Analytical Model of Valveless Micropumps

The flow driven by a valveless micropump with a single cylindrical pump chamber and two diffuser/nozzle elements is studied theoretically using a 1-D model. The pump cavity is driven at an angular frequency omega so that its volume oscillates with an amplitude V _m. The presence of diffuser/nozzle elements with pressure-drop coefficients zeta₊, zeta_- (> zeta +) and throat cross-sectional area A ₁ creates a rectified mean flow. In the absence of frictional forces the maximum mean volume flux (with zero pressure head) is Q ₀ where Q ₀/V _momega = (zeta_- - zeta₊)pi/16(zeta_-+ zeta₊), while the maximum pressure that can be overcome is DeltaP _max where DeltaP _max A ₁ ²/V _m ² omega² = (zeta_- - zeta₊)/16. These analytical results agree with numerical calculations for the coupled system of equations and compare well with the experimental results of Stemme and Stemme.