A significant fraction of all metal-poor stars are carbon-rich. Most of these carbon-enhanced metal-poor (CEMP) stars also show enhancement in elements produced mainly by the s-process (CEMP-s stars) and evidence suggests that the origin of these non-standard abundances can be traced to mass transfer from a binary asymptotic giant branch (AGB) companion. Thus, observations of CEMP-s stars are commonly used to infer the nucleosynthesis output of low-metallicity AGB stars. A crucial step in this exercise is understanding what happens to the accreted material after mass transfer ceases. Here we present models of the post-mass-transfer evolution of CEMP-s stars considering the physics of thermohaline mixing and atomic diffusion, including radiative levitation. We find that stars with typical CEMP-s star masses (M ~ 0.85 Msun) have very shallow convective envelopes (Menv < 1e-7 Msun). Hence, the surface abundance variations arising from the competition between gravitational settling and radiative levitation should be orders of magnitude larger than observed (e.g. [C/Fe]<-1 or [C/Fe]>+4). We are therefore unable to reproduce the spread in the observed abundances with these models and conclude that some other physical process must largely suppress atomic diffusion in the outer layers of CEMP-s stars. We demonstrate that this could be achieved by some additional (turbulent) mixing process operating at the base of the convective envelope, as found by other authors. Alternatively, mass-loss rates around 1e-13 Msun/yr could also negate most of the abundance variations by eroding the surface layers and forcing the base of the convective envelope to move inwards in mass. Since atomic diffusion cannot have a substantial effect on the surface abundances of CEMP-s stars, the dilution of the accreted material, while variable in degree from one star to the next, is most likely the same for all elements.
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