Conditions for a microfluidic creep experiment for microparticles using a cross-slot extensional flow device

The micromechanical measurement field has struggled to establish repeatable techniques because the deforming stresses can be difficult to model. A recent numerical study [Lu <i>et al.</i>, J. Fluid Mech. <b>962</b>, A26 (2023)] 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 the capsule's elastic behavior can be captured in continuous device operation. However, no experimental microfluidic cross-slot studies have reported quasi-steady strains for suspended cells or particles to our knowledge. Here, we demonstrate experimentally the conditions necessary for the cross-slot microfluidic device to replicate a uniaxial creep test at the microscale and at relatively high throughput. By using large dimension cross-slots relative to the microparticle diameter, our cross-slot implementation creates an extensional flow region that is 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 viscoelastic properties of small microscale biological objects. We propose an analytical mechanical model to extract linear viscoelastic mechanical properties from observed particle strain histories. Particle image velocimetry measurements of the unperturbed velocity field is used to estimate where in the device particles experienced extensional flow and where the mechanical model might be applied to extract mechanical property measurements. 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.