UC Davis

Biological membranes are made of phospholipids and host numerous surface active components.They are ubiquitous in nature and exhibit a non-trivial rheology, where the surface shear viscosity of an insoluble monolayer often depends on its surface-pressure. In this work, we extend the current Newtonian framework to account for this non-Newtonian behavior and unravel its eect on particles translating under low-Reynolds number hydrodynamics. We use a perturbative approach to model a weakly non-Newtonian membrane and compute its leading order eect on rigid disks by employing the Lorentz Reciprocal theorem. In particular, we show that a rigid disk translating on a free-standing membrane with background shear, experiences a force due to membrane rheology and undergoes non-intuitive trajectories, similar to the Saman-lift force on spheres. We explored the eect of this force on the collective dynamics of rigid disks by simulating the uniform translation of multiple rigid disks on a membrane. We report the formation of disk aggregates with a hexatic order that is found to be sensitive to the surface pressure-viscosity dependence.