Evaluation of the Cox equation to derive dynamic contact angle at nanopores imbibition: A Molecular dynamics study

Molecular dynamics (MD) simulation is employed to simulate the imbibition of a designed nanopore by a fluid. The fluid is considered as a simple Lennard-Jones (LJ) fluid. For this system (i.e., LJ fluid and nanopore), the length of imbibition as a function of time for various interactions between the fluid and the pore wall is recorded. In almost all cases, the kinetics of imbibition is successfully described with the Lucas-Washburn (LW) equation. However, the deviation from the LW equation is observed in some cases. This nonconformity is contributed to the neglecting of the dynamic contact angle (DCA) in the LW equation. A hydrodynamic model (i.e., the Cox equation) is taken into consideration to calculate the DCA. It is demonstrated that the LW equation together with the Cox equation is able to justify the simulation results for those cases, which are not in good agreement with the simple LW equation. Further investigation on the MD simulation data reveals that the Cox equation is only appropriate to derive the DCA at small capillary numbers. This finding is in consonance with the theoretical background of this equation as well as experimental work.