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

Abstract

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.

Recent advances in microscale pumping technologies: a review and evaluation

“…An analytical model for micro-diaphragm pumps with active valves based on the peristaltic working principle has been developed (Goldschmidtboing et al 2005). It applies to both fast and slow actuation mechanisms such that it can be used for piezoelectric, pneumatic, thermopneumatic and other driving mechanisms.…”

A New Concept of a Drug Delivery System with Improved Precision and Patient Safety Features

“…The piezoelectrically actuated micropump is a displacement pump [6,7]. A detailed description of the fabrication process for the pump can be found in [6].…”

“…A lumped parameter model can be used to model a fluidic system [6,7,[12][13][14][15] . Based on the equation of a mechanically oscillating system, Equation (1) describes an incompressible laminar flow for a Newtonian fluid in steady state [16]:…”

“…To circumvent the mathematical problem of differentiation of this square wave function, Equation (5) is integrated, see Equation (6). Equation (6) is used in the lumped parameter model for the deflection of the piezoelectrically actuated membranes and the storage membrane, see elements 3 and 4 in Figure 4:…”

Efficiency characteristics of piezostack pump for linear actuators

“…Presently, most piezoelectric pumps are developed for liquid delivery with piezoelectric membrane actuators, such as valveless pumps [7,8], check-valve pumps [9,10], and peristaltic pumps [11,12]. These piezomembrane pumps are characterized by their simple structure and small volume.…”