Smoothed profile-lattice Boltzmann method for non-penetration and wetting boundary conditions in two and three dimensions

• Published in: Computers & fluids Vol. 159; pp. 64 - 80
• Main Authors: Seta, Takeshi, Uchiyama, Tomomi, Takano, Noboru
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 15.12.2017; Elsevier BV
• Subjects: Boundary conditions; Boundary layer transition; Chemical potential; Circular cylinders; Computational fluid dynamics; Contact angle; Fluid-solid interactions; Fluids; Fluxes; Hydrophilicity; Hydrophobicity; Lattice Boltzmann method; Mathematical models; Non-penetration condition; Order parameters; Penetration; Permeability; Smoothed profile method; Solid surfaces; Velocity; Wetting; Wetting boundary condition; Smoothed profile method; Hydrophobicity; Lattice Boltzmann method; Wetting boundary condition; Hydrophilicity; Non-penetration condition
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/j.compfluid.2017.09.012

•Two types of indicator functions are introduced to implement boundary conditions.•The exact satisfaction of the non-penetration condition is demonstrated.•The proposed method can calculate the static contact angle on the curved boundary.•The proposed method can predict spreading behavior of a drop on a plate.•A significant reduction in the computer time is shown. In this study, the smoothed profile-lattice Boltzmann method (SP-LBM) is proposed to determine the contact line dynamics on a hydrophobic or a hydrophilic curved wall. Two types of smoothed indicator functions are introduced, namely a function that identifies the solid domain for non-slip and non-penetration conditions and a function that denotes the boundary layer for no mass-flux and the wetting boundary conditions. In order to prevent fluid penetration into the solid boundary, the fluid-solid interaction force is computed based on the definition of the fluid velocity as proposed by Guo et al. [1]. In order to implement the Neumann boundary conditions for the order parameter and the chemical potential, the fluxes from the solid surfaces are distributed to relevant physical valuables through a smoothed profile. Several two-dimensional and three-dimensional numerical investigations including those determining the Couette flows, flow around a circular cylinder, transition layer on a wetting boundary, and dynamic behavior of a droplet on a flat or curved plate demonstrate the efficiency of the present method in calculating the contact angle of a droplet on curved surfaces with wall impermeability. The present model provides a simple algorithm to compute the surface normal vector and contact line dynamics on an arbitrarily shaped boundary by using a smoothed-profile.