A non-local phase field model is used to define surface tension in liquid mixtures at non equilibrium, or dynamic, conditions, in terms of the composition gradient in the interfacial region. Therefore, during mixing, the non-equilibrium surface tension decreases as the inverse square root of time, while during processes involving topological changes its variations are more complex. For example, during phase separation, when nuclei coagulate, the dynamic surface tension increases exponentially to its equilibrium value, while during the detachment of a wall-bound pendant drop, it grows in the neck region, until reaching a value well above its equilibrium limit, thus enhancing the adhesion of the drop. In fact, we see that the critical Bond number, defining the minimum size of a detaching drop, is about twice larger than its sharp-interface value, based on the numerical integration of the Young-Laplace equation, where surface tension is assumed to be an equilibrium, constant quantity. We argue that this discrepancy is due to the inability of the sharp interface analysis to describe processes taking place over distances comparable with the interface thickness. Thus, in the necking regime of drop detachment, the sharpening of concentration gradients produces an effective increase in the dynamic surface tension, ultimately leading to a reduced tendency to detachment or an increase of the critical Bond number. Finally, we show that that the critical Bond number decreases as the static contact angle increases, until it vanishes for completely unwettable solid surfaces.