Simplified model and lattice Boltzmann algorithm for microscale electro-osmotic flows and heat transfer

The extremely small length scale of the electric double layer (EDL) of electro-osmotic flows (EOF) in a microchannel makes it difficult to simulate such flows and associated thermal behaviors. A feasible solution to this problem is to neglect the details in the thin EDL and replace its effects on the bulk flow and heat transfer with effective velocity-slip and temperature-jump boundary conditions outside the EDL. In this paper, by carrying out a scale analysis on the fluid flow and heat transfer in the thin EDL, we analytically obtain the velocity and the temperature at the interface between the EDL and the bulk flow region. The Navier-Stokes equations and the conservation equation of energy, along with the interfacial velocity and temperature as the velocity-slip and temperature-jump boundary conditions, form a simple model for the electro-osmotic flows with thermal effects in a microchannel with a thin EDL. We use the double distribution function lattice Boltzmann algorithm to solve this model and found that numerical results are in good agreement with those by the conventional complete model with inclusion of the EDL, particularly for the cases when channel size is about 400 times larger than the Debye length. Moreover, we found that the present model can substantially reduce the computational time by four to five times of that using the conventional complete model. Therefore, the simplified model proposed in this work is an efficient tool for simulating electro-osmosis-based microfluidic systems.