  Gradient, chemically modified, flat surfaces enable directed transport of
droplets. Calculation of apparent contact angles inherent for gradient surfaces
is challenging even for atomically flat ones. Wetting of gradient, flat solid
surfaces is treated within the variational approach, under which the contact
line is free to move along the substrate. Transversality conditions of the
variational problem give rise to the generalized Young equation valid for
gradient solid surfaces. The apparent (equilibrium) contact angle of a droplet,
placed on a gradient surface depends on the radius of the contact line and the
values of derivatives of interfacial tensions. The linear approximation of the
problem is considered. It is demonstrated that the contact angle hysteresis is
inevitable on gradient surfaces. Electrowetting of gradient surfaces is
discussed.
