Microfluidic creep experiment for measuring linear viscoelastic mechanical properties of microparticles in a cross-slot extensional flow device

The micromechanical measurement field has struggled to establish repeatable techniques, likely because the deforming stresses can be complicated and difficult to model. Here we demonstrate experimentally the ability of cross-slot microfluidic device to create a quasi-steady deformation state in agarose hydrogel microparticles to replicate a traditional uniaxial creep test at the microscale and at relatively high throughput. A recent numerical study by Lu et al. [Lu, Guo, Yu, Sui. J. Fluid Mech. , 2023, 962, A26] showed that viscoelastic capsules flowing through a cross-slot can achieve a quasi-steady strain near the extensional flow stagnation point that is equal to the equilibrium static strain, thereby implying that continuous operation of a cross-slot can accurately capture capsule elastic mechanical behavior in addition to transient behavior. However, no microfluidic cross-slot studies have reported quasi-steady strains for suspended cells or particles, to our knowledge. By using large dimension cross-slots relative to the microparticle diameter, our cross-slot implementation created an extensional flow region that was large enough for agarose hydrogel microparticles to achieve a strain plateau while dwelling near the stagnation point. This strain plateau will be key for accurately and precisely measuring linear viscoelastic properties of small microscale biological objects. The mechanical test was performed in the linear regime, so an analytical mechanical model derived using the elastic-viscoelastic correspondence principle was proposed to extract linear viscoelastic mechanical properties from observed particle strain histories. Particle image velocimetry measurements of the unperturbed velocity field were used to determine where in the device particles experienced extensional flow and the mechanical model should be applied. The measurement throughput in this work was 1 – 2 particles achieving a quasi-steady strain plateau per second, though measurement yield and throughput can be increased with particle-centering upstream device design features. Finally, we provide recommendations for applying the cross-slot microscale creep experiment to other biomaterials and criteria to identify particles that likely achieved a quasi-steady strain state.