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Damping of Thermocapillary Destabilization of a Liquid Film in Zero Gravity Through the Use of an Isothermal Porous Substrate

Aneet D. Narendranath

Aneet D. Narendranath

Department of Mechanical Engineering-Engineering Mechanics, Michigan Technological UniversityHoughton,
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Narendranath, Aneet D.
  
21 jul 2020
Damping of Thermocapillary Destabilization of a Liquid Film in Zero Gravity Through the Use of an Isothermal Porous Substrate's Cover Image
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Categoría del artículo: Research Article
Publicado en línea: 21 jul 2020
Páginas: 35 - 42
DOI: https://doi.org/10.2478/gsr-2017-0009
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© 2017 Aneet D. Narendranath, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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.
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).
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).
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).
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).
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).
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).

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=0.05Liquid film on IS-sub vs. IP-sub with ɛ=0.0005
Time (non-dimensional)Recurrence Rate (RR%)SignificanceTime (non-dimensional)Recurrence Rate (RR%)Significance
0.0100.0Similar dynamics0.0100.0Similar dynamics
400.0100.0Similar dynamics400.033.66Dynamics within 33.66% of each other
800.045.94Dynamics within 45.94% of each other800.06.86Dynamics within 6.86% of each other
1650.0 (time rupture of film on IS-sub)39.79Dynamics within 39.79% of each other1650.05.29Dynamics within 5.29% of each other
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