Dynamic permeability of fluids in rectangular and square microchannels: Shift and coupling of viscoelastic bidimensional resonances

Pulsatile dynamics of Newtonian and Maxwellian fluids is exactly solved by theoretical analytical means when confined within rectangular microchannels subject to oscillatory driving forces. The analytical solution exhibits a complex behavior caused by the fluid dynamics along the smallest and the secondary confinement dimensions. For Newtonian fluids, the maximum and average flow velocities within the microchannel differ considerably from the ones predicted by simplified one-dimensional models when fluids are subject to moderate and high driving force frequencies. This is caused by the stagnation of flow velocity in the vicinity of the channel walls at the secondary confinement dimension. For Maxwellian fluids, the secondary confinement incorporates flow resonances that are coupled to the ones caused by the smallest confinement, leading to a shift of the main resonance and the arising of resonances when bidimensional vibration modes are excited. These effects depend on the aspect ratio between channel width and height and on the magnitude of the driving force frequency, compared to the characteristic viscous frequency of the microchannel. The theoretical results are compared with recent experimental results in the literature in pulsatile microfluidics for hyaluronic acid solutions with viscoelastic properties, as well as for water. In both cases, an agreement is found between theoretical and experimental results.