Liquid argon is used as active medium in a variety of neutrino and Dark Matter experiments thanks to its excellent properties of charge yield and transport and as a scintillator. Liquid argon scintillation photons are emitted in a narrow band of 10~nm centered around 127 nm and with a characteristic time profile made by two components originated by the decay of the lowest lying singlet and triplet state of the excimer Ar$_2^*$ to the dissociative ground state. A model is proposed which takes into account the quenching of the long lived triplet states through the self-interaction with other triplet states or through the interaction with molecular Ar$_2^+$ ions. The model predicts the time profile of the scintillation signals and its dependence on the intensity of an external electric field and on the density of deposited energy, if the relative abundance of the unquenched fast and slow components is know. The model successfully explains the experimentally observed dependence of the characteristic time of the slow component on the intensity of the applied electric field and the increase of photon yield of liquid argon when doped with small quantities of xenon (at the ppm level). The model also predicts the dependence of the pulse shape parameter, F$_{prompt}$, for electron and nuclear recoils on the recoil energy and the behavior of the relative light yield of nuclear recoils in liquid argon, $mathcal{L}_{eff}$
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