Figure 1
Various stabilizing and destabilizing mechanisms that affect a liquid film on an isothermal solid substrate, where film is flat and parallel to the substrate. Periodic boundary conditions were used on the left and right edge. In this article, evaporation and concomitant vapor recoil effects were neglected.
Figure 2
Evolution of a liquid film towards thermocapillary-driven rupture from a cosine initial condition. An isothermal porous substrate allows for the film to persist without rupture for longer than with an isothermal solid substrate. T, time (dimensionless); X, span-wise coordinate (dimensionless); H(X,T), nonlinear time evolution of a non-evaporating liquid film's interface thickness (dimensionless).
Figure 3
Recurrence plot for a liquid film evolving on an IS-sub in zero gravity. Cut-off length, ɛ=0.0005. X, span-wise coordinate (dimensionless); T, time (dimensionless).
Figure 4
Recurrence plot for a liquid film evolving on an IP-sub in zero gravity. Cut-off length, ɛ=0.0005. X, span-wise coordinate (dimensionless); T, time (dimensionless).
Figure 5
Cross-recurrence plots (CRPs) of liquid film states for cut-off length, ɛ=0.0005. The CRPs visually compare the film dynamics on the IS-sub versus those on the IP-sub for a recurrence of states within 0.05% of each other. Because the IS-sub film ruptures at T=1650.0, CRP comparisons were made through T=1650.0. X, span-wise coordinate (dimensionless); T, time (dimensionless).
Figure 6
Cross-recurrence plots (CRPs) of liquid film states for cut-off length, ɛ=0.05. The CRPs visually compare the film dynamics on the IS-sub versus those on the IP-sub for a recurrence of states within 5% of each other. X, span-wise coordinate (dimensionless); T, time (dimensionless).
Table 1
Rates of recurrence comparing similarity of liquid films dynamics on IS-sub vs. IP-sub. Two different cut-off distances, ɛ, were used to describe the similarity between dynamics of liquid films. IS-sub, isothermal solid substrate; IP-sub, isothermal porous substrate.
| Liquid film on IS-sub vs. IP-sub with ɛ=0.05 | Liquid film on IS-sub vs. IP-sub with ɛ=0.0005 | ||||
|---|---|---|---|---|---|
| Time (non-dimensional) | Recurrence Rate (RR%) | Significance | Time (non-dimensional) | Recurrence Rate (RR%) | Significance |
| 0.0 | 100.0 | Similar dynamics | 0.0 | 100.0 | Similar dynamics |
| 400.0 | 100.0 | Similar dynamics | 400.0 | 33.66 | Dynamics within 33.66% of each other |
| 800.0 | 45.94 | Dynamics within 45.94% of each other | 800.0 | 6.86 | Dynamics within 6.86% of each other |
| 1650.0 (time rupture of film on IS-sub) | 39.79 | Dynamics within 39.79% of each other | 1650.0 | 5.29 | Dynamics within 5.29% of each other |