Theoretical aspects of electrical power generation from two-phase flow streaming potentials
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RESEARCH PAPER
Theoretical aspects of electrical power generation from two-phase flow streaming potentials J. D. Sherwood • Y. Xie • A. van den Berg J. C. T. Eijkel
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Received: 27 September 2012 / Accepted: 4 February 2013 / Published online: 26 February 2013 Ó Springer-Verlag Berlin Heidelberg 2013
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. Keywords Streaming potential Two-phase flow Bubbly flow Electrical power generation
1 Introduction Streaming potentials generated by fluid flow adjacent to a charged surface are a source of electrical energy. The electrical power is usually low. However, the process may
J. D. Sherwood (&) Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK e-mail: [email protected] Y. Xie A. van den Berg J. C. T. Eijkel Bios/Lab on a Chip, MESA? Institute for Nanotechnology, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands
nevertheless be attractive when no other source of electricity is available, and so research to improve power output continues: Mansouri et al. (2012) recently reported power outputs as large as 1 mW at an efficiency of 1.3 %. It has been shown that power can be generated by single-phase flow in a capillary (Olthuis et al. 2005; van der Heyden et al. 2007; Xie et al. 2008). If a second, insulating fluid is added to the flow, the resulting two-phase mixture has an increased electrical resistance and the efficiency of the generating device is thereby improved (Xie et al. 2011). Here we propose and investigate a model of twophase flow to estimate the power that can be generated and to determine how this power can be optimized. At a given volumetric flow rate Q, the presence of a low-viscosity bubble tends to reduce the shear rate at the capillary wall and thereby reduces the convected electrical streaming current Ic. Conversely, a high-viscosity fluid droplet increases the wall shear rate and the streaming current, albeit at the expense of an increase in the differential pressure required to generate the flow. If the fluid droplet is non conducting, the mean electrical resistance of the fluid in the capillary is increased. If there is no external path for the streaming current, a
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