  Viscosity is a key property of cell membranes that controls mobility of
embedded proteins and membrane remodeling. Measuring it is challenging because
existing approaches involve complex experimental designs and/or models, and the
applicability of some is limited to specific systems and membrane compositions.
As a result there is scarcity of data and the reported values for membrane
viscosity vary by orders of magnitude for the same system. Here, we show how
viscosity of bilayer membranes can be obtained from the transient deformation
of giant unilamellar vesicles. The approach enables a non-invasive,
probe-independent and high-throughput measurement of the viscosity of bilayers
made of lipids or polymers with a wide range of compositions and phase state.
Pure lipid and single-phase mixed bilayers are found to behave as Newtonian
fluids with strain-rate independent viscosity, while phase-separated and
diblock-copolymers systems exhibit shear-thinning in the explored range of
strain rates 1-2000 $s^{-1}$. The results also reveal that electrically
polarized bilayers can be significantly more viscous than charge-neutral
bilayers. These findings suggest that biomembrane viscosity is a dynamic
property that can be actively modulated not only by composition but also by
membrane polarization, e.g., as in action potentials.
