Pattern formation in liquid-vapor systems under periodic potential and shear.

Area of Science:

• Fluid dynamics
• Nonlinear physics
• Statistical mechanics

Background:

• Understanding phase behavior and pattern formation is crucial in fluid dynamics.
• Sheared nonideal fluids under periodic potentials exhibit complex phenomena.
• Lattice Boltzmann methods offer a powerful tool for simulating such systems.

Purpose of the Study:

• To investigate the phase behavior and pattern formation in a sheared nonideal fluid subjected to a periodic potential.
• To analyze the transition from stable striped phases to dynamic patterns under varying shear rates.
• To characterize the resulting velocity field patterns.

Main Methods:

• Developed and validated an isothermal two-dimensional lattice Boltzmann scheme for a liquid-vapor system using the van der Waals equation of state.
• Applied shear using moving walls and introduced a periodic potential varying along the flow direction.
• Examined parameter space regions where a striped phase is stable in the absence of flow.

Main Results:

• At low shear rates, periodic patterns were preserved with slight distortions.
• At high shear rates, the striped phase became unstable, leading to the observation of traveling waves on the liquid-vapor interface.
• These traveling waves spanned the entire system, with wavelength dependent only on system length.
• Velocity field patterns characterized by a single vortex were also observed.

Conclusions:

• The study reveals a transition in fluid behavior from stable striped patterns to dynamic traveling waves under increasing shear rates.
• The lattice Boltzmann method effectively simulates complex fluid phenomena, including pattern formation and instability.
• The findings provide insights into the fundamental physics of sheared fluids and their potential applications.