  We use a simple generic model to study the desorption of atoms from a solid
surface in contact with a liquid, by using a combination of Monte Carlo and
molecular dynamics simulations. The behavior of the system depends on two
parameters: the strength $\epsilon_{LS}$ of the solid-liquid interaction energy
and the strength $\epsilon_{LL}$ of the liquid-liquid interaction energy. The
contact with the solid surface modifies the structure of the adjacent liquid.
Depending on the magnitude of the parameters $\epsilon_{LS}$ and
$\epsilon_{LL}$ the density of the liquid oscillates with the distance from the
surface for as far as five atomic layers. For other values of the parameters
the density of the liquid near the surface is much lower than that of the bulk
liquid, a process sometimes called dewetting. To describe the desorption rate
we have determined the number $N(t)$ of atoms that were adsorbed initially and
are still adsorbed at time $t$. The average of this quantity decays
exponentially and this allows us to define a desorption rate coefficient
$k_{d}$. We found that $k_{d}$ satisfies the Arrhenius relation. The logarithm
of the pre-exponential is a linear function of the activation energy (the
so-called compensation effect). We have also examined two approximate
mean-field like theories of the rate constant: one calculates the activation
free energy for desorption; the other uses transition state theory applied to
the potential of mean force. Both methods fail to reproduce the exact
desorption rate constant $k_{d}$. We show that this failure is due to the
presence of substantial recrossing of the barrier (which introduces errors in
transition state theory) and the presence of large fluctuations in the
desorption rate of individual molecules whose effect is not captured by
mean-field theories.
