Analysis of valveless micropumps with inertial effects

Through flow field simplification, a set of differential equations governing the fluid flow and fluid–membrane coupling are obtained for a valveless micropump. The dimensional analysis on the equations reveals that the ratio of the inertial force of the fluid to the viscous loss is dependent on the size ratios among internal elements of the pump. For a micropump working at high frequencies, these two forces possess the same order of magnitude, and this phenomenon is independent of the excitation frequency and fluid type. For the liquid medium, the inertial force of the fluid is around O(10²)–O(10³) times as that of the plate membrane, and is also larger than the elastically deformed force of the plate when the excitation frequency is close to the plate fundamental frequency. For the case where there is no pressure difference between the inlet and the outlet, an approximate analytical solution is derived for the micropump under the action of an external sinusoidal excitation force. It shows that a phase shift lagging the excitation force exists in the vibration response. For certain combinations of micropump size and fluid–solid density ratios, the phase shift can come to 90° at a specific excitation frequency ω* due to the action of fluid inertia. Away from ω*, the phase shift becomes smaller. The amplitude response of coupling vibration changes nonlinearly with the excitation frequency and reaches maximum at another frequency ω** ≠ ω*. Due to the nonlinearity of viscous loss, resonance does not seem to occur at any frequency. To obtain a larger average flux, the two loss coefficients of the nozzle should be minimized while their difference should be maximized. Under the action of the fluid inertia, there exists an optimal working frequency (equal to ω*) at which the average flux is maximum. This optimal frequency is dependent on the size of the micropump, the material properties of the plate, the fluid properties and has no relation with the excitation force. For the case where a pressure difference between the inlet and the outlet exists, a constraint condition between the excitation force and the pressure difference is obtained.