Context : The majority of galactic chemical evolution models assumes the instantaneous mixing approximation ( IMA ) .
This assumption is probably not realistic as indicated by the existence of chemical inhomogeneities , although current chemical evolution models of the Milky Way can reproduce the majority of the observational constraints under the IMA .

Aims : The aim of this paper is to test whether relaxing this approximation in a detailed chemical evolution model can improve or worsen the agreement with observations .
To do that , we investigated two possible causes for relaxing of the instantaneous mixing : i ) the “ galactic fountain time delay effect ” and ii ) the “ metal cooling time delay effect ” .

Methods : We considered various galactic fountain time delays for the chemical enrichment from massive stars .
We then tested a time delay in the enrichment from stars of all masses due to gas cooling in the range 0.5-1 Gyr .

Results : We found that the effect of galactic fountains is negligible if an average time delay of 0.1 Gyr , as suggested in a previous paper , is assumed .
Longer time delays produce differences in the results but they are not realistic .
We also found that the O abundance gradient in the disk is not affected by galactic fountains .
The metal cooling time delays produce strong effects on the evolution of the chemical abundances only if we adopt stellar yields depending on metallicity .
If instead , the yields computed for to the solar chemical composition are adopted , negligible effects are produced , as in the case of the galactic fountain delay .

Conclusions : The relaxation of the IMA by means of the galactic fountain model , where the delay is considered only for massive stars and only in the disk , does not affect the chemical evolution results .
The combination of metal dependent yields and time delay in the chemical enrichment from all stars starting from the halo phase , instead , produces results at variance with observations .