Fig. 3.

Lumens at steady state. (A) The steady state size of the lumen as a function of pumping efficiency displays an unstable and a stable branch represented in blue and red, respectively (${\xi }_V={\xi }_i=0.5$). The dashed arrows represent the direction of variation of lumen radius for any deviation from its steady state value. There is no stable state lumen at low enough pumping efficiency $\delta {\rho }_i$. Any lumen of any size would shrink off. Above a critical $\delta {\rho }_i$, any small lumen above the unstable branch will grow to finally reach a larger steady lumen size. (B) Variation of the steady lumen size as a function of lumen efficiency for different screening lengths ${\xi }_V$ and ${\xi }_i$.