A novel numerical method for simulating a droplet in a Leidenfrost state on soft substrates

Area of Science:

• Multiphase flow dynamics
• Computational fluid dynamics
• Soft matter physics

Background:

• Simulating complex fluid-structure interactions (FSI) with phase transitions is challenging.
• Existing models often simplify solid substrates, limiting applicability to phenomena like the Leidenfrost effect on deformable materials.
• Accurate modeling requires robust methods for handling sharp interfaces and coupled heat/mass transfer.

Purpose of the Study:

• To develop and validate a numerical framework for three-phase systems (liquid, gas, viscoelastic solid).
• To investigate the Leidenfrost effect on soft substrates, considering substrate deformation.
• To provide a tool for simulating complex FSI with heat and mass transfer.

Main Methods:

• Utilized an extended discontinuous Galerkin (XDG) method coupled with a level-set approach.
• Implemented a robust interface-tracking technique ensuring sharp phase boundaries without artificial smoothing.
• Incorporated a Winkler foundation model to represent the soft substrate's mechanical response.

Main Results:

• Verified optimal convergence using a fluid-solid Taylor-Couette benchmark.
• Validated quasi-static droplet shapes against existing rigid models and a novel analytical solution for soft substrates.
• Successfully simulated a Leidenfrost droplet on an inclined soft substrate, capturing asymmetric shapes, substrate deformation, and interfacial waves.

Conclusions:

• The developed numerical framework accurately simulates three-phase FSI, including heat and mass transfer.
• The study provides a novel analytical extension for the Leidenfrost effect on soft substrates.
• The framework demonstrates robustness in capturing complex phenomena like substrate deformation and interfacial wave generation.