The Role of Surface-Charge Transport in Electrohydrodynamics and Electromechanics of a Dielectric Sphere

  • V. V. Datsyuk Taras Shevchenko National University of Kyiv, Faculty of Physics
  • O. R. Pavlyniuk Taras Shevchenko National University of Kyiv, Faculty of Physics
Keywords: dielectrophoresis, electrohydrodynamics, leaky-dielectric model

Abstract

To simulate the electrokinetic processes in weakly-conducting dielectric media, the Taylor–Melcher leaky-dielectric model is widely used, though its applicability conditions are unknown. To define them, the electric-potential distributions inside and outside a dielectric sphere placed in an electric field are determined, by assuming the sphere and the environment are weakly conducting and by considering the electric and diffusion interfacial currents and the surface-charge decay. Earlier, an electric-field characteristic of a dielectric sphere, for example, the real part of the Clausius–Mossotti factor found for a direct current (DC) field was commonly thought to be a single-valued function of two parameters, the conductivities of the sphere and the environment. Now, it depends on a larger number of parameters and, in the dc case, can range from the perfect-dielectric to perfect-conductor values even for a particle of a good insulator. Using the proposed theory, a variety of the experimental results on the electrohydrodynamic (EHD) fluid circulation and dielectrophoretic (DEP) motion of microparticles in the dielectric drops are explained for the first time or in a new way. The dielectrophoretic inflection and cross-over frequencies are defined allowing for the decay of the surface charge. A dependence of the effective conductivity of a sphere on the angular field distribution is predicted for the first time.

References

N.G. Green, H. Morgan. Separation of submicrometre particles using a combination of dielectrophoretic and electrohydrodynamic forces. J. Phys. D 31, L25 (1998). https://doi.org/10.1088/0022-3727/31/7/002

T.B. Jones. Electromechanics of Particles (Cambridge Univ. Press, 1995) [ISBN: 9780521019101]. https://doi.org/10.1017/CBO9780511574498

A.V. Delgado. Interfacial Electrokinetics and Electrophoresis (Dekker, 2001) [ISBN: 0-8247-0603-X]. https://doi.org/10.1201/9781482294668

M.P. Hughes. Nanoelectromechanics in Engineering and Biology (CRC Press, 2003) [ISBN: 0-8493-1183-7].

H.-C. Chang, L. Yeo. Electrokinetically driven Microfluidics and Nanofluidics (Cambridge Univ. Press, 2010) [ISBN: 9780521860253].

A. Ramos. Electrokinetics and Electrohydrodynamics in Microsystems (Springer, 2011) [ISBN: 978-3-7091- 0899-4]. https://doi.org/10.1007/978-3-7091-0900-7

B. Cetin, D. Li. Dielectrophoresis in microfluidics technology. Electrophoresis 32, 2410 (2011). https://doi.org/10.1002/elps.201100167

T.Z. Jubery, S.K. Srivastava, P. Dutta. Dielectrophoretic separation of bioparticles in microdevices: A review. Electrophoresis 35, 691 (2014). https://doi.org/10.1002/elps.201300424

R.R. Pethig. Dielectrophoresis: Theory, Methodology and Biological Applications (Wiley, 2017) [ISBN: 9781118671450]. https://doi.org/10.1002/9781118671443

Q. Chen, Y.J. Yuan. A review of polystyrene bead manipulation by dielectrophoresis. RSC Adv. 9, 4963 (2019). https://doi.org/10.1039/C8RA09017C

S. Nudurupati, M. Janjua, N. Aubry, P. Singh. Concentrating particles on drop surfaces using external electric fields. Electrophoresis 29, 1164 (2008), https://doi.org/10.1002/elps.200700676

S. Nudurupati, M. Janjua, P. Singh, N. Aubry. Effect of parameters on redistribution and removal of particles from drop surfaces. Soft Mat. 6, 1157 (2010). https://doi.org/10.1039/b912723b

P.F. Salipante, P.M. Vlahovska. Electrohydrodynamics of drops in strong uniform dc electric fields. Phys. Fluids 22, 112110 (2010). https://doi.org/10.1063/1.3507919

P. Dommersnes, Z. Rozynek, A. Mikkelsen, R. Castberg, K. Kjerstad, K. Hersvik, J.O. Fossum. Active structuring of colloidal armour on liquid drops. Nat. Comm. 4, 2066 (2013). https://doi.org/10.1038/ncomms3066

Z. Rozynek, P. Dommersnes, A. Mikkelsen, L. Michels, J. Fossum. Electrohydrodynamic controlled assembly and fracturing of thin colloidal particle films confined at drop interfaces, Eur. Phys. J. Spec. Top. 223, 1859 (2014). https://doi.org/10.1140/epjst/e2014-02231-x

H. Yan, L. He, X. Luo, J.Wang, X. Huang, Y. L¨u, D. Yang. Investigation on transient oscillation of droplet deformation before conical breakup under alternating current electric field. Langmuir 31, 8275 (2015). https://doi.org/10.1021/acs.langmuir.5b01642

R. Vaidyanathan, S. Dey, L.G. Carrascosa, M.J.A. Shiddiky, M. Trau. Alternating current electrohydrodynamics in microsystems: Pushing biomolecules and cells around on surfaces. Biomicrofluidics 9, 061501 (2015). https://doi.org/10.1063/1.4936300

E. Amah, K. Shah, I. Fischer, P. Singh. Electro- hydrodynamic manipulation of particles adsorbed on the surface of a drop. Soft Mat. 12, 1663 (2016). https://doi.org/10.1039/C5SM02195B

Q. Brosseau, P. M. Vlahovska. Streaming from the equator of a drop in an external electric field. Phys. Rev. Lett. 119, 034501 (2017). https://doi.org/10.1103/PhysRevLett.119.034501

A. Mikkelsen, K. Khobaib, F.K. Eriksen, K.J. Maloy, Z. Rozynek. Particle-covered drops in electric fields: drop deformation and surface particle organization. Soft Mat. 14, 5442 (2018). https://doi.org/10.1039/C8SM00915E

P.M. Vlahovska. Electrohydrodynamics of drops and vesicles. Ann. Rev. Fluid Mech. 51, 305 (2019). https://doi.org/10.1146/annurev-fluid-122316-050120

L. Novotny, B. Hecht. Principles of nano-optics (Cambridge Univ. Press, 2006) [ISBN: 978-0-511-16811-6]. https://doi.org/10.1017/CBO9780511813535

G. Taylor. Studies in electrohydrodynamics. I. The circulation produced in a drop by electrical field. Proc. Roy. Soc. Lond. A 291, 159 (1966). https://doi.org/10.1098/rspa.1966.0086

J.R. Melcher, G.I. Taylor. Electrohydrodynamics: A review of the role of interfacial shear stresses. Ann. Rev. Fluid Mech. 1, 111 (1969). https://doi.org/10.1146/annurev.fl.01.010169.000551

D.A. Saville. Electrohydrodynamics: The Taylor- Melcher leaky dielectric model. Ann. Rev. Fluid Mech. 29, 27 (1997). https://doi.org/10.1146/annurev.fluid.29.1.27

S. Torza, R.G. Cox, S.G. Mason. Electrohydrodynamic deformation and burst of liquid drops. Phil. Trans. R. Soc. Lond. A 269, 295 (1971). https://doi.org/10.1098/rsta.1971.0032

R. Pethig. Dielectrophoresis: Status of the theory, technology, and applications. Biomicrofluidics 4, 022811 (2010). https://doi.org/10.1063/1.3456626

B.A. Kemp, C.J. Sheppard. Field and material stresses predict observable surface forces in optical and electrostatic manipulation. Proc. SPIE 9922, 9922 (2016). https://doi.org/10.1117/12.2237820

W. Arnold, H. Schwan, U. Zimmermann. Surface conductance and other properties of latex particles measured by electrorotation J. Phys. Chem. 91, 5093 (1987). https://doi.org/10.1021/j100303a043

L. Gorre-Talini, S. Jeanjean, P. Silberzan. Sorting of brownian particles by the pulsed application of an asymmetric potential. Phys. Rev. E 56, 2025 (1997). https://doi.org/10.1103/PhysRevE.56.2025

M.P. Hughes, H. Morgan, M.F. Flynn. The dielectrophoretic behavior of submicron latex spheres: Influence of surface conductance. J. Coll. Int. Sci. 220, 454 (1999). https://doi.org/10.1006/jcis.1999.6542

M. Jim'enez, F. Arroyo, F. Carrique, U. Kaatze, A. Delgado. Determination of stagnant layer conductivity in polystyrene suspensions: temperature effects. J. Coll. Int. Sci. 281, 503 (2005). https://doi.org/10.1016/j.jcis.2004.08.093

A. Delgado, F. Gonz'alez-Caballero, R. Hunter, L. Koopal, J. Lyklema. Measurement and interpretation of electrokinetic phenomena. J. Coll. Int. Sci. 309, 194 (2007). https://doi.org/10.1016/j.jcis.2006.12.075

S. Basuray, H.-C. Chang. Induced dipoles and dielectrophoresis of nanocolloids in electrolytes. Phys. Rev. E 75, 060501 (2007). https://doi.org/10.1103/PhysRevE.75.060501

M.D. Vahey, J. Voldman. High-throughput cell and particle characterization using isodielectric separation. Anal. Chem. 81, 2446 (2009). https://doi.org/10.1021/ac8019575

S. Basuray, H.-C. Chang. Designing a sensitive and quantifiable nanocolloid assay with dielectrophoretic crossover frequencies. Biomicrofluidics 4, 013205 (2010). https://doi.org/10.1063/1.3294575

T. Honegger, K. Berton, E. Picard, D. Peyrade. Determination of Clausius-Mossotti factors and surface capacitances for colloidal particles. Appl. Phys. Lett. 98, 181906 (2011). https://doi.org/10.1063/1.3583441

P.-Y. Weng, I.-A. Chen, C.-K. Yeh, P.-Y. Chen, J.-Y. Juang. Size-dependent dielectrophoretic crossover frequency of spherical particles. Biomicrofluidics 10, 011909 (2016). https://doi.org/10.1063/1.4941853

H.P. Schwan. Electrical properties of tissue and cell suspensions. Adv. Biol. Med. Phys. 5, 147 (1957). https://doi.org/10.1016/B978-1-4832-3111-2.50008-0

C.T. O'Konski. Electric properties of macromolecules. V. Theory of ionic polarization in polyelectrolytes. J. Phys. Chem. 64, 605 (1960). https://doi.org/10.1021/j100834a023

G. Schwarz. A theory of the low-frequency dielectric dispersion of colloidal particles in electrolyte solution. J. Phys. Chem. 66, 2636 (1962). https://doi.org/10.1021/j100818a067

S. Tsukahara, T. Sakamoto, H. Watarai. Positive dielectrophoretic mobilities of single microparticles enhanced by the dynamic diffusion cloud of ions. Langmuir 16, 3866 (2000). https://doi.org/10.1021/la980441k

I. Ermolina, H. Morgan. The electrokinetic properties of latex particles: Comparison of electrophoresis and dielectrophoresis. J. Coll. Int. Sci. 285, 419 (2005). https://doi.org/10.1016/j.jcis.2004.11.003

M.-T.Wei, J. Junio, aH. D. Ou-Yang. Direct measurements of the frequency-dependent dielectrophoresis force. Biomicrofluidics 3, 012003 (2009). https://doi.org/10.1063/1.3058569

S. Basuray, H.-H. Wei, H.-C. Chang. Dynamic double layer effects on ac-induced dipoles of dielectric nanocolloids. Biomicrofluidics 4, 022801 (2010). https://doi.org/10.1063/1.3455720

C.-K. Yeh, J.-Y. Juang,.Dimensional analysis and prediction of dielectrophoretic crossover frequency of spherical particles. AIP Adv. 7, 065304 (2017). https://doi.org/10.1063/1.4985666

K.K. Rangharajan, S. Prakash. Surface-modified microfluidics and nanofluidics. In: Encyclopedia of Nanotechnology (Springer Netherlands, 2014). https://doi.org/10.1007/978-94-007-6178-0_395-2

N.G. Green, H. Morgan. Dielectrophoresis of submicrometer latex spheres. 1. Experimental results. J. Phys. Chem. B 103, 41 (1999). https://doi.org/10.1021/jp9829849

L.A. Rosen, D.A. Saville. Dielectric spectroscopy of colloidal dispersions: Comparisons between experiment and theory. Langmuir 7, 36 (1991). https://doi.org/10.1021/la00049a009

S.S. Dukhin, V.N. Shilov. Dielectric Phenomena and Double Layer in Disperse Systems and Polyelectrolytes (Naukova Dumka, 1972) (in Russian).

A. Korzhenko, M. Tabellout, J. Emery. Dielectric relaxation properties of the polymer coating during its exposition to water. Mat. Chem. Phys. 65, 253 (2000). https://doi.org/10.1016/S0254-0584(00)00214-5

J. Lyklema, A. de Keizer, B.H. Bijsterbosch, G.J. Fleer, M.A. Cohen Stuart. Fundamentals of Interface and Colloid Science. Volume 2: Solid-Liquid Interfaces (Academic Press, 1995) [ISBN: 0-12-460521-9]. https://doi.org/10.1016/S1874-5679(06)80002-4

J. Lyklema, M. Minor. On surface conduction and its role in electrokinetics. Coll. Surf. A 140, 33 (1998). https://doi.org/10.1016/S0927-7757(97)00266-5

A.I. Zhakin. Electrohydrodynamics of charged surfaces. Phys.-Uspekhi 56, 141 (2013). https://doi.org/10.3367/UFNe.0183.201302c.0153

R. Fuchs, F. Claro. Multipolar response of small metallic spheres: Nonlocal theory. Phys. Rev. B 35, 3722 (1987). https://doi.org/10.1103/PhysRevB.35.3722

E. Bichoutskaia, A.L. Boatwright, A. Khachatourian, A.J. Stace. Electrostatic analysis of the interactions between charged particles of dielectric materials. J. Chem. Phys. 133, 024105 (2010). https://doi.org/10.1063/1.3457157

V.V. Datsyuk, O.R. Pavlyniuk. Properties of longitudinal electromagnetic oscillations in metals and their excitation at planar and spherical surfaces. Nanoscale Res. Lett. 12, 473 (2017). https://doi.org/10.1186/s11671-017-2230-6

V.V. Datsyuk, O.M. Tovkach. Optical properties of a metal nanosphere with spatially dispersive permittivity. J. Opt. Soc. Am. B 28, 1224 (2011). https://doi.org/10.1364/JOSAB.28.001224

E.B. Lindgren, H.-K. Chan, A. J. Stace, E. Besley. Progress in the theory of electrostatic interactions between charged particles. Phys. Chem. Chem. Phys. 18, 5883 (2016). https://doi.org/10.1039/C5CP07709E

H. Watarai, T. Sakamoto, S. Tsukahara. In Situ measurement of dielectrophoretic mobility of single polystyrene microparticles. Langmuir 13, 2417 (1997). https://doi.org/10.1021/la961057v

T. Tsukada, T. Katayama, Y. Ito, M. Hozawa. Theoretical and experimental studies of circulations inside and outside a deformed drop under a uniform electric field. J. Chem. Eng. Japan 26, 698 (1993). https://doi.org/10.1252/jcej.26.698

V.V. Datsyuk, O.R. Pavlyniuk. The role of surface conductivity in electro-mechanics of microparticles in a meakly-conducting dielectric drop, in 2019 IEEE 39th International Conference on Electronics and Nanotechnology (EL-NANO, 2019). https://doi.org/10.1109/ELNANO.2019.8783832

G. Supeene, C.R. Koch, S. Bhattacharjee. Deformation of a droplet in an electric field: Nonlinear transient response in perfect and leaky dielectric media. J. Coll. Int. Sci. 318, 463 (2008). https://doi.org/10.1016/j.jcis.2007.10.022

Y.-W. Liu, S. Pennathur, C.D. Meinhart. Electrophoretic mobility of a spherical nanoparticle in a nanochannel. Phys. Fluids 26, 112002 (2014). https://doi.org/10.1063/1.4901330

Published
2020-06-09
How to Cite
Datsyuk, V., & Pavlyniuk, O. (2020). The Role of Surface-Charge Transport in Electrohydrodynamics and Electromechanics of a Dielectric Sphere. Ukrainian Journal of Physics, 65(6), 521. https://doi.org/10.15407/ujpe65.6.521
Section
Physics of liquids and liquid systems, biophysics and medical physics

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