On the energy conversion in electrokinetic transports

doi:10.1007/s10483-022-2810-7

Applied Mathematics and Mechanics (English Edition) ›› 2022, Vol. 43 ›› Issue (2): 263-274.doi: https://doi.org/10.1007/s10483-022-2810-7

On the energy conversion in electrokinetic transports

Zhaodong DING¹, Long CHANG², Kai TIAN¹, Yongjun JIAN¹

1. School of Mathematical Science, Inner Mongolia University, Hohhot 010021, Inner Mongolia, China;
2. School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010021, Inner Mongolia, China

收稿日期:2021-05-07 修回日期:2021-11-10 发布日期:2022-01-25
通讯作者: Yongjun JIAN, E-mail:jianyj@imu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11902165, 11772162, and 11862018), the Natural Science Foundation of Inner Mongolia Autonomous Region of China (Nos. 2019BS01004 and 2021MS01007), and the Inner Mongolia Grassland Talent (No. 12000- 12102013)

On the energy conversion in electrokinetic transports

Zhaodong DING¹, Long CHANG², Kai TIAN¹, Yongjun JIAN¹

1. School of Mathematical Science, Inner Mongolia University, Hohhot 010021, Inner Mongolia, China;
2. School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot 010021, Inner Mongolia, China

Received:2021-05-07 Revised:2021-11-10 Published:2022-01-25
Contact: Yongjun JIAN, E-mail:jianyj@imu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11902165, 11772162, and 11862018), the Natural Science Foundation of Inner Mongolia Autonomous Region of China (Nos. 2019BS01004 and 2021MS01007), and the Inner Mongolia Grassland Talent (No. 12000- 12102013)

摘要/Abstract

摘要： Energy conversion in micro/nano-systems is a subject of current research, among which the electrokinetic energy conversion has attracted extensive attention. However, there exist two difierent deflnitions on the electrokinetic energy conversion e–ciency in literature. A few researchers deflned the e–ciency using the pure pressure-driven flow rate, while other groups deflned the e–ciency based on the flow rate with the inclusion of the efiect of the streaming potential fleld. In this work, both deflnitions are investigated for difierent fluid types under the periodic electrokinetic flow condition. For Newtonian fluids, the two deflnitions give similar results. However, for viscoelastic fluids, these two deflnitions lead to signiflcant difierence. The e–ciency deflned by the pure pressure-driven flow rate even exceeds 100% in a certain range of the parameters. The result shows that in the case of viscoelastic flow, it is incorrect to deflne the energy conversion e–ciency by pure pressure-driven flow rate. At the same time, the reason for this problem is clarifled through comprehensive analysis.

关键词: electrokinetic transport, energy conversion e–ciency, Newtonian fluid, viscoelastic fluid, streaming potential fleld

Abstract: Energy conversion in micro/nano-systems is a subject of current research, among which the electrokinetic energy conversion has attracted extensive attention. However, there exist two difierent deflnitions on the electrokinetic energy conversion e–ciency in literature. A few researchers deflned the e–ciency using the pure pressure-driven flow rate, while other groups deflned the e–ciency based on the flow rate with the inclusion of the efiect of the streaming potential fleld. In this work, both deflnitions are investigated for difierent fluid types under the periodic electrokinetic flow condition. For Newtonian fluids, the two deflnitions give similar results. However, for viscoelastic fluids, these two deflnitions lead to signiflcant difierence. The e–ciency deflned by the pure pressure-driven flow rate even exceeds 100% in a certain range of the parameters. The result shows that in the case of viscoelastic flow, it is incorrect to deflne the energy conversion e–ciency by pure pressure-driven flow rate. At the same time, the reason for this problem is clarifled through comprehensive analysis.

Key words: electrokinetic transport, energy conversion e–ciency, Newtonian fluid, viscoelastic fluid, streaming potential fleld

中图分类号:

76A05
76D05

Zhaodong DING, Long CHANG, Kai TIAN, Yongjun JIAN. On the energy conversion in electrokinetic transports[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(2): 263-274.

参考文献

[1] MAHAPATRA, B. and BANDOPADHYAY, A. Electroosmosis of a viscoelastic fluid over non-uniformly charged surfaces: effect of fluid relaxation and retardation time. Physics of Fluids, 32(3), 032005 (2020)
[2] SADEK, S. H. and PINHO, F. T. Electro-osmotic oscillatory flow of viscoelastic fluids in a microchannel. Journal of Non-Newtonian Fluid Mechanics, 266, 46-58 (2019)
[3] CHAKRABORTY, S. and DAS, S. Streaming-field-induced convective transport and its influence on the electroviscous effects in narrow fluidic confinement beyond the Debye-Hückel limit. Physical Review E, 77(3), 037303 (2008)
[4] DAS, S., GUHA, A., and MITRA, S. K. Exploring new scaling regimes for streaming potential and electroviscous effects in a nanocapillary with overlapping electric double layers. Analytica Chimica Acta, 804, 159-166 (2013)
[5] FERRÁS, L. L., AFONSO, A., ALVES, M., NÓBREGA, J., and PINHO, F. Electro-osmotic and pressure-driven flow of viscoelastic fluids in microchannels: analytical and semi-analytical solutions. Physics of Fluids, 28(9), 093102 (2016)
[6] GHOSH, U. Electrokinetic effects in helical flow of non-linear viscoelastic fluids. Physics of Fluids, 32(5), 052004 (2020)
[7] MAHAPATRA, B. and BANDOPADHYAY, A. Numerical analysis of combined electroosmotic-pressure driven flow of a viscoelastic fluid over high zeta potential modulated surfaces. Physics of Fluids, 33(1), 12001 (2021)
[8] SARMA, R., DEKA, N., SARMA, K., and MONDAL, P. K. Electroosmotic flow of Phan-Thien-Tanner fluids at high zeta potentials: an exact analytical solution. Physics of Fluids, 30(6), 062001 (2018)
[9] FAN, B., BHATTACHARYA, A., and BANDARU, P. R. Enhanced voltage generation through electrolyte flow on liquid-filled surfaces. Nature Communications, 9, 4050 (2018)
[10] ALI, N., HUSSAIN, S., and ULLAH, K. Theoretical analysis of two-layered electro-osmotic peristaltic flow of FENE-P fluid in an axisymmetric tube. Physics of Fluids, 32(2), 023105 (2020)
[11] SCHNITZER, O. and YARIV, E. Streaming-potential phenomena in the thin-Debye-layer limit. Part 3. Shear-induced electroviscous repulsion. Journal of Fluid Mechanics, 786, 84-109 (2016)
[12] SIRIA, A., PONCHARAL, P., BIANCE, A. L., FULCRAND, R., BLASE, X., PURCELL, S. T., and PURCELL, L. Giant osmotic energy conversion measured in a single transmembrane boron nitride nanotube. nature, 794(7438), 455-458 (2013)
[13] OSTERLE, J. F. Electrokinetic energy conversion. Journal of Applied Mechanics, 31, 161-164 (1964)
[14] DAIGUJI, H., YANG, P., SZERI, A., and MAJUMDAR, A. Electrochemomechanical energy conversion in nanofluidic channels. Nano Letters, 4, 2315-2321 (2004)
[15] VAN DER HEYDEN, F. H., BONTHUIS, D. J., STEIN, D., MEYER, C., and DEKKER, C. Electrokinetic energy conversion efficiency in nanofluidic channels. Nano Letters, 6, 2232-2237 (2006)
[16] VAN DER HEYDEN, F. H., BONTHUIS, D. J., STEIN, D., MEYER, C., and DEKKER, C. Power generation by pressure-driven transport of ions in nanofluidic channels. Nano Letters, 7, 1022-1025 (2007)
[17] WANG, M. and KANG, Q. Electrochemomechanical energy conversion efficiency in silica nanochannels. Microfluidics and Nanofluidics, 9(2-3), 181-190 (2010)
[18] CHANG, C. C. and YANG, R. J. Electrochemomechanical energy conversion efficiency in silica nanochannels. Applied Physics Letters, 99(8), 083102 (2011)
[19] PENNATHUR, S., EIJKEL, J. C. T., and VAN DEN BERG, A. Energy conversion in microsystems: is there a role for micro/nanofluidics? Lab on a Chip, 7(10), 1234-1237 (2007)
[20] YANG, J., LU, F., KOSTIUK, L. W., and KWOK, D. Y. Electrokinetic microchannel battery by means of electrokinetic and microfluidic phenomena. Journal of Micromechanics and Microengineering, 13, 963-970 (2003)
[21] DAIGUJI, H., OKA, Y., ADACHI, T., and SHIRONO, K. Theoretical study on the efficiency of nanofluidic batteries. Electrochemistry Communications, 8, 1796-1800 (2006)
[22] ZHANG, R., WANG, S., YEH, M. H., PAN, C., LIN, L., YU, R., ZHANG, Y., ZHENG, L., JIAO, Z., and WANG, Z. L. A streaming potential/current-based microfluidic direct current generator for self-powered nanosystems. Advanced Materials, 27, 6482-6487 (2015)
[23] CHANDA, S., SINHA, S., and DAS, S. Streaming potential and electroviscous effects in soft nanochannels: towards designing more efficient nanofluidic electrochemomechanical energy converters. Soft Matter, 10, 7558-7568 (2014)
[24] PATWARY, J., CHEN, G., and DAS, S. Efficient electrochemomechanical energy conversion in nanochannels grafted with polyelectrolyte layers with pH-dependent charge density. Microfluidics and Nanofluidics, 20, 37 (2016)
[25] KORANLOU, A., ASHRAFIZADEH, S. N., and SADEGHI, A. Enhanced electrokinetic energy harvesting from soft nanochannels by the inclusion of ionic size. Journal of Physics D: Applied Physics, 52, 155502 (2019)
[26] XUAN, X. and LI, D. Thermodynamic analysis of electrokinetic energy conversion. Journal of Power Sources, 156, 677-684 (2006)
[27] GOSWAMI, P. and CHAKRABORTY, S. Energy transfer through streaming effects in time-periodic pressure-driven nanochannel flows with interfacial slip. Langmuir, 26, 581-590 (2010)
[28] BANDOPADHYAY, A. and CHAKRABORTY, S. Giant augmentations in electro-hydro-dynamic energy conversion efficiencies of nanofluidic devices using viscoelastic fluids. Applied Physics Letters, 101, 043905 (2012)
[29] NGUYEN, T., XIE, Y., VREEDE, L. J. D., VAN DEN BERG, A., and EIJKEL, J. C. T. Highly enhanced energy conversion from the streaming current by polymer addition. Lab on a Chip, 13, 3210-3216 (2013)
[30] MEI, L., YEH, L. H., and QIAN, S. Buffer anions can enormously enhance the electrokinetic energy conversion in nanofluidics with highly overlapped double layers. Nano Energy, 32, 374-381 (2017)
[31] DING, Z. D. and JIAN, Y. J. Electrokinetic oscillatory flow and energy conversion of viscoelastic fluids in microchannels: a linear analysis. Journal of Fluid Mechanics, 919, A20 (2021)
[32] DING, Z., JIAN, Y., and TAN, W., Electrokinetic energy conversion of two-layer fluids through nanofluidic channels. Journal of Fluid Mechanics, 863, 1062-1090 (2019)
[33] ECKMANN. D. and GROTBERG, J. Experiments on transition to turbulence in oscillatory pipe flow. Journal of Fluid Mechanics, 222, 329-350 (1991)
[34] CASANELLAS, L. and ORTÍN, J. Laminar oscillatory flow of Maxwell and Oldroyd-B fluids: theoretical analysis. Journal of Non-Newtonian Fluid Mechanics, 166, 1315-1326 (2011)
[35] DEL RÍO, J., DE HARO, M. L., and WHITAKER, S. Enhancement in the dynamic response of a viscoelastic fluid flowing in a tube. Physical Review E, 58, 6323-6327 (1998)
[36] DING, Z. and JIAN, Y. Resonance behaviors in periodic viscoelastic electrokinetic flows: a universal Deborah number. Physics of Fluids, 33, 032023 (2021)
[37] OLTHUIS, W., SCHIPPERS, B., EIJKEL, J. C. T., and VAN DEN BERG, A. Energy from streaming current and potential. Sensors and Actuators B: Chemical, 111-112, 385-389 (2005)

On the energy conversion in electrokinetic transports

On the energy conversion in electrokinetic transports

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	D. BANERJEE, S. PATI, P. BISWAS. Analytical study of pulsatile mixed electroosmotic and shear-driven flow in a microchannel with a slip-dependent zeta potential[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(6): 1007-1022.
[2]	Shujuan AN, Kai TIAN, Zhaodong DING, Yongjun JIAN. Electromagnetohydrodynamic (EMHD) flow of fractional viscoelastic fluids in a microchannel[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(6): 917-930.
[3]	Jie SU, Hongxia SONG, Liaoliang KE, S. M. AIZIKOVICH. The size-dependent elastohydrodynamic lubrication contact of a coated half-plane with non-Newtonian fluid[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(7): 915-930.
[4]	Yanli QIAO, Xiaoping WANG, Huanying XU, Haitao QI. Numerical analysis for viscoelastic fluid flow with distributed/variable order time fractional Maxwell constitutive models[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(12): 1771-1786.
[5]	N. A. ZAINAL, R. NAZAR, K. NAGANTHRAN, I. POP. Unsteady flow of a Maxwell hybrid nanofluid past a stretching/shrinking surface with thermal radiation effect[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(10): 1511-1524.
[6]	M. I. KHAN, F. ALZAHRANI. Transportation of heat through Cattaneo-Christov heat flux model in non-Newtonian fluid subject to internal resistance of particles[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(8): 1157-1166.
[7]	S. I. ABDELSALAM, M. M. BHATTI. Anomalous reactivity of thermo-bioconvective nanofluid towards oxytactic microorganisms[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(5): 711-724.
[8]	S. A. SHEHZAD, S. U. KHAN, Z. ABBAS, A. RAUF. A revised Cattaneo-Christov micropolar viscoelastic nanofluid model with combined porosity and magnetic effects[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(3): 521-532.
[9]	P. NAG, M. M. MOLLA, M. A. HOSSAIN. Non-Newtonian effect on natural convection flow over cylinder of elliptic cross section[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(2): 361-382.
[10]	Chen YIN, Chunwu WANG, Shaowei WANG. Thermal instability of a viscoelastic fluid in a fluid-porous system with a plane Poiseuille flow[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(11): 1631-1650.
[11]	J. NAGLER. Jeffery-Hamel flow of non-Newtonian fluid with nonlinear viscosity and wall friction[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(6): 815-830.
[12]	S. MAITI, S. K. PANDEY. Rheological fluid motion in tube by metachronal waves of cilia[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(3): 393-410.
[13]	Yanhai LIN, Liancun ZHENG, Lianxi MA. Heat transfer characteristics of thin power-law liquid films over horizontal stretching sheet with internal heating and variable thermal coefficient[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(12): 1587-1596.
[14]	M. HATAMI, S. E. GHASEMI, S. A. R. SAHEBI, S. MOSAYEBIDORCHEH, D. D. GANJI, J. HATAMI. Investigation of third-grade non-Newtonian blood flow in arteries under periodic body acceleration using multi-step differential transformation method[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(11): 1449-1458.
[15]	A. MASTROBERARDINO. Accurate solutions for viscoelastic boundary layer flow and heat transfer over stretching sheet[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(2): 133-142.