In spite of the relevance of Classical Cepheids as primary distance indicators , a general consensus on the dependence of the Period-Luminosity ( PL ) relation on the Cepheid chemical composition has not been achieved yet .
From the theoretical point of view , our previous investigations were able to reproduce some empirical tests for suitable assumptions on the helium to metal relative enrichment , but those results relied on specific assumptions concerning the Mass-Luminosity relation and the efficiency of the convective transfer in the pulsating envelopes .
In this paper , we investigate the effects of the assumed value of the mixing length parameter l / H _ { p } on the pulsation properties and we release the assumption of a fixed Mass-Luminosity relation .
To this purpose , new nonlinear convective fundamental pulsation models have been computed for various chemical compositions ( Z =0.004 , 0.008 , 0.01 and 0.02 ) and adopting l / H _ { p } =1.7-1.8 , which is larger than the one ( 1.5 ) used in our previous papers .
From the extended model set , synthetic PL relations in the various photometric bands are derived using the predicted instability strip together with recent evolutionary tracks .
We show that as the \l / H _ { p } value increases the pulsation region gets narrower , mostly due to the blueward shift of the red edge for fundamental pulsation , with the effect becoming more important at the higher metal contents ( Z \geq 0.01 ) .
However , the comparison of the new models with the previously computed ones shows that the \l / H _ { p } variation has no consequence on the predicted Period-Wesenheit ( PW ) relations , which instead are influenced by the pulsator metal content .
On this ground , we present a straightforward way to infer the distance and metal content of variables with observed BVI or BVK magnitudes .
As for the PL relations , we show that either the zero-point and the slope are very slightly modified by the \l / H _ { p } variation , at constant chemical composition .
In the meanwhile , we confirm that : ( 1 ) moving from visual to longer wavelengths , the predicted Period-Magnitude distribution for a given metal content becomes narrower and its slope becomes steeper ; ( 2 ) decreasing the metal content , the PL relations become steeper and brighter , with the amount of this metallicity effect decreasing from optical to near-infrared bands .
As a whole , we show that our pulsation relations appear fully consistent with the observed properties of Galactic and Magellanic Cloud Cepheids , supporting the predicted steepening and brightening of the PL relations when moving from metal-rich to metal-poor variables .
Moreover , we show that the distances inferred by the predicted PW relations agree with recently measured trigonometric parallaxes , whereas they suggest a correction to the values based on the Infrared Surface Brightness technique , as already found from an independent method .
Finally , also the pulsation metal contents suggested by the predicted PW relations appear in statistical agreement with spectroscopic [ Fe/H ] measurements .