In this paper, we focus on the motion of the interface between two fl uids in contact with a solid surface so called the moving contact line problem. Although the Navier-Stokes equations are applicable for fl uid fl ows at micro-scales, the moving interface and surface tension occur at the level of molecules at which the classical mechanics break down. Qian et al. [1] Proposed Generalized Navier Boundary Condition (GNBC) on the basis of molecular dynamics simulation. The GNBC model can eliminate the non-physical singularity in the vicinity of the contact line. Moreover, it can accurately predict the condition with small capillary numbers.

We combine GNBC with a macro-micro scale dynamic contact line approach Y. Yamamoto et al. [3]. The relationship between the macro-micro contact angle is modelized thanks to Cox theory [2]. The evolving and deforming interface is carried out by J. Glimm et al. [4] and the Navier-Stokes equations are solved by Notus CFD [5] developed at I2M. We show numerical simulation result of capillary rise in tubes that are consistent with theory and experiment. Simulation of a spreading droplet on a surface is also presented and discussed.

References

[1] Qian, TZ, et al., Molecular scale contact line hydrodynamics of immiscible fl ows, Physics Review E (2003).
[2] Y. Yamamoto, et al., Modeling of the dynamic wetting behavior in a capillary tube by the macro-scopic-microscopic contact angle and generalized relationship Navier boundary condition, Int. J. Multiphase Flow (2014).
[3] RG Cox, The dynamics of the spreading of liquids on a solid surface. Fluid Mech (1986).
[4] J. Du, B. Fix, J. Glimm, et al., A simple package for front tracking, J. Comput. Phys. (2006).
[5] M. Cockroach, S. Glockner, A fourth-order accurate curvature computation in a level set framework for two-phase fl ows subjected to surface tension forces, J. Comput. Phys. (2015)