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Theoretical aspects of electrical power generation from two-phase flow streaming potentials

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Abstract

A theoretical analysis of the generation of electrical streaming currents and electrical power by two-phase flow in a rectangular capillary is presented. The injection of a second, non-conducting fluid phase tends to increase the internal electrical resistance of the electrical generator, thereby increasing the power output. If the viscosity of the injected fluid is large, the resulting high shear rate in the low-viscosity fluid at the wall generates a large streaming current and the power generated is further enhanced. However, if the injected fluid viscosity is low, the wall shear rate in the more viscous suspending fluid is reduced, as are streaming currents. Power generation would be small but for capillary effects at the ends of the bubbles that increase the pressure drop along the capillary above that expected for annular flow.

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References

  • Abramowitz M, Stegun IA (eds) (1972) Handbook of mathematical functions. Dover, New York

  • Alty T (1924) The cataphoresis of gas bubbles in water. Proc R Soc A 106:315–340

    Article  Google Scholar 

  • Antraygues P, Aubert M (1993) Self potential generated by two-phase flow in a porous medium: experimental study and volcanological applications. J Geophys Res B 98:22273–22281

    Article  Google Scholar 

  • Bolève A, Crespy A, Revil A, Janod F, Mattiuzzo JL (2007) Streaming potentials of granular media: influence of the Dukhin and Reynolds numbers. J Geophys Res B 112:08204

    Article  Google Scholar 

  • Bretherton FP (1961) The motion of long bubbles in tubes. J Fluid Mech 10:166–188

    Article  MathSciNet  MATH  Google Scholar 

  • de Lózar A, Hazel AL, Juel A (2008) Scaling properties of coating flows in rectangular channels. Phys Rev Lett 99:234501

    Article  Google Scholar 

  • de Lózar A, Juel A, Hazel AL (2008) The steady propagation of an air finger into a rectangular tube. J Fluid Mech 614:173–195

    Article  MathSciNet  MATH  Google Scholar 

  • Fuerstman MJ, Lai A, Thurlow ME, Shevkoplyas SS, Stone HA, Whitesides GM (2007) The pressure drop along rectangular microchannels containing bubbles. Lab Chip 7:1479–1489

    Article  Google Scholar 

  • Ginley GM, Radke CJ (1989) Influence of soluble surfactants on the flow of long bubbles through a cylindrical capillary. In: Borchardt JK, Yen TF (eds) Oil-field Chemistry, ACS Symposium Series 396, pp 480–501

  • Graciaa A, Morel G, Saulner P, Lachaise J, Schechter RS (1995) The ζ-potential of gas bubbles. J Colloid Interface Sci 172:131–136

    Article  Google Scholar 

  • Guichet X, Jouniaux L, Pozzi J-P (2003) Streaming potential of a sand column in partial saturation conditions. J Geophys Res B108:2141 ECV 2-1–2-12

  • Gupta A, Kumar R (2010) Flow regime transition at high capillary numbers in a microfluidic T-junction: viscosity contrast and geometry effect. Phys Fluids 22:122001

    Article  Google Scholar 

  • Hamlin BS, Ristenpart WD (2012) Transient reduction of the drag coefficient of charged droplets via the convective reversal of stagnant caps. Phys Fluids 24:012101

    Article  Google Scholar 

  • Hazel AL, Heil M (2002) The steady propagation of a semi-infinite bubble into a tube of elliptical or rectangular cross-section. J Fluid Mech 470:91–114

    Article  MATH  Google Scholar 

  • Jackson MD (2010) Multiphase electrokinetic coupling: insights into the impact of fluid and charge distribution at the pore scale from a bundle of capillary tubes model. J Geophys Res 115:B07206

    Article  Google Scholar 

  • Kim C, Hsieh Y-L (2001) Wetting and absorbency of nonionic surfactant solutions on cotton fabrics. Colloids Surf A PhysicoChem Eng 187–188:385–397

    Google Scholar 

  • Kim N, Evans ET, Park DS, Soper SA, Murphy MC, Nikitopoulos DE (2011) Gas-liquid two-phase flows in rectangular micro-channels. Exp Fluids 51:373–393

    Google Scholar 

  • Lac E, Sherwood JD (2009) Streaming potential generated by a drop moving along the centreline of a capillary. J Fluid Mech 640:55–77

    Article  MathSciNet  MATH  Google Scholar 

  • Liron N, Shahar R (1978) Stokes flow due to a Stokeslet in a pipe. J Fluid Mech. 86:727–744

    Article  MathSciNet  MATH  Google Scholar 

  • McTaggart HA (1922) On the electrification at the boundary between a liquid and a gas. Philos Mag 44:386–395

    Google Scholar 

  • Mansouri A, Bhattacharjee A, Kostiuk L (2012) High-power electrokinetic conversion in a glass microchannel array. Lab Chip 12:4033–4036

    Article  Google Scholar 

  • Mason G, Morrow NR (1984) Meniscus curvatures in capillaries of uniform cross-section. J Chem Soc Faraday Trans 1 80:2375–2393

    Google Scholar 

  • Morgan FD, Williams ER, Madden TR (1989) Streaming potential properties of westerly granite with applications. J Geophys Res B 94:12449–12461

    Article  Google Scholar 

  • Olthuis W, Schippers B, Eijkel J, van den Berg A (2005) Energy from streaming current and potential. Sens Act B 111–112:385–389

  • Patist A, Bhagwat SS, Penfield KW, Aikens P, Shah DO (2000) On the measurement of critical micelle concentrations of pure and technical-grade nonionic surfactants. J Surfactants Deterg 3:53–58

    Article  Google Scholar 

  • Raj R, Mathur N, Buwa VV (2010) Numerical simulations of liquid-liquid flows in microchannels. Ind Eng Chem Res 49:10606–10614

    Article  Google Scholar 

  • Ransohoff TC, Radke CJ (1988) Laminar flow of a wetting liquid along the corners of a predominantly gas-occupied noncircular pore. J Colloid Interface Sci 121:392–401

    Article  Google Scholar 

  • Rebrov EV (2010) Two-phase flow regimes in microchannels. Theor Found Chem Eng 44:355–367

    Article  Google Scholar 

  • Revil A, Pezard PA, Glover PWJ (1999) Streaming potential in porous media: 1. Theory of the zeta potential. J Geophys Res B 104:20021–20031

    Article  Google Scholar 

  • Revil A, Cerepi A (2004) Streaming potentials in two-phase flow conditions. Geophys Res Lett 31:L11605

    Google Scholar 

  • Revil A, Linde N, Cerepi A, Jougnot D, Mattäi S, Finsterle S (2007) Electrokinetic coupling in unsaturated porous media. J Colloid Interface Sci 313:315–327

    Article  Google Scholar 

  • Rodriguez Nino MR, Rodriguez Patino JM (1995) Surface tension of bovine serum albumin and Tween 20 at the air-aqueous interface. J Am Oil Chem Soc 75:1241–1248

    Article  Google Scholar 

  • Salim A, Fourar M, Pironon J, Sausse J (2008) Oil-water two-phase flow in microchannels: flow patterns and pressure drop measurements. Can J Chem Eng 86:978–988

    Article  Google Scholar 

  • Shao N, Gavriilidis A, Angei P (2009) Flow regimes for adiabatic gas-liquid flow in microchannels. Chem Eng Sci 64:2749–2761

    Article  Google Scholar 

  • Sherwood JD (1986) Electrophoresis of gas bubbles in a rotating fluid. J Fluid Mech 162:129–137

    Article  MathSciNet  MATH  Google Scholar 

  • Sherwood JD (2007) Streaming potential generated by two-phase flow in a capillary. Phys Fluids 19:053101

    Article  Google Scholar 

  • Sherwood JD (2008) Streaming potential generated by a long viscous drop in a capillary. Langmuir 24:10011–10018

    Article  Google Scholar 

  • Sherwood JD, Lac E (2010) Streaming potential generated by two-phase flow in a polygonal capillary. J Colloid Interface Sci 349:417–423

    Article  Google Scholar 

  • Sprunt ES, Mercer TB, Djabbarah NF (1994) Streaming potential from multiphase flow. Geophys Astrophys Fluid Dyn 59:707–711

    Article  Google Scholar 

  • Takahashi M (2005) ζ potential of microbubbles in aqueous solutions: electrical properties of the gas-water interface. J Phys Chem B 109:21858–21864

    Article  Google Scholar 

  • Vanapalli SA, Banpurkar AG, van den Ende D, Duits MHG, Mugele F (2009) Hydrodynamic resistance of single confined moving drops in rectangular microchannels. Lab Chip 9:982–990

    Article  Google Scholar 

  • van der Heyden FHJ, Bonthuis DJ, Stein D, Meyer C, Dekker C (2006) Electrokinetic energy conversion efficiency in nanofluidic channels. Nano Lett 6:2232–2237

    Article  Google Scholar 

  • van der Heyden FHJ, Bonthuis DJ, Stein D, Meyer C, Dekker C (2007) Power generation by pressure-driven transport of ions in nanofluidic channels. Nano Lett 7:1022–1025

    Article  Google Scholar 

  • Watillon A, de Backer R (1970) Potential d’écoulement, courant d’écoulement et conductance de surface à l’interface eau-verre. J Electroanal Chem Interfacial Electrochem 25:181–196

    Article  Google Scholar 

  • Wong H, Morris S, Radke CJ (1995) The motion of long bubbles in polygonal capillaries. Part 1. Thin films. J Fluid Mech 292:71–94

    Article  MATH  Google Scholar 

  • Wong H, Morris S, Radke CJ (1995) The motion of long bubbles in polygonal capillaries. Part 2. Drag, fluid pressure and fluid flow. J Fluid Mech 292:95–110

    Article  Google 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 93:163116

    Article  Google Scholar 

  • Xie Y, Sherwood JD, Shui L, van den Berg A, Eijkel JCT (2011) Strong enhancement of streaming current power by application of two phase flow. Lab Chip 11:4006–4011

    Article  Google Scholar 

  • Zhao Y, Chen G, Yuan Q (2006) Liquid-liquid two-phase flow patterns in a rectangular microchannel. AIChE J 52:4052–4060

    Article  Google Scholar 

Download references

Acknowledgments

J.D.S. thanks the Department of Applied Mathematics and Theoretical Physics, University of Cambridge, for hospitality.

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Authors and Affiliations

  1. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, UK

    J. D. Sherwood

  2. Bios/Lab on a Chip, MESA+ Institute for Nanotechnology, University of Twente, PO Box 217, 7500 AE, Enschede, The Netherlands

    Y. Xie, A. van den Berg & J. C. T. Eijkel

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  1. J. D. Sherwood
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  2. Y. Xie
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  3. A. van den Berg
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  4. J. C. T. Eijkel
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Correspondence to J. D. Sherwood.

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Sherwood, J.D., Xie, Y., van den Berg, A. et al. Theoretical aspects of electrical power generation from two-phase flow streaming potentials. Microfluid Nanofluid 15, 347–359 (2013). https://doi.org/10.1007/s10404-013-1151-7

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  • DOI: https://doi.org/10.1007/s10404-013-1151-7

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