Analytical study of mixed electroosmotic-pressure-driven flow in rectangular micro-channels

Operational state of many miniaturized devices deals with flow field in microchannels. Pressure-driven flow (PDF) and electroosmotic flow (EOF) can be recognized as the two most important types of the flow field in such channels. EOF has many advantages in comparison with PDF, such as being vibration free and not requiring any external mechanical pumps or moving parts. However, the disadvantages of this type of flow such as Joule heating, electrophoresis demixing, and not being suitable for mobile devices must be taken into consideration carefully. By using mixed electroosmotic/pressure-driven flow, the role of EOF in producing desired velocity profile will be reduced. In this way, the advantages of EOF can be exploited, and its disadvantages can be prevented. Induced pressure gradient can be utilized in order to control the separation in the system. Furthermore, in many complicated geometries such as T-shape microchannels, turns may induce pressure gradient to the electroosmotic velocity. While analytical formulas are completely essential for analysis and control of any industrial and laboratory microdevices, lack of such formulas in the literature for solving Poisson–Boltzmann equation and predicting electroosmotic velocity field in rectangular domains is evident. In the present study, first a novel method is proposed to solve Poisson–Boltzmann equation (PBE). Subsequently, this solution is utilized to find the electroosmotic and the mixed electroosmotic/pressure-driven velocity profile in a rectangular domain of the microchannels. To demonstrate the accuracy of the presented analytical method in solving PBE and finding electroosmotic velocity, a general nondimensional example is analyzed, and the results are compared with the solution of boundary element method. Additionally, the effects of different nondimensional parameters and also aspect ratio of channels on the electroosmotic part of the flow field will be investigated.