A Network Model for Electroosmotic and Pressure-Driven Flow in Porous Microfluidic Channels

Gonzalo García-Ros, Juan Francisco Sánchez-Pérez, Julio Valenzuela, Manuel Conesa and Manuel Cánovas
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Gonzalo García-Ros: Civil and Mining Engineering Department, Universidad Politécnica de Cartagena (UPCT), 30202 Cartagena, Spain
Juan Francisco Sánchez-Pérez: Department of Applied Physics and Naval Technology, Universidad Politécnica de Cartagena (UPCT), 30202 Cartagena, Spain
Julio Valenzuela: Metallurgical and Mining Engineering Department, Universidad Católica del Norte, Antofagasta 1240000, Chile
Manuel Conesa: Department of Applied Physics and Naval Technology, Universidad Politécnica de Cartagena (UPCT), 30202 Cartagena, Spain
Manuel Cánovas: Metallurgical and Mining Engineering Department, Universidad Católica del Norte, Antofagasta 1240000, Chile

Mathematics, 2022, vol. 10, issue 13, 1-19

Abstract: In this work, the network simulation method is presented as a tool for the numerical resolution of the electroosmotic and pressure-driven flow problem in microchannels with rectangular and cylindrical geometries. Based on the Brinkman equation for steady flow and constant porosity, the network model is designed using spatial discretization. An equivalent electrical circuit is obtained by establishing an analogy between the physical variable fluid velocity and electric potential. The network model is solved quickly and easily employing an electrical circuit resolution code, providing solutions for the velocity profile in the channel cross-section and the total circulating flow. After simulating two practical cases, the suitability of the grid is discussed, relating the relative errors made in the variables of interest with the number of cells used. Finally, two other applications, one for rectangular geometries and the other for cylindrical channels, show the effects the main parameters controlling the flow in these types of channels have on velocities and total flow: the zeta potential of the soil pores, applied potential and pressure gradients, and the boundary condition modified by the zeta potential in the walls of the channel.

Keywords: electroosmotic flow; network simulation method; zeta potential; parallel plate channel; porous cylinder (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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