Streaming Potential and Electroosmotic Flow in Heterogeneous Circular Microchannels with Nonuniform Zeta Potentials: Requirements of Flow Rate and Current Continuities Jun Yang, † J. H. Masliyah, ‡ and Daniel Y. Kwok* ,† Nanoscale Technology and Engineering Laboratory, Department of Mechanical Engineering and Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta T6G 2G8, Canada Received July 9, 2003. In Final Form: December 3, 2003 Real surfaces are typically heterogeneous, and microchannels with heterogeneous surfaces are commonly found due to fabrication defects, material impurities, and chemical adsorption from solution. Such surface heterogeneity causes a nonuniform surface potential along the microchannel. Other than surface heterogeneity, one could also pattern the various surface potentials along the microchannels. To understand how such variations affect electrokinetic flow, we proposed a model to describe its behavior in circular microchannels with nonuniform surface potentials. Unlike other models, we considered the continuities of flow rate and electric current simultaneously. These requirements cause a nonuniform electric field distribution and pressure gradient along the channel for both pressure-driven flow (streaming potential) and electric-field-driven flow (electroosmosis). The induced nonuniform pressure and electric field influence the electrokinetic flow in terms of the velocity profile, the flow rate, and the streaming potential. I. Introduction The presence of an electric double layer (EDL) at the solid-liquid interface and its electrokinetic phenomena have been used to develop various chemical and biological instruments. 1-3 A common assumption is the uniformity of surface properties during electrokinetic fluid transport in microchannels. 4-9 Nevertheless, surface heterogeneity can easily arise from fabrication defects or chemical adsorption onto microchannels. For example, Norde et al. 10 studied the relationship between protein adsorption and streaming potentials. Ajdari 11,12 presented a theoreti- cal solution for electroosmotic flow through inhomogeneous charged surfaces. Ren and Li 13 numerically studied electroosmotic flow in heterogeneous circular microchan- nels with axial variation of the surface potential. Anderson and Idol 14 studied electroosmosis through pores with nonconformed charged walls. They showed that the mean electroosmotic velocity within the capillary was given by the classical Helmholtz equation with the local surface potential replaced by the average surface potential. Keely et al. 15 theoretically provided flow profiles inside capillaries with nonuniform surface potentials. Herr et al. 16 theoreti- cally and experimentally investigated electroosmotic flow in cylindrical capillaries with nonuniform surface charge distributions. A nonintrusive caged fluorescence imaging technique was used to image the electroosmotic flow; a parabolic velocity profile induced by the pressure gradient due to the heterogeneity of the capillary surfaces was observed. Cohen and Radke studied streaming potentials of a slit with a nonuniform surface charge density. 17 Erickson and Li 18 studied microchannel flow with patch- wise and periodic surface heterogeneity. However, all the above studies 10-18 assumed uniform axial electric fields along the microchannel and did not consider continuity of electric current. Phenomenologically, let us consider two independent microchannels with the same geometry, electrolyte, and flow rate. If these two channels have different surface potentials, the electric fields associated with the electric double layer would have to be different. If we assemble these two independent channels in series as sections of a channel, the electric field should be nonuniform along the flow direction and current continuity should also be satisfied. It is the purpose of this paper to study oscillating electrokinetic (streaming potential and electroosmotic) flow in a microchannel with different surface potentials in every section which satisfy both flow rate and current continuity requirements. * To whom correspondence should be addressed. Phone: (780) 492-2791. Fax: (780) 492-2200. 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