Explicit Thickness Formulae for the Potential, Field and Charge Density of a Planar Electric Double Layer at High Zeta Potential.

In the present paper a new model is proposed for electric double layer (EDL) overlapped in nanochannels. The model aimed to obtain a deeper insight of transport phenomena in nanoscale. Two-dimensional Nernst and ionic conservation equations are used to obtain electroosmotic potential distribution in flow field. In the proposed study, transport equations for flow, ionic concentration and electroosmotic potential are solved numerically via finite volume method. Moreover, Debye-Hu¨ckle (DH) approximation and symmetry condition, which limit the application, are avoided. Thus, the present model is suitable for prediction of electroosmotic flows through nanochannels as well as complicated asymmetric geometries with large nonuniform zeta potential distribution. For homogeneous zeta potential distribution, it has been shown that by reduction of channel height to values comparable with EDL thickness, Poisson-Boltzmann model produces inaccurate results and must be avoided. Furthermore, for overlapped electric double layer in nanochannels with heterogeneous zeta potential distribution it has been found that the present model returns modified ionic concentration and electroosmotic potential distribution compare to previous EDL overlapped models due to 2D solution of ionic concentration distribution. Finally, velocity profiles in EDL overlapped nanochannels are investigated and it has been showed that for pure electroosmotic flow the velocity profile deviates from the expected plug-like profile towards a parabolic profile.

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Effect of charge density gradient on characteristics of electric double layer for salt melts

Russian Journal of Electrochemistry ◽

10.1134/s1023193507120063 ◽

2007 ◽

Vol 43 (12) ◽

pp. 1369-1376 ◽

Cited By ~ 3

Author(s):

N. K. Tkachev ◽

M. A. Kobelev

Keyword(s):

Charge Density ◽

Density Gradient ◽

Double Layer ◽

Electric Double Layer ◽

Salt Melts

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Ferroelectric field control of charge density in oxide films with polarization reversal by electric double layer

Applied Physics Letters ◽

10.1063/1.5047558 ◽

2018 ◽

Vol 113 (14) ◽

pp. 143501 ◽

Cited By ~ 4

Author(s):

Ryutaro Nishino ◽

Yusuke Kozuka ◽

Fumitaka Kagawa ◽

Masaki Uchida ◽

Masashi Kawasaki

Keyword(s):

Charge Density ◽

Double Layer ◽

Electric Double Layer ◽

Oxide Films ◽

Polarization Reversal ◽

Field Control

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Effects of the internal structure of spheroidal divalent ions on the charge density profiles of the electric double layer

The Journal of Chemical Physics ◽

10.1063/1.4768448 ◽

2012 ◽

Vol 137 (22) ◽

pp. 224701 ◽

Cited By ~ 7

Author(s):

José Guadalupe Ibarra-Armenta ◽

Alberto Martín-Molina ◽

Klemen Bohinc ◽

Manuel Quesada-Pérez

Keyword(s):

Charge Density ◽

Internal Structure ◽

Double Layer ◽

Electric Double Layer ◽

Divalent Ions ◽

Density Profiles

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Electric Double Layer and Orientational Ordering of Water Dipoles in Narrow Channels within a Modified Langevin Poisson-Boltzmann Model

Entropy ◽

10.3390/e22091054 ◽

2020 ◽

Vol 22 (9) ◽

pp. 1054

Author(s):

Mitja Drab ◽

Ekaterina Gongadze ◽

Veronika Kralj-Iglič ◽

Aleš Iglič

Keyword(s):

Charge Density ◽

Double Layer ◽

Electric Double Layer ◽

Energy Functional ◽

Large Radius ◽

Charged Surface ◽

Volume Charge ◽

Volume Charge Density ◽

Poisson Boltzmann ◽

Orientational Ordering

The electric double layer (EDL) is an important phenomenon that arises in systems where a charged surface comes into contact with an electrolyte solution. In this work we describe the generalization of classic Poisson-Boltzmann (PB) theory for point-like ions by taking into account orientational ordering of water molecules. The modified Langevin Poisson-Boltzmann (LPB) model of EDL is derived by minimizing the corresponding Helmholtz free energy functional, which includes also orientational entropy contribution of water dipoles. The formation of EDL is important in many artificial and biological systems bound by a cylindrical geometry. We therefore numerically solve the modified LPB equation in cylindrical coordinates, determining the spatial dependencies of electric potential, relative permittivity and average orientations of water dipoles within charged tubes of different radii. Results show that for tubes of a large radius, macroscopic (net) volume charge density of coions and counterions is zero at the geometrical axis. This is attributed to effective electrolyte charge screening in the vicinity of the inner charged surface of the tube. For tubes of small radii, the screening region extends into the whole inner space of the tube, leading to non-zero net volume charge density and non-zero orientational ordering of water dipoles near the axis.

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Effective Excess Charge Density in Water Saturated Porous Media

VNU Journal of Science Mathematics - Physics ◽

10.25073/2588-1124/vnumap.4294 ◽

2018 ◽

Vol 34 (4) ◽

Author(s):

Luong Duy Thanh

Keyword(s):

Porous Media ◽

Zeta Potential ◽

Double Layer ◽

Electric Double Layer ◽

Electrical Potential ◽

Debye Length ◽

Excess Charge ◽

Geophysical Research ◽

Colloid Science ◽

Capillary Pore

A model for the effective excess charge in a capillary as well as in porous media is developed for arbitrary pore scales. The prediction of the model is then compared with another published model that is limited for a thin electric double layer (EDL) assumption. The comparison shows that there is a deviation between two models depending on the ratio of capillary/pore radius and the Debye length. The reasons for the deviation between two models are not only due to the thin EDL assumption to get electrical potential and charge distribution in pores but also to some other approximations for integral evaluations. The results suggest that the model developed in this work can be used with arbitrary capillary/pore scale and thus is not restricted to the thin EDL assumption. Keywords: Zeta potential, porous media, electric double layer, effective excess charge. References [1] M. Aubert, Q.Y. Atangana, Groundwater, 34 (1996) 1010–1016.[2] A. Finizola, J.-F. Lénat, O. Macedo, D. Ramos, J.-C. Thouret, F. Sortino, J. Volcanol. Geoth. Res., 135 (2004) 343–360.[3] C. Doussan, L. Jouniaux, J.-L. Thony, Journal of Hydrology 267 (2002) 173–185.[4] F. Perrier, M. Trique, B. Lorne, J.-P. Avouac, S. Hautot, P. Tarits, Geophys. Res. Lett. 25 (1998) 1955–1958.[5] Martinez-Pagan, P., A. Jardani, A. Revil, and A. Haas, Geophysics 75 (2010) WA17–WA25.[6] Naudet, V., A. Revil, J.-Y. Bottero, and P. Bgassat, Geophysical Research Letters 30 (2003).[7] V. Naudet, M. Lazzari, A. Perrone, A. Loperte, S. Piscitelli, V. Lapenna, Engineering Geology 98 (2008) 156-167.[8] A. Perrone, A. Iannuzzi, V. Lapenna, P. Lorenzo, S. Piscitelli, E. Rizzo, F. Sdao, Journal of Applied Geophysics 56 (2004) 17-29.[9] Jouniaux, L., A. Maineult, V. Naudet, M. Pessel, and P. Sailhac, C. R. Geoscience 341 (2009).[10] Revil, A., and A. Jardani, The Self-Potential Method: Theory and Applications in Environmental Geosciences, Cambridge University Press, 2013.[11] Hunter, R., Zeta Potential in Colloid Science: Principles and Applications, Colloid Science Series, Academic Press, 1981.[12] Leroy, P., and A. Revil, Journal of Colloid and Interface Science, 270 (2004) 371–380.[13] T. Ishido, H. Mizutani, Journal of Geophysical Research 86 (1981) 1763-1775.[14] P. W. J. Glover, E. Walker, M. Jackson, Geophysics 77 (2012) D17–D43.[15] Revil, A., and P. Leroy, Journal of Geophysical Research 109 (2004).[16] Linde, N., D. Jougnot, A. Revil, S. K. Matthäi, T. Arora, D. Renard, and C. Doussan, Geophys. Res. Lett. 34 (2007) L03306.[17] Revil A. and Mahardika H, Water Resources Research 49 (2013) 744–766.[18] Jardani, A., A. Revil, A. Bolève, A. Crespy, J. Dupont, W. Barrash and B. Malama, Geophysical Research Letters, 34 (2007) L24,403.[19] L. Guarracino, D. Jougnot, Journal of Geophysical Research - Solid Earth 123 (2018) 52-65.[20] Jackson M.D., Leinov E., International Journal of Geophysics 2012 (2012).[21] Gierst L., J. Am. Chem. Soc. 88 (1966) 4768.[22] Rice, C., and R. Whitehead, J. Phys. Chem. 69 (1965) 4017–4024.[23] Pride, S., Physical Review B 50 (1994) 15,678–15,696.[24] Bear, J., Dynamics of Fluids in Porous Media, Dover Publications, New York, 1988. [25] Chan I. Chung, Extrusion of Polymers: Theory & Practice, Hanser-2nd edition, 2010.[26] J. Vinogradov, M. Z. Jaafar, M. D. Jackson, Journal of Geophysical Research 115 (2010).

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