  Thermohaline mixing is a favoured mechanism for the so-called "extra mixing"
on the red giant branch of low-mass stars. The mixing is triggered by the
molecular weight inversion created above the hydrogen shell during first
dredge-up when helium-3 burns via 3He(3He,2p)4He. The standard 1D diffusive
mixing scheme cannot simultaneously match carbon and lithium abundances to NGC
6397 red giants. We investigate two modifications to the standard scheme: (1)
an advective two stream mixing algorithm, and (2) modifications to the standard
1D thermohaline mixing formalism. We cannot simultaneously match carbon and
lithium abundances using our two stream mixing approach. However we develop a
modified diffusive scheme with an explicit temperature dependence that can
simultaneously fit carbon and lithium abundances to NGC 6397 stars. Our
modified diffusive scheme induces mixing that is faster than the standard
theory predicts in the hotter part of the thermohaline region and mixing that
is slower in the cooler part. Our results infer that the extra mixing mechanism
needs further investigation and more observations are required, particularly
for stars in different clusters spanning a range in metallicity.
