 Accretion trajectories in a compact viscous similarity disk

For the $a=1$ compact self-similar disk with density-linear viscosity, radial drift is $\dot{r}=r/(2t)-R/(10t)$. An integrating factor gives the displayed trajectories. From $0<r_i<R(t_i)$, the arrival time at the origin is $t_i[1-r_i/R(t_i){]}^{-10}$, finite for every interior point. The outer-edge trajectory has zero surface density of a disk and carries no mass.