Lattice Boltzmann method for oscillatory Stokes flow with applications to micro- and nanodevices

Abstract

A lattice Boltzmann (LB) method based on the linearized Boltzmann Bhatnagar-Gross-Krook equation for numerical simulation of oscillatory (unsteady) Stokes flow is proposed. Unlike the conventional (nonlinear) LB method that utilizes the time domain exclusively, the proposed method is formulated in the frequency domain to allow for direct access to the complex-valued stress, force, and velocity field--these parameters are of direct interest in characterizing microelectromechanical systems (MEMS) and nanoelectromechanical systems (NEMS). The proposed method circumvents the requirement for time-dependent boundary velocities, as is needed in the conventional LB method, and convergence of the two methods is compared. Validity of the proposed method is assessed using three classical (unsteady) flows: (1) one-dimensional oscillatory Couette flow between two plates; (2) two-dimensional flow generated by an oscillating circular cylinder; (3) three-dimensional flow generated by an oscillating sphere. The observed excellent numerical performance in all three cases demonstrates that this linear lattice Boltzmann method can be used to study the dynamics of micro- and nanoscale devices of any dimensionality. This is particularly relevant to MEMS and NEMS, where the resonance properties of individual nanomechanical components immersed in fluid can underpin overall device performance.