Proteinaceous microstructure in a capillary: a study of non-linear bending dynamics.

The flap of bendable structures under continuous flow impacts a variety of fields, ranging from energy harvesting to active mixing in microfluidic devices. Similar physical principles determine the flapping dynamics in a variety of systems with different sizes, but a thorough investigation of the bending dynamics at the microscale is still lacking. We employ here two-photon laser polymerization to fabricate elongated proteinaceous flexible microstructures directly within a micro-capillary and we characterize their bending dynamics. The elastic properties of the microstructures with different (circular and square) cross-sections are tested by Atomic Force Microscopy and by studying the deflection-flow dependence in microfluidic experiments at intermediate Reynolds numbers (Rey ≲ 150). The retrieved Young's modulus of the fabricated matrix (100 kPa ≤ E ≤ 4 MPa) falls in the range of most typical biological tissues and solely depends on the laser fabrication intensity. The elastic constant of the microstructures falls in the range of 0.8 nN µm-1 ≤ k ≤ 50 nN µm-1, and fully agrees with the macroscopic Euler Bernoulli theory. For soft microstructures (0.8 nN µm-1 ≤ k ≤ 8 nN µm-1) we reveal undamped bending oscillations under continuous microfluidic flow, corresponding to ∼10% of the total structure deflection. This behavior is ascribed to the coupling of the viscoelasticity and non-linear elasticity of the polymer matrix with non-linear dynamics arising from the time-dependent friction coefficient of the bendable microstructures. We envision that similar instabilities may lead to the development of promising energy conversion nanoplatforms.