INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF MICROMECHANICS AND MICROENGINEERING J. Micromech. Microeng. 12 (2002) 252–256 PII: S0960-1317(02)28846-4 On electroviscous effects in microchannels P Vainshtein and C Gutfinger Faculty of Mechanical Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel Received 17 September 2001, in final form 24 February 2002 Published 28 March 2002 Online at stacks.iop.org/JMM/12/252 Abstract This paper contains results of a theoretical investigation on the effect of the diffusive electric double layer (EDL) at the solid–liquid interface on liquid flow through a microchannel between two parallel plates. Unlike previous works, the electrical charge connected with the EDL at the inlet of a channel is accounted for. The Debye–Huckel linear approximation of the surface potential distribution is used to describe the EDL field near the solid–liquid interface. The electrokinetic distance is assumed to be arbitrary. The electrical body force resulting from the double layer field is considered in the equation of motion. This equation is solved for steady-state flow. Effects of the EDL field on the apparent viscosity are discussed. 1. Introduction Liquid–solid friction at microscopic scales has been the subject of extensive studies for a long time. For recent reviews see [1, 2]. For fluid flows in microelectromechanical systems, new phenomena arise because of certain surface forces that are usually ignored in macro scales [3]. An understanding of electrokinetic flow through narrow capillaries and microchannels is of considerable importance in many fields of science, medicine and engineering. In this paper we develop a model of electrokinetic liquid flow, which accounts for friction originated from electrical effects. Surface effects dominate the flow through microchannels because of the large surface-to-volume ratio. In particular, problems arising from electrostatic effects often occur because of rather uncontrollable surface-trapped charges. In fact, any surface is likely to carry some charge because of broken bonds and surface charge traps. For charged surfaces in liquids (e.g., water), new phenomena occur mainly as a result of charge redistribution in the liquid. Basically, the final surface charge is balanced by counterions (oppositely charged ions) in the liquid by an equal but opposite total charge. The surface electrical potential attracts counterions to the wall and forms a thin (<1 nm) layer of immovable ions. Outside this layer, the distribution of the counterions in liquid mainly follows the exponential-decay dependence away from the surface. This is called the diffusive electric double layer (EDL). The electrical potential at the boundary between the diffusive double layer and the compact layer is called zeta-potential. The EDL has a characteristic thickness, known as the Debye thickness, which depends on the inverse of the square root of the ion concentration in the liquid. It also depends on the surface potential of the flow boundary. The thickness of the EDL ranges from a few nanometers up to several hundreds of nanometers; for example, in pure water the Debye thickness is about 1 µm [4]. Inside the EDL, a very large electrostatic force exists. This electrostatic force, acting across the channel, may cause changes in fluid flow [5]. Note that the ratio of the channel characteristic width to the EDL thickness is called the electrokinetic distance. The consequences of the existence of the EDL in capillaries and microchannels are well known, namely, electro- osmosis and streaming potential. When a liquid is forced through a microchannel under pressure gradient, the ions in the mobile part of the EDL are carried towards one end. This causes an electrical current, called streaming current, to flow in the direction of the liquid flow. The accumulation of ions downstream sets up a longitudinal electrical field with an electrical potential called the streaming potential. This field causes a current, called conduction current, to flow back in the opposite direction. The basic relationships of these phenomena have been formulated long ago, mainly by Smoluchowski (see [4, 5]). These relationships are based on the assumption that the electrokinetic distance is very large. Nevertheless, Smoluchovski’s classical result for the streaming potential is still frequently used during routine experimental determinations of the zeta-potential in fine capillaries and microchannels. There are few recent analytical studies in the literature which account for the effects of EDL on flow characteristics. Rice and Whitehead [6] have calculated the correction factors that must be applied to Smoluchovski’s results for narrow channels having arbitrary values of the electrokinetic distance. The authors have studied the effect 0960-1317/02/030252+05$30.00 © 2002 IOP Publishing Ltd Printed in the UK 252