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The moving contact-line problem is of both theoretical and practicalinterest. The dynamic contact angle changes with the capillary number definedby the contact-line speed, and the correlation also depends on the equilibriumcontact angle measured at the static state. This correlation is usuallyrequired as an input to the traditional solvers based on the Navier-Stokes-likeequations, but it is simulated as an output in the current study using thelattice Boltzmann method (LBM) in a displacement process of two-immisciblefluids. The macroscopic theory and the molecular dynamics (MD) simulation hadshown a linear scaling law for the cosine of dynamic contact angle, which isalso observed in the previous LBM study in a short range of small capillarynumbers and for two neutral wetting conditions. However, our study shows thatthis linear scaling law holds in the whole range of capillary numbers and isuniversal for all wetting conditions. In a special case of complete wetting(spreading) with a zero equilibrium contact angle, a thin film of the wettingfluid occurs when the wettability is very strong, which leads to a hysteresisthat substantial capillary number is required to initiate the deviation of thedynamic contact angle from its equilibrium state. This observation isconsistent with the previous report on a new mechanism for the static contactangle hysteresis due to the presence of free liquid films. With an increasingcapillary number, the fluid-fluid interface starts oscillating beforefingering. Different fingering patterns are observed for cases with differentequilibrium contact angles.

Correlation of the dynamic contact angle with the capillary number and its hysteresis