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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.

Pulsatile flows of viscoelastic fluids are very important for lab-on-a-chip devices, because most biofluids have viscoelastic character and respond distinctively to different periodic forcing. They are also very important for organ-on-a-chip devices, where the natural mechanical conditions of cells are emulated. The resonance frequency of a fluid refers to a particular pulsatile periodicity of the pressure gradient that maximizes the amplitude of flow velocity. For viscoelastic fluids, this one has been measured experimentally only at macroscales, since fine tuning of rheological properties and system size is needed to observe it at microscales. We study the dynamics of a pulsatile (zero-mean flow) fluid slug formed by a viscoelastic fluid bounded by two air-fluid interfaces, in a microchannel of polymethyl methacrylate. We drive the fluid slug by a single-mode periodic pressure drop, imposed by a piezoactuator. We use three biocompatible polymer solutions of polyethylene oxide as model viscoelastic fluids, and find resonances. We propose a model accounting for surface tension and fluid viscoelasticity that has an excellent agreement with our experimental findings. It also provides an alternative way of measuring relaxation times. We validate the method with parameters reported in the literature for two of the solutions, and estimate the relaxation time for the third one.

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