Inspired by the chemical etching processes, where experiments show that
growth rates depending on the local environment might play a fundamental role
in determining the properties of the etched surfaces, we study here a model for
kinetic roughening which includes explicitly an anisotropic effect in the
growth rules. Our model introduces a dependence of the growth rules on the
local environment conditions, i.e. on the local curvature of the surface.
Variables with different local curvatures of the surface, in fact, present
different quenched disorder and a parameter p (which could represent
different experimental conditions) is introduced to account for different time
scales for the different classes of variables. We show that the introduction of
this {\em time scale separation} in the model leads to a cross-over effect on
the roughness properties. This effect could explain the scattering in the
experimental measurements available in the literature. The interplay between
anisotropy and the cross-over effect and the dependence of critical properties
on parameter p is investigated as well as the relationship with the known
universality classes.Comment: 11 pages, 21 figures. submitted to PR