Studying the contact point and interface moving in a sinusoidal tube with lattice Boltzmann method

The multicomponent nonideal gas lattice Boltzmann model by Shan and Chen (S -C) is used to study the immiscible displacement in a sinusoidal tube. The movement of interface and the contact point (contact line in three-dimensio n) is studied. Due to the roughness of the boundary, the contact point show s "stick-slip" mechanics. The "stick-slip" effect decreases as the speed of the interface increases. For fluids that are nonwetting, the interface is almost perpendicular to the boundaries at most time, although its shapes at different position of the tube are rather different. When the tube becomes narrow, the interface turns a complex curves rather than remains simple me nisci. The velocity is found to vary considerably between the neighbor node s close to the contact point, consistent with the experimental observation that the velocity is multi-values on the contact line. Finally, the effect of three boundary conditions is discussed. The average speed is found diffe rent for different boundary conditions. The simple bounce-back rule makes t he contact point move fastest. Both the simple bounce-back and the no-slip bounce-back rules are more sensitive to the roughness of the boundary in co mparison with the half-way bounce-back rule. The simulation results suggest that the S-C model may be a promising tool in simulating the displacement behaviour of two immiscible fluids in complex geometry.