  Progress in ultracold experiments with polar molecules requires a clear
understanding of their interactions and reactivity at ultra-low collisional
energies. Two important theoretical steps in this process are the
characterization of interaction potentials between molecules and the modeling
of reactive scattering mechanism. Here, we report on the {\it abinitio}
calculation of isotropic and anisotropic van der Waals interaction potentials
for polar KRb and RbCs colliding with each other or with ultracold atoms. Based
on these potentials and two short-range scattering parameters we then develop a
single-channel scattering model with flexible boundary conditions. Our
calculations show that at low temperatures (and in absence of an external
electric field) the reaction rates between molecules or molecules with atoms
have a resonant character as a function of the short-range parameters. We also
find that both the isotropic and anisotropic van der Waals coefficients have
significant contributions from dipole coupling to excited electronic states.
Their values can differ dramatically from those solely obtained from the
permanent dipole moment. A comparison with recently obtained reaction rates of
fermionic $^{40}$K$^{87}$Rb shows that the experimental data can not be
explained by a model where the short-range scattering parameters are
independent of the relative orbital angular momentum or partial wave.
