Shape Evolution of Droplets Growing on Linear Microgrooves

Anisotropic
spreading of liquids and elongated droplet shapes are
often encountered on surfaces decorated with a periodic micropattern
of linear surface topographies. Numerical calculations and wetting
experiments show that the shape evolution of droplets that are slowly
growing on a surface with parallel grooves can be grouped into two
distinct morphological regimes. In the first regime, the liquid of
the growing droplet spreads only into the direction parallel to the
grooves. In the second regime, the three-phase contact line advances
also perpendicular to the grooves, whereas the growing droplets approach
a scale-invariant shape. Here, we demonstrate that shapes of droplets
in contact with a large number of linear grooves are identical to
the shapes of droplets confined to a plane chemical stripe, where
this mapping of shapes is solely based on the knowledge of the cross
section of the linear grooves and the material contact angle. The
spectrum of interfacial shapes on the chemical stripe can be exploited
to predict the particular growth mode and the asymptotic value of
the base eccentricity in the limit of droplets covering a large number
of grooves. The proposed model shows an excellent agreement with experimentally
observed base eccentricities for droplets on grooves of various cross
sections. The universality of the model is underlined by the accurate
match with available literature data for droplet eccentricities on
parallel chemical stripes.