Hostname: page-component-848d4c4894-pjpqr Total loading time: 0 Render date: 2024-06-16T04:56:21.542Z Has data issue: false hasContentIssue false
  • English
  • Français

Electrokinetic energy conversion of two-layer fluids through nanofluidic channels

Published online by Cambridge University Press:  29 January 2019

Zhaodong Ding ,
Yongjun Jian Open the ORCID record for Yongjun Jian [Opens in a new window]  and
Wenchang Tan
Zhaodong Ding
Affiliation:
School of Mathematical Science, Inner Mongolia University, Hohhot, Inner Mongolia 010021, PR China
Yongjun Jian*
Affiliation:
School of Mathematical Science, Inner Mongolia University, Hohhot, Inner Mongolia 010021, PR China
Wenchang Tan
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, and Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing 100871, PR China
*
†Email address for correspondence: jianyj@imu.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

Based on the Onsager reciprocal relation in the linear response regime, we first clarify the equivalence of thermodynamic and electric circuit analyses for electrokinetic energy conversion. Then we present a streaming-potential-based nanofluidic energy conversion system which comprises two immiscible fluids that form a flat interface in a slit-like channel. The validity of the Onsager reciprocal relation to such a two-fluid system is verified. The performance of such an energy converter is illustrated by considering two concrete oil–water systems with different properties. In both cases, we predict that the binary system with a thin oil layer increases both the maximum output power and the energy conversion efficiency, and this enhancement depends strongly on the mobile charges present at the oil–water interface, the salt concentration and the interface location. Concretely, for negatively charged interfaces, we find that the optimal efficiency increases with the interfacial charge for relatively thin oil layers; while for relatively thick oil layers, the interfacial charge has the opposite effect (i.e. reduction effect) on the energy conversion efficiency in the ranges of the parameters. We further investigate these systems from the viewpoint of energy transfer by deriving the related energy equation. We find that viscous dissipation consumes most of the power (more than 90 %), in both single-phase and two-fluid flows. However, the ratio of the viscous dissipation to the power input decreases with increase of the interfacial charge density for the case of a relatively thin oil layer in two-fluid flows. Meanwhile, although the presence of interfacial charges can lead to an increase in electrical dissipation, the amount of the increased power consumption is less than that of the reduced viscous dissipation in the case of a thin oil layer. Therefore, for two-fluid energy converters, the total power consumption can be reduced and the efficiency is improved.

JFM classification

Micro-/Nano-fluid dynamics: Microfluidics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 863 , 25 March 2019 , pp. 1062 - 1090
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bandopadhyay, A. & Chakraborty, S. 2011 Steric-effect induced alterations in streaming potential and energy transfer efficiency of non-Newtonian fluids in narrow confinements. Langmuir 27 (19), 12243–12252.10.1021/la202273eGoogle Scholar
Bandopadhyay, A. & Chakraborty, S. 2012 Giant augmentations in electro-hydro-dynamic energy conversion efficiencies of nanofluidic devices using viscoelastic fluids. Appl. Phys. Lett. 101 (4), 043905.10.1063/1.4739429Google Scholar
Barry, P. H. & Lynch, J. W. 1991 Liquid junction potentials and small cell effects in patch-clamp analysis. J. Membr. Biol. 121 (2), 101–117.10.1007/BF01870526Google Scholar
Behrens, S. H. & Grier, D. G. 2001 The charge of glass and silica surfaces. J. Chem. Phys. 115 (14), 6716–6721.10.1063/1.1404988Google Scholar
Berli, C. L. A. 2010 Electrokinetic energy conversion in microchannels using polymer solutions. J. Colloid Interface Sci. 349 (1), 446–448.10.1016/j.jcis.2010.05.083Google Scholar
Bird, R. B., Stewart, W. E. & Lightfoot, E. N. 1960 Transport Phenomena. Wiley.Google Scholar
Bocquet, L. & Charlaix, E. 2010 Nanofluidics, from bulk to interfaces. Chem. Soc. Rev. 39, 1073–1095.10.1039/B909366BGoogle Scholar
Brunet, E. & Ajdari, A. 2004 Generalized Onsager relations for electrokinetic effects in anisotropic and heterogeneous geometries. Phys. Rev. E 69 (1), 16306.Google Scholar
Chanda, S., Sinha, S. & Das, S. 2014 Streaming potential and electroviscous effects in soft nanochannels: towards designing more efficient nanofluidic electrochemomechanical energy converters. Soft Matt. 10 (38), 7558–7568.10.1039/C4SM01490AGoogle Scholar
Chang, C. C. & Yang, R. J. 2010 Electrokinetic energy conversion in micrometer-length nanofluidic channels. Microfluid Nanofluid 9 (2–3), 225–241.10.1007/s10404-009-0538-yGoogle Scholar
Chang, C. C. & Yang, R. J. 2011 Electrokinetic energy conversion efficiency in ion-selective nanopores. Appl. Phys. Lett. 99 (8), 083102.10.1063/1.3625921Google Scholar
Choi, W. S., Sharma, A., Qian, S., Lim, G. & Joo, S. W. 2011 On steady two-fluid electroosmotic flow with full interfacial electrostatics. J. Colloid Interface Sci. 357 (2), 521–526.10.1016/j.jcis.2011.01.107Google Scholar
Conboy, J. C. & Richmond, G. L. 1997 Examination of the electrochemical interface between two immiscible electrolyte solutions by second harmonic generation. J. Phys. Chem. B 101 (6), 983–990.10.1021/jp962775tGoogle Scholar
Daiguji, H., Oka, Y., Adachi, T. & Shirono, K. 2006 Theoretical study on the efficiency of nanofluidic batteries. Electrochem. Commun. 8 (11), 1796–1800.10.1016/j.elecom.2006.08.003Google Scholar
Daiguji, H., Yang, P. & Majumdar, A. 2004a Ion transport in nanofluidic channels. Nano Lett. 4 (1), 137–142.10.1021/nl0348185Google Scholar
Daiguji, H., Yang, P., Szeri, A. & Majumdar, A. 2004b Electrochemomechanical energy conversion in nanofluidic channels. Nano Lett. 4 (12), 2315–2322.10.1021/nl0489945Google Scholar
Das, S., Guha, A. & Mitra, S. K. 2013 Exploring new scaling regimes for streaming potential and electroviscous effects in a nanocapillary with overlapping electric double layers. Anal. Chim. Acta 804 (804), 159–166.10.1016/j.aca.2013.09.061Google Scholar
Davidson, C. & Xuan, X. 2008a Effects of Stern layer conductance on electrokinetic energy conversion in nanofluidic channels. Electrophoresis 29 (5), 1125–1130.10.1002/elps.200700549Google Scholar
Davidson, C. & Xuan, X. 2008b Electrokinetic energy conversion in slip nanochannels. J. Power Sources 179 (1), 297–300.10.1016/j.jpowsour.2007.12.050Google Scholar
Ding, Z., Jian, Y., Wang, L. & Yang, L. 2017 Analytical investigation of electrokinetic effects of micropolar fluids in nanofluidic channels. Phys. Fluids 29 (8), 082008.10.1063/1.4999487Google Scholar
Gillespie, D. 2012 High energy conversion efficiency in nanofluidic channels. Nano Lett. 12 (3), 1410–1416.10.1021/nl204087fGoogle Scholar
Gopmandal, P. P. & Ohshima, H. 2017 Modulation of electroosmotic flow through electrolyte column surrounded by a dielectric oil layer. Colloid Polym. Sci. 295 (7), 1141–1151.10.1007/s00396-017-4108-7Google Scholar
Goswami, P. & Chakraborty, S. 2010 Energy transfer through streaming effects in time-periodic pressure-driven nanochannel flows with interfacial slip. Langmuir 26 (1), 581–590.10.1021/la901209aGoogle Scholar
Gu, Y. & Li, D. 1998 Electric charge on small silicone oil droplets dispersed in ionic surfactant solutions. Colloids Surf. A 139 (2), 213–225.10.1016/S0927-7757(98)00283-0Google Scholar
van der Heyden, F. H. J., Bonthuis, D. J., Stein, D., Meyer, C. & Dekker, C. 2006 Electrokinetic energy conversion efficiency in nanofluidic channels. Nano Lett. 6 (10), 2232–2237.10.1021/nl061524lGoogle Scholar
van der Heyden, F. H. J., Bonthuis, D. J., Stein, D., Meyer, C. & Dekker, C. 2007 Power generation by pressure-driven transport of ions in nanofluidic channels. Nano Lett. 7 (4), 1022–1025.10.1021/nl070194hGoogle Scholar
van der Heyden, F. H. J., Stein, D. & Dekker, C. 2005 Streaming currents in a single nanofluidic channel. Phys. Rev. Lett. 95 (11), 116104.10.1103/PhysRevLett.95.116104Google Scholar
Jian, Y., Li, F., Liu, Y., Chang, L., Liu, Q. & Yang, L. 2017 Electrokinetic energy conversion efficiency of viscoelastic fluids in a polyelectrolyte-grafted nanochannel. Colloids Surf. B 156, 405–413.10.1016/j.colsurfb.2017.05.039Google Scholar
Jian, Y., Su, J., Chang, L., Liu, Q. & He, G. 2014 Transient electroosmotic flow of general Maxwell fluids through a slit microchannel. Z. Angew. Math. Phys. 65 (3), 435–447.10.1007/s00033-013-0341-1Google Scholar
Lee, J. S. H., Barbulovic-Nad, I., Wu, Z., Xuan, X. & Li, D. 2006 Electrokinetic flow in a free surface-guided microchannel. J. Appl. Phys. 99 (5), 054905.Google Scholar
Lee, J. S. H. & Li, D. 2006 Electroosmotic flow at a liquid–air interface. Microfluid Nanofluid 2 (4), 361–365.10.1007/s10404-006-0084-9Google Scholar
Leunissen, M. E., Zwanikken, J., Van Roij, R., Chaikin, P. M. & Van Blaaderen, A. 2007 Ion partitioning at the oil–water interface as a source of tunable electrostatic effects in emulsions with colloids. Phys. Chem. Chem. Phys. 9 (48), 6405–6414.10.1039/b711300eGoogle Scholar
Li, D. 2004 Electrokinetics in Microfluidics, vol. 2. Elsevier.10.1016/S1573-4285(04)80022-XGoogle Scholar
Liu, K., Ding, T., Mo, X., Chen, Q., Yang, P., Li, J., Xie, W., Zhou, Y. & Zhou, J. 2016 Flexible microfluidics nanogenerator based on the electrokinetic conversion. Nano Energy 30, 684–690.10.1016/j.nanoen.2016.10.058Google Scholar
Marinova, K. G., Alargova, R. G., Denkov, N. D., Velev, O. D., Petsev, D. N., Ivanov, I. B. & Borwankar, R. P. 1996 Charging of oil–water interfaces due to spontaneous adsorption of hydroxyl ions. Langmuir 12 (8), 2045–2051.10.1021/la950928iGoogle Scholar
Masliyah, J. H. & Bhattacharjee, S. 2006 Electrokinetic and Colloid Transport Phenomena. Wiley.10.1002/0471799742Google Scholar
Mei, L., Yeh, L.-H. & Qian, S. 2017 Buffer anions can enormously enhance the electrokinetic energy conversion in nanofluidics with highly overlapped double layers. Nano Energy 32, 374–381.10.1016/j.nanoen.2016.12.036Google Scholar
Movahed, S., Khani, S., Wen, J. Z. & Li, D. 2012 Electroosmotic flow in a water column surrounded by an immiscible liquid. J. Colloid Interface Sci. 372 (1), 207–211.10.1016/j.jcis.2012.01.044Google Scholar
Munshi, F. & Chakraborty, S. 2009 Hydroelectrical energy conversion in narrow confinements in the presence of transverse magnetic fields with electrokinetic effects. Phys. Fluids 21 (12), 122003.10.1063/1.3276291Google Scholar
Nguyen, T., Xie, Y., de Vreede, L. J., van den Berg, A. & Eijkel, J. C. T. 2013 Highly enhanced energy conversion from the streaming current by polymer addition. Lab on a Chip 13 (16), 3210–3216.10.1039/c3lc41232fGoogle Scholar
Ohshima, H., Nomura, K., Kamaya, H. & Ueda, I. 1985 Liquid membrane: equilibrium potential distribution across lipid monolayer-coated oil/water interface. J. Colloid Interface Sci. 106 (2), 470–478.10.1016/S0021-9797(85)80022-9Google Scholar
Olthuis, W., Schippers, B., Eijkel, J. & van den Berg, A. 2005 Energy from streaming current and potential. Sensors Actuators B 111, 385–389.10.1016/j.snb.2005.03.039Google Scholar
Osterle, J. F. 1964 Electrokinetic energy conversion. Trans. ASME J. Appl. Mech. 31 (2), 161–164.10.1115/1.3629580Google Scholar
Patwary, J., Chen, G. & Das, S. 2016 Efficient electrochemomechanical energy conversion in nanochannels grafted with polyelectrolyte layers with pH-dependent charge density. Microfluid. Nanofluid. 20 (2), 37.10.1007/s10404-015-1695-9Google Scholar
Pennathur, S., Eijkel, J. C. T. & van den Berg, A. 2007 Energy conversion in microsystems: Is there a role for micro/nanofluidics? Lab on a Chip 7 (10), 1234.Google Scholar
Prigogine, I. 1968 An Introduction to Thermodynamics of Irreversible Processes. Interscience.Google Scholar
Ren, Y. & Stein, D. 2008 Slip-enhanced electrokinetic energy conversion in nanofluidic channels. Nanotechnology 19 (19), 195707.10.1088/0957-4484/19/19/195707Google Scholar
Saha, S., Gopmandal, P. P. & Ohshima, H. 2017 Steady/unsteady electroosmotic flow through nanochannel filled with electrolyte solution surrounded by an immiscible liquid. Colloid Polym. Sci. 295 (12), 2287–2297.Google Scholar
Schoch, R. B., Han, J. & Renaud, P. 2008 Transport phenomena in nanofluidics. Rev. Mod. Phys. 80 (3), 839.10.1103/RevModPhys.80.839Google Scholar
Sherwood, J. D., Xie, Y., van den Berg, A. & Eijkel, J. C. T. 2013 Theoretical aspects of electrical power generation from two-phase flow streaming potentials. Microfluid. Nanofluid. 15 (3), 347–359.10.1007/s10404-013-1151-7Google Scholar
Shit, G. C., Mondal, A., Sinha, A. & Kundu, P. K. 2016 Two-layer electro-osmotic flow and heat transfer in a hydrophobic micro-channel with fluid–solid interfacial slip and zeta potential difference. Colloids Surf. A 506, 535–549.10.1016/j.colsurfa.2016.06.050Google Scholar
Siria, A., Poncharal, P., Biance, A.-L., Fulcrand, R., Blase, X., Purcell, S. T. & Bocquet, L. 2013 Giant osmotic energy conversion measured in a single transmembrane boron nitride nanotube. Nature 494 (7438), 455–458.10.1038/nature11876Google Scholar
Sparreboom, W., van den Berg, A. & Eijkel, J. C. T. 2010 Transport in nanofluidic systems: a review of theory and applications. New J. Phys. 12 (1), 015004.Google Scholar
Stein, D., Kruithof, M. & Dekker, C. 2004 Surface-charge-governed ion transport in nanofluidic channels. Phys. Rev. Lett. 93 (3), 035901.10.1103/PhysRevLett.93.035901Google Scholar
Su, J., Jian, Y., Chang, L. & Li, Q. 2013 Transient electro-osmotic and pressure driven flows of two-layer fluids through a slit microchannel. Acta Mechanica Sin. 29 (4), 534–542.10.1007/s10409-013-0051-0Google Scholar
Volkov, A. G., Deamer, D. W., Tanelian, D. L. & Markin, V. S. 1996 Electrical double layers at the oil/water interface. Prog. Surf. Sci. 53 (1), 1–134.10.1016/S0079-6816(97)82876-6Google Scholar
Wang, M. & Kang, Q. 2010 Electrochemomechanical energy conversion efficiency in silica nanochannels. Microfluid Nanofluid 9 (2–3), 181–190.10.1007/s10404-009-0530-6Google Scholar
Xie, Y., Sherwood, J. D., Shui, L., van den Berg, A. & Eijkel, J. C. T. 2011 Strong enhancement of streaming current power by application of two phase flow. Lab on a Chip 11 (23), 4006.10.1039/c1lc20423hGoogle Scholar
Xie, Y., Wang, X., Xue, J., Jin, K., Chen, L. & Wang, Y. 2008 Electric energy generation in single track-etched nanopores. Appl. Phys. Lett. 93 (16), 163116.10.1063/1.3001590Google Scholar
Xuan, X. & Li, D. 2006 Thermodynamic analysis of electrokinetic energy conversion. J. Power Sources 156 (2), 677–684.10.1016/j.jpowsour.2005.05.057Google Scholar
Yang, J., Lu, F., Kostiuk, L. W. & Kwok, D. Y. 2003 Electrokinetic microchannel battery by means of electrokinetic and microfluidic phenomena. J. Micromech. Microengng 13 (6), 963–970.10.1088/0960-1317/13/6/320Google Scholar
Zhang, R., Wang, S., Yeh, M.-H., Pan, C., Lin, L., Yu, R., Zhang, Y., Zheng, L., Jiao, Z. & Wang, Z. L. 2015 A streaming potential/current-based microfluidic direct current generator for self-powered nanosystems. Adv. Mater. 27 (41), 6482–6487.10.1002/adma.201502477Google Scholar