Motion and hydrodynamic resistance of an elastic bead confined in a square microchannel

Cells and other soft particles are often forced to flow in confined geometries in both laboratory and natural environments, where the elastic deformation induces an additional drag and pressure drop across the particle. In contrast with other multiphase flows, the physical parameters that determine this additional pressure are still not known. Here, we start by measuring the pressure drop across a single spherical hydrogel particle as it flows in a microfluidic comparator. This pressure is found to depend on the amount of confinement, elastic modulus, fluid viscosity, and velocity. A force balance model for the particle is then proposed by incorporating these factors and relying on simulations of bead geometry and lubrication flow considerations. The final model collapses the force measurements onto a single scaling law spanning several decades, while providing physical insights by recalling elements from classic multiphase flows and contact mechanics.