  We present the results of an investigation of the dredge-up and mixing during
the merger of two white dwarfs with different chemical compositions by
conducting hydrodynamic simulations of binary mergers for three representative
mass ratios. In all the simulations, the total mass of the two white dwarfs is
$\lesssim1.0~{\rm M_\odot}$. Mergers involving a CO and a He white dwarf have
been suggested as a possible formation channel for R Coronae Borealis type
stars, and we are interested in testing if such mergers lead to conditions and
outcomes in agreement with observations. Even if the conditions during the
merger and subsequent nucleosynthesis favor the production of $^{18}{\mathrm
O}$, the merger must avoid dredging up large amounts of $^{16}{\mathrm O}$, or
else it will be difficult to produce sufficient $^{18}{\mathrm O}$ to explain
the oxygen ratio observed to be of order unity. We performed a total of 9
simulations using two different grid-based hydrodynamics codes using fixed and
adaptive meshes, and one smooth particle hydrodynamics (SPH) code. We find that
in most of the simulations, $>10^{-2}~{\rm M_\odot}$ of $^{16}{\mathrm O}$ is
indeed dredged up during the merger. However, in SPH simulations where the
accretor is a hybrid He/CO white dwarf with a $\sim 0.1~{\rm M_\odot}$ layer of
helium on top, we find that no $^{16}{\mathrm O}$ is being dredged up, while in
the $q=0.8$ simulation $<10^{-4}~{\rm M_\odot}$ of $^{16}{\mathrm O}$ has been
brought up, making a WD binary consisting of a hybrid CO/He WD and a companion
He WD an excellent candidate for the progenitor of RCB stars.
