Thermocapillary thin-film flows on a compliant substrate

Area of Science:

• Fluid Dynamics
• Materials Science
• Surface Science

Background:

• Thin liquid films on compliant substrates are crucial in various industrial applications.
• Thermocapillary effects, driven by temperature gradients, significantly influence fluid behavior.
• Understanding substrate compliance is key to predicting film dynamics.

Purpose of the Study:

• To investigate the dynamics of thin liquid films on compliant substrates under thermocapillary effects.
• To analyze the influence of fluid gravity, inertia, and Marangoni stresses on film and substrate.
• To examine behaviors on both horizontal and vertical compliant substrates.

Main Methods:

• Derivation of long-wave equations governing film and substrate dynamics.
• Linear stability analysis to identify different instability modes.
• Time-dependent computations to simulate film evolution.
• Seeking nonlinear traveling-wave solutions for specific configurations.

Main Results:

• On horizontal substrates (β=0), fluid gravity drives a sinuous mode, while Marangoni stresses induce a varicose mode.
• On vertical substrates (β=π/2), fluid inertia and Marangoni stresses drive a varicose mode, modified by gravity.
• Fluid inertia and heating enhance traveling wave speed and height.
• Strong wall heating causes significant deformations in both the liquid film and the compliant substrate.

Conclusions:

• The interplay of gravity, inertia, and thermocapillarity dictates thin film behavior on compliant substrates.
• Substrate compliance and heating are critical factors leading to large deformations.
• The findings provide insights into controlling thin film instabilities and deformations.