  The shape of a liquid-air interface advancing on a heterogeneous surface was
studied experimentally, together with the force induced by the pinning of the
contact line to surface defects. Different surfaces were considered with
circular defects introduced as arrays of cocoa butter patches or small circular
holes. These heterogeneous surfaces were submerged into aqueous ethanol
solutions, while measuring the additional force arising from the deformation of
the advancing contact line and characterising the interface shape and its
pinning on the defects. Initially, the submersion force is linear with
submerged depth, suggesting a constant defect-induced stiffness. This regime
ends when the contact line de pins from the defects. A simple scaling is
proposed to describe the depinning force and the depinning energy. We find
that, as the defect separation increases, the interface stiffness increases
too, with a weak dependency on the defect radius. This interaction between
defects cannot be captured by the simple scaling, but can be well predicted by
a theory considering the interface deformation in presence of periodic arrays
of holes. Creating a 4-phase contact line, by including solid defects (cocoa
butter) reduced pinning forces. The radius of the defect had a nonlinear effect
on the depinning depth. The 4-phase contact line resulted in depinning before
the defects are fully submerged. These experimental results and the associated
theory help understanding quantitatively the extent to which surface
heterogeneities can slow down wetting. This in turn paves the way to tailor the
design of heterogeneous surfaces, towards desired wetting performances.
