Single droplet or bubble and its stability: Kinetic theory and dynamical system approaches

Area of Science:

• Thermodynamics
• Fluid Dynamics
• Statistical Mechanics

Background:

• Investigating droplet and bubble behavior in van der Waals fluids is crucial for understanding phase transitions.
• Existing kinetic models provide a foundation for analyzing fluid dynamics at a microscopic level.

Purpose of the Study:

• To investigate steady solutions of single droplets or bubbles in van der Waals fluid using a proposed kinetic model.
• To analyze density distributions as flows in a low-dimensional phase space under thermal equilibrium and isotropic conditions.

Main Methods:

• Reduction of the kinetic equation to an ordinary differential equation for density under specific assumptions.
• Analysis of density distribution as a flow in a low-dimensional phase space.
• Direct numerical experiments to study the stability of obtained solutions.

Main Results:

• Identified single droplet/bubble solutions as fixed points in the phase space.
• Demonstrated qualitative differences in flow behavior between unstable and metastable parameter regions.
• Characterized the density distributions within these distinct regions.

Conclusions:

• The kinetic model effectively describes droplet and bubble steady states as dynamical system flows.
• The stability and features of these fluid structures are dependent on the thermodynamic parameters of the van der Waals fluid.