Transient analysis of electro-osmotic transport by a reduced-order modelling approach

Transient behaviour of electro-osmotic transport in typical electrokinetic channels is studied in this paper. The time needed for the electro-osmotic ow to reach steady-state exhibits multiple time scales depending on whether the ow is governed by either a viscous force, electrokinetic force or by a combination of both. When an intersection is present in the electrokinetic channel, such as in a cross or a T-channel, the ow in the main channel and in the intersection gets to steady-state at di erent times. A weighted Karhunen–Lo eve (KL) decomposition method is proposed in this paper to generate the global basis function for reduced-order simulation. The key idea in a weighted KL approach is that, instead of minimizing a least-squares measure of ‘error’ between the linear subspace spanned by the basis functions and the observation space, we minimize the weighted ‘error’ between the two spaces. The global basis functions in a weighted KL approach can be generated by computing the singular value decomposition (SVD) of the matrix containing the weighted snapshots. We show that the weighted KL decomposition based reduced-order model is computationally more e cient and can capture the multiple time scales encountered in electro-osmotic transport much more e ectively compared to the classical KL decomposition based reduced-order model.