Modeling an Electrostatically Actuated MEMS Diaphragm Pump

The recent advent of microelectromechanical systems (MEMS) or micro-devices has generated excitement in many diverse fields. In the area of micro-fluidics liquid pumps are highly desirable for fluid transport and atomization. A recent and popular example of this is the inkjet, which self-aspirates ink from a reservoir and then transports it to a chamber for expulsion as a single droplet during the printing process. Extending this technology to other potential applications requires analytical and computational tools for design. Several computational software packages are commercially available, such as CoventorWare, FLUENT, and ANSYS [1-3], but each is difficult to use and to date only ANSYS has been able to solve this fully coupled multi-physics problem. Thus, simplified analytical models are attractive for preliminary design and analysis. This paper describes a quasi one-dimensional model developed for the design and analysis of an electrostatically actuated diaphragm pump. The attributes and assumptions of this model will be presented. Finally, performance results obtained for a MEMS diaphragm pump will be compared to ANSYS three-dimensional time-accurate results. w square diaphragm length or width Nomenclature y deflection A area d diameter E modulus of elasticity, electric field strength α Roarke constant εo relative permittivity F force εr dielectric constant g gravitational constant λ1 1 eigenvalue from       − = 2 1 n a n π λ G capacitive gap (also same as fluid gap height) h fluid gap height μ viscosity ks spring constant ν kinematic viscosity, Poisson’s ratio L length m& mass flow rate ρ density MEMS microelectromechanical systems or structures τ time constant p gauge pressure relative to ambient subscripts e electrostatic ∆p pressure drop f final r radius i, 0 initial Rh channel hydraulic radius k spring force t thickness l liquid u, v velocity n eigenvalue equation indice V voltage, volume V& volumetric flow rate