Approach to analytic solutions for electroosmotic flow in micro-ducts by eigenfunctions of the Helmholtz equation
Journal
Microfluidics and Nanofluidics
Journal Volume
20
Journal Issue
8
Date Issued
2016
Author(s)
Abstract
In the literature, a limited number of analytical solutions for electroosmotic (EO) flow in micro-ducts were obtained. In this study, we present a general formulation using eigenfunctions of the Helmholtz equation to obtain analytic solutions for steady and unsteady EO flow in micro-ducts under Debye–Hückel approximation. The key observation is that the differential operator associated with the equation for the EO flow is strictly positive definite. Examples that add to analytic solutions for EO flow include exact series and closed-form solutions to the steady flow, and the starting flow and the oscillatory flow in three triangular ducts are found. It is easy to deduce some salient features of flow physics, such as the flow rate, transient time and phase lag as well as the velocity profile from the general solution, and they are given quantitative values in the individual examples.
SDGs
Type
journal article