Figure 5.

Vesicles spreading on a substrate. (a) Initial geometry of composite drop in $\left(r,z\right)$ coordinates (negative values of r are drawn by symmetry). The gray zone has viscosity ${\mu }_d$, white have viscosity ${\mu }_s$, and the solid line represents the inextensible membrane. (b) Solid line, geometry of a spreading vesicle with infinite viscosity contrast, dashed line, of a vesicle of viscosity contrast ${\mu }_d/{\mu }_s={10}^5$. To allow spreading, the membrane wrinkles are depleted everywhere for infinite viscosity contrast, only close to the substrate for finite viscosity contrast. Compare shape of vesicle at infinite viscosity contrast with Fig. 3a, at finite viscosity contrast with Fig. 3b. (c) Close-up of (b), with initial geometry overlaid in gray. Note the depletion of the wrinkles. (d) Growth of aligned area as a function of time for different viscosity contrasts. For contrasts up to 10⁵, an initial P₁ phase with $A\propto t$ is noted, followed by a slower P₂ regime $A\propto t^{1/2}$. Transition reduced area $a^{\ast }$ falls from 0.6 for ${\mu }_d/{\mu }_s=100$ to 0.08 for ${\mu }_d/{\mu }_s={10}^5$. For infinite contrast, the $A\propto t$ regime is not observed at all.