Poiseuille flow in curved spaces

Abstract

We investigate Poiseuille channel flow through intrinsically curved media, equipped with localized metric perturbations. To this end, we study the flux of a fluid driven through the curved channel in dependence of the spatial deformation, characterized by the parameters of the metric perturbations (amplitude, range and density). We find that the flux depends only on a specific combination of parameters, which we identify as the average metric perturbation, and derive a universal flux law for the Poiseuille flow. For the purpose of this study, we have improved and validated our recently developed lattice Boltzmann model in curved space by considerably reducing discrete lattice effects.

References in corpus (3)

• Non-local transport and the hydrodynamic shear viscosity in graphene
• Improved axisymmetric lattice Boltzmann scheme
• Dean Instability in Double-Curved Channels

Cited by in corpus (5)

• Lattice Boltzmann models based on the vielbein formalism for the simulation of flows in curvilinear geometries
• Fluid structure interaction with curved space lattice Boltzmann
• Lattice Wigner equation
• Volumetric Lattice Boltzmann Models in General Curvilinear Coordinates: Theoretical Formulation
• Lattice Boltzmann Model in General Curvilinear Coordinates Applied to Exactly Solvable 2D Flow Problems