Drag coefficient of a liquid domain in a two-dimensional membrane

TL;DR

This paper develops an analytical model to calculate the drag coefficient of a liquid domain in a 2D membrane, accounting for various domain sizes and viscosities, revealing how viscosity differences influence mobility.

Contribution

It introduces a comprehensive hydrodynamic theory with a momentum decay mechanism to derive an analytical expression for the drag coefficient across all domain sizes.

Findings

Drag coefficient decreases with lower domain viscosity.

Flow within the domain enhances fluid transport in the surrounding membrane.

Analytical expressions cover the entire range of domain sizes.

Abstract

Using a hydrodynamic theory that incorporates a momentum decay mechanism, we calculate the drag coefficient of a circular liquid domain of finite viscosity moving in a two-dimensional membrane. We derive an analytical expression for the drag coefficient which covers the whole range of domain sizes. Several limiting expressions are discussed. The obtained drag coefficient decreases as the domain viscosity becomes smaller with respect to the outer membrane viscosity. This is because the flow induced in the domain acts to transport the fluid in the surrounding matrix more efficiently.