  We studied several wetting boundary conditions (WBCs) in the simulation of
binary fluids based on phase-field theory. Five WBCs, three belonging to the
surface energy (SE) formulation using the linear, cubic and sine functions
(denoted as LinSE, CubSE and SinSE), the fourth using a geometric formulation
(Geom), and the fifth using a characteristic interpolation (CI), were compared
with each other through the study of several problems: (1) the static contact
angle of a drop; (2) a Poiseuille flow-driven liquid column; (3) a wettability
gradient (WG)-driven liquid column; (4) drop dewetting. It was found that while
all WBCs can predict the static contact angle fairly accurately, they may
affect the simulation outcomes of dynamic problems differently, depending on
the driving mechanism. For the flow-driven problem, to use different WBCs had
almost no effect on the flow characteristics over a large scale. But for other
capillarity-driven problems, the WBC had some noticeable effects. For the
WG-driven liquid column, Geom gave the most consistent prediction between the
drop velocity and dynamic contact angles, and LinSE delivered the poorest
prediction in this aspect. Except for Geom, the dynamic contact angle differed
from the prescribed (static) one when other WBCs were used. For drop dewetting,
Geom led to the most violent drop motion whereas CubSE caused the weakest
motion; the initial contact line velocity was also found to be dependent on the
WBC. For several problems, CubSE and SinSE gave almost the same results, and
those by Geom and CI were close as well, possibly due to similar consideration
in their design. Besides various comparisons, a new implementation that may be
used for all WBCs was proposed to mimic the wall energy relaxation and control
the degree of slip. This new procedure made it possible to allow the
simulations to match experimental measurements well.
