  Adsorption of liquid on a planar wall decorated by a hydrophilic stripe of
width $L$ is considered. Under the condition, that the wall is only partially
wet (or dry) while the stripe tends to be wet completely, a liquid drop is
formed above the stripe. The maximum height $\ell_m(\delta\mu)$ of the drop
depends on the stripe width $L$ and the chemical potential departure from
saturation $\delta\mu$ where it adopts the value $\ell_0=\ell_m(0)$. Assuming a
long-range potential of van der Waals type exerted by the stripe, the
interfacial Hamiltonian model is used to show that $\ell_0$ is approached
linearly with $\delta\mu$ with a slope which scales as $L^2$ over the region
satisfying $L\lesssim \xi_\parallel$, where $\xi_\parallel$ is the parallel
correlation function pertinent to the stripe. This suggests that near the
saturation there exists a universal curve $\ell_m(\delta\mu)$ to which the
adsorption isotherms corresponding to different values of $L$ all collapse when
appropriately rescaled. Although the series expansion based on the interfacial
Hamiltonian model can be formed by considering higher order terms, a more
appropriate approximation in the form of a rational function based on scaling
arguments is proposed. The approximation is based on exact asymptotic results,
namely that $\ell_m\sim\delta\mu^{-1/3}$ for $L\to\infty$ and that $\ell_m$
obeys the correct $\delta\mu\to0$ behaviour in line with the results of the
interfacial Hamiltonian model. All the predictions are verified by the
comparison with a microscopic density functional theory (DFT) and, in
particular, the rational function approximation -- even in its simplest form --
is shown to be in a very reasonable agreement with DFT for a broad range of
both $\delta\mu$ and $L$.
