. Int. Acad. Sci. Crac. 3, 184 (1903)
E. Hückel, Phys. Z. 25, 204 (1924)
B. Derjaguin, Y. Yalamov, J. Colloid Sci. 20, 555 (1965)
E. Ruckenstein, J. Colloid Interface Sci. 83, 77 (1981)
J.N. Agar, C.Y. Mou, J.L. Lin, J. Phys. Chem. 93, 2079 (1989)
J.L. Anderson, Annu. Rev. Fluid Mech. 21, 61 (1989)
A. Parola, R. Piazza, Eur. Phys. J. E 15, 255 (2004)
A. Ajdari, L. Bocquet, Phys. Rev. Lett. 96, 186102 (2006)
A. Würger, Phys. Rev. Lett. 98, 138301 (2007)
J.K. Dhont, S. Wiegand, S. Duhr, D. Braun, Langmuir 23, 1674 (2007)
A.S. Khair, T.M. Squires, Phys. Fluids 21, 042001 (2009)
J.F. Brady, J. Fluid Mech. 667, 216 (2011)
S. Semenov, M. Schimpf, J. Phys. Chem. B 119, 3510 (2015)
J. Morthomas, A. Würger, J. Phys.: Condens. Matter 21, 035103 (2009)
P. Gaspard, R. Kapral, J. Chem. Phys. 148, 134104 (2018)
R. Piazza, J. Phys.: Condens. Matter 16, S4195 (2004)
J.K.G. Dhont, W.J. Briels, Eur. Phys. J. E 25, 61 (2008)
J. Burelbach, D. Frenkel, I. Pagonabarraga, E. Eiser, Eur. Phys. J. E 41, 7 (2018)
S.R. De Groot, P. Mazur, Non-Equilibrium Thermodynamics (Courier Corporation, 2013)
R. Barber, D. Emerson, Analytical Solution of Low Reynolds Number Slip Flow Past a Sphere (Council for the Central Laboratory of the Research Councils, 2000)
N.V. Churaev, B.V. Derjaguin, V.M. Muller, Surface Forces (Consultants Bureau, New York, 1987)
S. Fayolle, T. Bickel, A. Würger, Phys. Rev. E 77, 041404 (2008)
J. Morthomas, A. Würger, Eur. Phys. J. E 27, 425 (2008)
L. Onsager, Phys. Rev. Lett. 37, 405 (1931)
L. Onsager, Phys. Rev. Lett. 38, 2265 (1931)
J. Burelbach, PhD Thesis, University of Cambridge (2018) https://doi.org/10.17863/CAM.21479
L. Landau, E. Lifshitz, Fluid Mechanics (London, 1959)
J. Burelbach, D.B. Brückner, D. Frenkel, E. Eiser, Soft Matter 14, 7446 (2018)
R. Piazza, A. Parola, J. Phys.: Condens. Matter 20, 153102 (2008)
A. Würger, Rep. Prog. Phys. 73, 126601 (2010)
S.A. Putnam, D.G. Cahill, Langmuir 21, 5317 (2005)
L.D. Landau, J. Bell, M. Kearsley, L. Pitaevskii, E. Lifshitz, J. Sykes, Electrodynamics of Continuous Media, Vol. 8 (Elsevier, 2013)
A. Würger, Phys. Rev. Lett. 101, 108302 (2008)
S. Duhr, D. Braun, Proc. Natl. Acad. Sci. U.S.A. 2006, 19678 (2006)
M. Reichl, PhD Thesis, Ludwig Maximilian University of Munich (2014)
L. Galla, A.J. Meyer, A. Spiering, A. Sischka, M. Mayer, A.R. Hall, P. Reimann, D. Anselmetti, Nano Lett. 14, 4176 (2014)
N. Takeyama, K. Nakashima, J. Solut. Chem. 17, 305 (1988)
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Burelbach, J., Stark, H. Determining phoretic mobilities with Onsager’s reciprocal relations: Electro- and thermophoresis revisited. Eur. Phys. J. E 42, 4 (2019). https://doi.org/10.1140/epje/i2019-11769-y
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DOI: https://doi.org/10.1140/epje/i2019-11769-y