Microfluidics and its applications to Lab-on-a-Chip have attracted a lot of attention. Because of the small length scale, the flow is characterized by a low Re number. The governing equations become linear. Boundary element method (BEM) is a very good option for simulating the fluid flow with high accuracy. In this paper, we present a 2D numerical modeling of the electrothermal flow using BEM. In electrothermal flow the volumetric force is caused by electric field and temperature gradient. The physics is mathematically modeled by (i) Laplace equation for the electrical potential, (ii) Poisson equation for the heat conduction caused by Joule heating, (iii) continuity and Stokes equation for the low Reynolds number flow. We begin by solving the electrical potential and electric field. The heat conduction is caused by the Joule heating as the heat generation term. Superposition principle is used to solve for the temperature field. The Coulomb and dielectric forces are generated by the electrical field and temperature gradient of the system. We analyze the Stokes flow problem by superposition of fundamental solution for free-space velocity caused by body force and BEM for the corresponding homogeneous Stokes equation. It is well known that a singularity integral arises when the source point approaches the field point. To overcome this problem, we solve the free-space velocity analytically. For the BEM part, we also calculate all the integral terms analytically. With this effort, our solution is more accurate. In addition, we improve the robustness of the matrix system by combining the velocity integral equation with the traction integral equation. Our purpose is to design a pump for the microfluidics system. Since the system is a long channel, the flow is fully developed in the area far away from the electrodes. With this assumption, the velocity profile is parabolic at the inlet and outlet of the channel. So we can get appropriate boundary conditions for the BEM part of Stokes equation. Consequently, we can simulate the electrothermal flow in an open channel. In this paper, we will present the formulation and implementation of BEM to model electrothermal flow. Results of electrical potential, temperature field, Joule heating, electrothermal force, and velocity field will be presented.

Electrokinetic transport in nanofluidics has attracted many attentions in recent years due to its potential applications in biomedical analysis and energy conversion systems. The biggest challenge to model the electrokinetic transport using atomistic simulations is the extensive cost in calculation of the long-range electrostatic force between ions. In this work, we develop an efficient molecular approach to simulate electrokinetic transport in nano-scale. The long-range Coulombic interactions are treated using the Particle-Particle Particle-Mesh (P 3 M) scheme and the Poisson equation for electric potential is solved in physical space using an iterative multi-grid technique. We implement this approach to systematically investigate two examples: the electroosmotic flow in random rough channels and the electrowetting on dielectric (EWOD). Both cases pose important engineering applications as a mechanism for transporting small amount of liquid in micro and nano devices.

The multiphysiochemical transport in electroosmosis of dilute electrolyte solutions (<1mM) through microporous media with granular random structures has been modeled in this work by our numerical framework consisting of three steps. First, the three-dimensional microstructures of porous media are reproduced by a random generation-growth method. Then the effects of chemical adsorption and electrical dissociation at the solid-liquid interfaces are considered to determine the electrical boundary conditions, which vary with the ionic concentration, the pH, and the temperature. Finally the nonlinear governing equations for the electrokinetic transport are solved by a highly efficient lattice Poisson-Boltzmann algorithm. The simulation results indicate that the electroosmotic permeability through the granular microporous media increases monotonically with the porosity, the ionic concentration, the pH and the environmental temperature. When the surface electric potential is higher than 50 mV, the permeability increases with the electric potential exponentially. The electroosmotic permeability increases with the pH exponentially, but with the temperature linearly. The present modeling results may improve our understanding of hydrodynamic and electrokinetic transport in geophysical systems, and help guide the design of porous electrodes in micro energy systems.

This study demonstrated electroosmotic pumping with high flow rate per unit area at a rather low applied voltage through an alumina nano-porous membrane driven by Platinum mesh electrodes. The electrode was placed perpendicular to, and had direct contact with nano-channel inlet to reduce the electric voltage drop in the reservoir. The complete set of the Poisson-Nernst-Planck equations for electrical potential and ionic concentration, coupled with the Navier-Stokes equation were solved for the purpose of a full understanding of the ionic transport and flow characteristics of EOF in nano-fluidics capillaries. The measured flowrate versus electrolyte (KCl) concentration reveals that the flowrate is usually high in low concentration (10 −5 M∼10 −7 M) regime in which a maximum value also occurs. In addition, a remarkable surge of flow rate is observed when the concentration surpasses below 10 −4 M. The maximum flowrate achieved from this study is 0.09 mL min −2 V −1 cm −2 and the energy transfer efficiency is 0.43% at an operation voltage of 20V. The flowrates investigated in this study are comparable to other existing results whereas the corresponding operation voltage used this study is about one to two order lower than most existing results. Numerical results exhibit correct trends for nano flows involving strong overlap of electrical double layers. Comparisons of numerical and experimental results were made and discussed.