  Many isolated white dwarfs (WDs) show spectral evidence of atmospheric metal
pollution. Since heavy element sedimentation timescales are short, this most
likely indicates ongoing accretion. Accreted metals encounter a variety of
mixing processes at the WD surface: convection, gravitational sedimentation,
overshoot, and thermohaline instability. We present MESA WD models that explore
each of these processes and their implications for inferred accretion rates. We
provide diffusion timescales for many individual metals, and we quantify the
regimes in which thermohaline mixing dominates over gravitational sedimentation
in setting the effective settling rate of the heavy elements. We build upon and
confirm earlier work finding that accretion rates as high as $10^{13} \, \rm g
\, s^{-1}$ are needed to explain observed pollution in DA WDs for $T_{\rm eff}
> 15,000 \, \rm K$, and we provide tabulated results from our models that
enable accretion rate inferences from observations of polluted DA WDs. If these
rates are representative of young WDs, we estimate that the total mass of
planetesimal material accreted over a WD lifetime may be as high as $10^{28} \,
\rm g$, though this estimate is susceptible to potential selection biases and
uncertainties about the nature of disk processes that supply accretion to the
WD surface. We also find that polluted DB WDs experience much less thermohaline
mixing than DA WDs, and we do not expect thermohaline instability to be active
for polluted DB WDs with $T_{\rm eff} < 18,000 \, \rm K$.
