Classical continuum theory of porous media based on partial differential equations is unsuited for use in predicting time scales of arrival of fluids or solutes over the pore network. But percolation theory, as applied to the pore network, by discretizing these equations at the pore scale, replaces differential equations with difference equations. Such difference equations on networks can predict scale dependences of important processes, such as the advance of wetting and drying fronts through porous media that may result, for example from intermittent water sources such as rainstorms. Applying these scaling results allows us to predict the rates at which wetting and drying fronts advance through porous media and, in fact also the time scale at which a given drying front will overtake its associated wetting front. Further implications are also discussed, such as the topology of the resulting wetted volume.