A generic analytical model for micro-diaphragm pumps with active valves

We present a fully analytical model for micro-diaphragm pumps with active valves, based on the peristaltic working principle. Our model is suited for very fast as well as for very slow actuation mechanisms. Therefore it can be applied to a variety of actuation principles, e.g. piezoelectric, pneumatic, thermo-pneumatic or pre-stressed shape memory actuation. We show that the dynamics of this kind of micropump can be fully described by a lumped element approach taking only the mechanical behaviour of the diaphragms and the viscous losses at the valves into account. The full flow versus frequency and backpressure characteristic is derived. Our model is capable of predicting the maximum achievable flow rate and the maximum sustainable backpressure of micro-diaphragm pumps with active valves. Different modes of operation, which are distinguished by the speed of the actuation mechanism, the pressure history inside the pump and the applied driving scheme, are identified. We show that micro-diaphragm pumps with active valves generally suffer from a linear dependence of the flow rate on the applied backpressure. This fact, which is already known from micropumps with passive valves, is remarkable, because it is in contradiction to the characteristics of macroscopic peristaltic pumps. A set of design rules for the dimensioning of the valves in dependence on the actuation force and the desired hydrodynamic characteristics (maximum flow rate and maximum sustainable backpressure) are derived. Our theoretical results are proven by experimental results of our piezoelectrically actuated micropump. A maximum flow rate of 1.4 ml min(-1) and a maximum sustainable backpressure of 40 kPa were achieved.