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.