  We examine the stability and observational consequences of mixing induced by
3He burning in the envelopes of first ascent red giants. We demonstrate that
there are two unstable modes: a rapid, nearly adiabatic mode that we cannot
identify with an underlying physical mechanism, and a slow, nearly radiative
mode that can be identified with thermohaline convection. We present
observational constraints that make the operation of the rapid mode unlikely to
occur in real stars. Thermohaline convection turns out to be fast enough only
if fluid elements have finger-like structures with a length to diameter ratio
l/d > 10. We identify some potentially serious obstacles for thermohaline
convection as the predominant mixing mechanism for giants. We show that
rotation-induced horizontal turbulent diffusion may suppress the 3He-driven
thermohaline convection. Another potentially serious problem for it is to
explain observational evidence of enhanced extra mixing. The 3He exhaustion in
stars approaching the red giant branch (RGB) tip should make the 3He mixing
inefficient on the asymptotic giant branch (AGB). In spite of this, there are
observational data indicating the presence of extra mixing in low-mass AGB
stars similar to that operating on the RGB. Overmixing may also occur in
carbon-enhanced metal-poor stars.
