Slip boundary condition for lattice Boltzmann modeling of liquid flows

Boundary slip phenomenon has been widely studied for microscale gas flow in recent years. However, researches on this topic for liquid flow are still rare. Boundary slip of liquid flow is caused by roughness and micro bubbles, while that of gas flow is caused by rarefied effect. Despite this difference, researchers found that some slip boundary conditions for gas flow can also be applied to liquid flow, except the different way of treating accommodation coefficients. Currently, a measurable physical parameter, slip length, is widely used for liquid flow, which can be obtained through experiential methods. If the relationship between the slip length and the accommodation coefficients can be found theoretically, these slip boundary conditions for liquid flow will be powerful tools to research slip related flow characteristics, for example, drag reduction with superhydrophobic surface. Based on the Navier slip model, this paper deducts the relationship between the accommodation coefficients and the slip length with the half-way and the modified slip boundary conditions, under the framework of the lattice Boltzmann method (LBM). The effectiveness of the proposed slip boundary conditions are verified with the Couette flow, the Poesueille flow, the water Cu nanofluid flow, and the 2-D Womersley flow. Results indicate that these boundary conditions are suitable for both linear and non-linear liquid flow.