Modelling of electromagnetic and piezoelectric peristaltic micropumps

Micropumps are devices that can handle microlitre-scale fluid volumes. Various pumping principles have been proposed in the literature and are often coupled to valves in order to ensure a positive mean flow. In this thesis, two original designs of peristaltic valveless micropumps are introduced. The fluid is moved by the peristaltic motion of a planar diaphragm which is bent either by the action of Lorentz force, in the electromagnetic micropump, or by piezoelectric elements, in the piezoelectric micropump. The reverse flow is avoided by ensuring the contact between the diaphragm and the micropump’s bottom. Several characteristic parameters of these devices have to be determined with accuracy: their flow rate, and the back pressure they can sustain ; equally important are the electromechanical limits, i.e. the maximum stress and electrical field in order to prevent any damage to the pump. Both micropump designs present similarities in their geometries and working principle, meaning they can be studied based on the same tool. This thesis has been dedicated to the development of an efficient tool to study devices where thin diaphragms, possibly multilayered, enter in contact with an obstacle. Special attention has been paid to the modelling of displacement, stress and electric field, using both micropumps as benchmark application cases. In the first part of this thesis, a theory is built considering a slender structure composed of several layers, using Euler-Bernoulli beam assumptions and quasistatic condition. The actions of the piezoelectric effect and of the transverse Lorentz force density, due to the interaction of electrical current density and a magnetic field, are taken into account through equivalent loads. The effect of the electrical field variation with respect to the thickness coordinate of the piezoelectric layers on the displacement is neglected but its impact on the stress is considered. Contact is taken into account by imposing three boundary conditions at the ends of the beam, considering its position as an unknown. The theory is applied to the micropump designs and compared to a 3D finite element model. This has shown that boundary and contact conditions in the width direction are not properly modelled, highlighting the need for a more sophisticated theory. This is developed in the second part of the thesis, using Kirchhoff-Love assumptions for thin plates. The electrical field is solved exactly and used to obtain a theory where the displacement components are the only unknowns. A full electromechanical coupling is therefore considered through equivalent loads and stiffness coefficients; dynamics are also taken into account. The contact condition is however quite difficult to handle in the differential form, so a variational form is used instead and solved by a finite element method, coupled to an active set strategy for contact management. This theory compares well with the 3D finite element model and the efficiency of the developed theories and algorithms, in terms of computational cost and memory requirements, opens the way to use it in a design process with short turn-around times or which requires a huge number of evaluations, such as in optimization process.