Article outline

Purpose: the development of a three-dimensional computer model of fluid flow in a channel with a hydrodynamic resistance, where the form of the hydro resistivity varies according to the periodic law and is determined by the deformation of the tube by the piezoelectric element.

Methodology: the Lame equations were solved by the finite element method in the FreeFem ++ package. The equations of hydrodynamics were discretized in time according to the Euler scheme and solved by the finite element method in the FreeFem ++ package; The solution of the nonlinear problem was found by Picard iterations.

The findings of research:

1. the interchangeability of the Neumann and Dirichlet boundary conditions is shown: by selecting the piezoelectric element pressure on the outer part of the tube, one can obtain the same deformation of the inner part of the tube as when setting the displacement of the contact surface inwards by a define value (the dependence is linear);
2. studied two fluid flow regime in the deformed tube: the tube inlet is closed, the flow induced tube deformation; both ends are open, the flow is induced both by the deformation of the tube and by the differential pressure applied to the layer. The first regime allows one to test the computer model, and the second regime allows one to offer a liquid dosing mechanism controlled by two parameters: the piezoelement compression rate and the differential pressure;
3. it is found that the fluid flow rate depends on the compression frequency of the piezoelectric element and, if there is no pressure drop, does not depend on the physical parameters of the fluid. This theoretically makes it possible to implement a hydraulic microdrive with a linear ”mechanical“ (consumable) characteristic;
4. under the influence of the pressure drop, a constant component inversely proportional to the viscosity of the liquid is added to the periodic component of the fluid flow;
5. it is shown that one can obtain a flow regime corresponding to the droplet extrusion by selecting parameters (frequency, pressure drop). The volume of the droplet squeezed out during the period decreases with increasing frequency.

   Originality/value: The proposed computer model describing the fluid behavior in microchannels using piezoelectric drives is the first step in developing a theoretical basis for creating microdrives and executive micromechanisms.