Mesoscopic modeling of heterogeneous boundary conditions for microchannel flows

Abstract

We present a mesoscopic model of the fluid-wall interactions for flows in microchannel geometries. We define a suitable implementation of the boundary conditions for a discrete version of the Boltzmann equations describing a wall-bounded single phase fluid. We distinguish different slippage properties on the surface by introducing a slip function, defining the local degree of slip for mesoscopic molecules at the boundaries. The slip function plays the role of a renormalizing factor which incorporates, with some degree of arbitrariness, the microscopic effects on the mesoscopic description. We discuss the mesoscopic slip properties in terms of slip length, slip velocity, pressure drop reduction (drag reduction), and mass flow rate in microchannels as a function of the degree of slippage and of its spatial distribution and localization, the latter parameter mimicking the degree of roughness of the ultra-hydrophobic material in real experiments. We also discuss the increment of the slip length in the transition regime, i.e. at O(1) Knudsen numbers. Finally, we compare our results with Molecular Dynamics investigations of the dependency of the slip length on the mean channel pressure and local slip properties (Cottin-Bizonne et al. 2004) and with the experimental dependency of the pressure drop reduction on the percentage of hydrophobic material deposited on the surface -- Ou et al. (2004).

arXiv comment21 pages, 10 figures

References in corpus (8)

• Simulation of non-ideal gases and liquid-gas phase transitions by lattice Boltzmann equation
• Low Friction Flows of Liquids at Nanopatterned Interfaces
• Kinetic boundary conditions in the lattice Boltzmann method
• Boundary conditions at a fluid - solid interface
• Dynamics of simple liquids at heterogeneous surfaces : Molecular Dynamics simulations and hydrodynamic description
• Role of the H theorem in lattice Boltzmann hydrodynamic simulations
• Analytical calculation of slip flow in lattice Boltzmann models with kinetic boundary conditions
• Lattice Boltzmann method at finite-Knudsen numbers

Cited by in corpus (11)

• Generalized Lattice Boltzmann Method with multi-range pseudo-potential
• Mesoscopic modeling of a two-phase flow in the presence of boundaries: the Contact Angle
• A note on the effective slip properties for microchannel flows with ultra-hydrophobic surfaces
• Quantifying effective slip length over micropatterned hydrophobic surfaces
• Effective slip over superhydrophobic surfaces in thin channels
• Mesoscopic two-phase model for describing apparent slip in micro-channel flows
• Regularization of the slip length divergence in water nanoflows by inhomogeneities at the Angstrom scale
• Molecular transport and flow past hard and soft surfaces: Computer simulation of model systems
• Boundary induced non linearities at small Reynolds Numbers
• Towards a mesoscopic model of water-like fluids with hydrodynamic interactions
• Mesoscale investigations of fluid-solid interaction: Liquid slip flow in a parallel-plate microchannel