The Electrical Potential in an Irregular Rectangular Domain: An Area-Averaging Approach
Electrostatic potentials are critically important for applications such as electrophoretic separation, microfluidics, and other electrokinetic-driven technology. As in other transport processes, the microscopic electrostatic equation and its boundary conditions depend upon the geometry of the domain, i.e. pore or capillary of the, for example, hydrogel used in this application. Since these materials display a complicated morphology of the pore network, "irregular domains" play an important role in capturing a realistic description of the electrostatic potential. Studies have shown that generally, diverging channels, a form of irregular channel, give better separation resolutions compared to regular channels. In this project, an area-averaging approach coupled with its closure condition are used for the analysis of the electrostatic potential in a diverging channel of rectangular geometry. Both area-averaged values of the electrostatic potential and its deviation are systematically determined and used to obtain the solution, i.e., the "local" or microscopic value of the potential without using other more mathematically involved techniques such as separation of variables. The presentation will discuss details about the up scaling of the microscopic electrostatic equation to the entire domain of the pore and some of its limitations as well as useful information such as the significance of the entrance effect.