High-Throughput Microfluidic Creep Relaxation Experiments in an Extensional Flow Device*

Many microfluidic platforms that measure the mechanical properties of single cells rely on extensive approximations and empirical calibration due to complicated cell deformations and viscous stresses. We present a microfluidic system that closely matches the mechanical modeling field equations and boundary conditions so that true mechanical properties can be extracted from observed deformations. We previously demonstrated the feasibility of a microfluidic extensional flow device that stretches single cells to measure viscoelastic mechanical properties (stiffness and fluidity) of cells using a phenomenological mechanical modeling approach. Here we rigorously derive the mechanical equation for this microfluidic mechanical measurement system using the elastic-viscoelastic correspondence principle. The new equation is applied to a creep relaxation technique to measure the properties of alginate hydrogel microparticles. With this mechanically-consistent analytic formula, the measured mechanical properties are independent of the measurement platform. The properties can be used in numerical simulations that investigate physiologically relevant situations with confidence that the predicted mechanical responses are quantitatively accurate.