Poiseuille flow in curved spaces

Area of Science:

• Fluid dynamics
• Non-Newtonian fluid mechanics
• Computational physics

Background:

• Poiseuille flow describes fluid dynamics in channels.
• Intrinsically curved media introduce geometric complexities.
• Localized metric perturbations alter channel geometry.

Purpose of the Study:

• To investigate Poiseuille channel flow in intrinsically curved media.
• To analyze the impact of localized metric perturbations on fluid flux.
• To derive a universal flux law for such flows.

Main Methods:

• Utilizing a lattice Boltzmann model adapted for curved space.
• Improving and validating the model by reducing discrete lattice effects.
• Systematically varying parameters of metric perturbations (amplitude, range, density).

Main Results:

• Fluid flux depends on a specific combination of perturbation parameters.
• This combination is identified as the average metric perturbation.
• A universal flux law for Poiseuille flow in curved media was derived.

Conclusions:

• The derived universal flux law simplifies the understanding of fluid dynamics in curved geometries.
• The validated lattice Boltzmann model provides a robust tool for studying such complex flows.
• This research offers insights into fluid behavior in deformable, curved channels.