# Lipid Bilayer Hydrodynamic Drag

## TL;DR

This study measures the hydrodynamic drag on freely diffusing lipid vesicles to determine the boundary condition at the membrane surface, finding it consistent with no-slip conditions rather than stress-free assumptions.

## Contribution

The paper provides the first direct experimental measurement of the membrane boundary condition, confirming it aligns with no-slip rather than stress-free models.

## Key findings

- Measured hydrodynamic drag coefficient C ≈ 6
- Results match the no-slip boundary condition
- Contradicts the assumption of stress-free membrane surfaces

## Abstract

The hydrodynamic drag at a lipid bilayer surface determines in part the flow properties of suspensions of cells and liposomes. Given the fluidity of lipid bilayers, it is not obvious a priori whether solid-like no-slip, liquid-like no-stress, or intermediate boundary conditions apply at the water-bilayer interface. Though no-slip conditions have been widely assumed for many decades, this fundamental aspect of membrane rheology has, to our knowledge, never been directly measured for free bilayers. We applied light sheet fluorescence microscopy to image freely diffusing phospholipid vesicles and determined the hydrodynamic drag coefficient $C \pi \eta R$, where $\eta$ is the external fluid viscosity, $R$ is the vesicle radius, and the dimensionless $C$ characterizes the flow boundary condition. We find that $C = 5.92 \pm 0.13$ (stat.) $\pm 0.16$ (syst.), matching the theoretical value of $C=6$ for a no-slip boundary and far from the $C=4$ value for a zero shear stress boundary