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(m)omega = (zeta(-)-zeta(+))pi/16(zeta(-)+zeta(+)), while the maximum pressure that can be overcome is Delta P(max) where Delta P(max)A(1)(2)/V(m)(2)omega(2) = (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.