A general adsorption model is developed to describe the interactions between near-wall fluid molecules and solid surface. This model serves as a framework for the theoretical modelling of the boundary slip phenomena. Based on this adsorption model, a new general model for the slip velocity of fluids on solid surfaces is introduced. The slip boundary condition at a fluid-solid interface has hitherto been considered separately for gases and liquids. In this paper, we show that the slip velocity in both gases and liquids may originate from dynamical adsorption processes at the interface. A unified analytical model that is valid for both gas-solid and liquid-solid slip boundary conditions is proposed based on surface science theory. The corroboration with experimental data extracted from the literature shows that the proposed model provides an improved prediction compared to existing analytical models for gases at higher shear rates and close agreement for liquid-solid interfaces in general.