Simulation of Stokes flow over microelectrodes with least-squares meshfree method

Microelectrode structures in alternating current (AC) electrokinetics can generate high electric field strength to manipulate, characterize and separate particles in suspending medium. It has been widely used in biological, pharmaceutical and medical fields. In this paper, a least-squares meshfree method (LSMFM) based on the first-order velocity–pressure–vorticity formulation for the Stokes flow, electric potential–electric field strength expression for electric field and temperature–heat flux equations for heat transfer problem is presented to study two-dimensional electrothermally induced fluid flow over microelectrodes. Joule heat generated from electric field acts as heat source and gives rise to electric force and buoyancy force acting on the fluid. The discretization of all system of equations is completed by the least-squares method. The equal-order moving least-squares (MLS) approximation is used with Gaussian quadrature in the background cells constructed by the quadtree algorithm. A matrix-free element-by-element Jacobi preconditioned conjugate gradient method is applied to solve the resulting systems. Finally, an example of steady heat transfer problem with analytical solution is devised to analyze the error estimates of the LSMFM, and the examples of electric field of shielded microstrip line and Stokes flow over microelectrode are also solved to investigate the features of the LSMFM.