Thermohaline instability and rotation-induced mixing. I - Low- and intermediate-mass solar metallicity stars up to the end of the AGB

(abridged) Numerous spectroscopic observations provide compelling evidence for non-canonical processes that modify the surface abundances of low- and intermediate-mass stars beyond the predictions of standard stellar theory. We study the effects of thermohaline instability and rotation-induced mixing in the 1-4 Msun range at solar metallicity. We present evolutionary models by considering both thermohaline and rotation-induced mixing in stellar interior. We discuss the effects of these processes on the chemical properties of stars from the zero age main sequence up to the end of the second dredge-up on the early-AGB for intermediate-mass stars and up to the AGB tip for low-mass stars. Model predictions are compared to observational data for lithium,12C/13C,[N/C],[Na/Fe],16O/17O, and 16O/18O in Galactic open clusters and in field stars with well-defined evolutionary status,as well as in planetary nebulae. Thermohaline mixing simultaneously accounts for the observed behaviour of 12C/13C,[N/C], and lithium in low-mass stars that are more luminous than the RGB bump, and its efficiency is increasing with decreasing initial stellar mass. On the TP-AGB,thermohaline mixing leads to lithium production, although the 7Li yields remain negative. Although the 3He stellar yields are much reduced thanks to this process, we find that solar-metallicity, low-mass stars remain net 3He producers. Rotation-induced mixing is found to change the stellar structure so that in the mass range between \sim 1.5 and 2.2 Msun the thermohaline instability occurs earlier on the red giant branch than in non-rotating models. Finally rotation accounts for the observed star-to-star abundance variations at a given evolutionary status, and is necessary to explain the features of CN-processed material in intermediate-mass stars.