A non-equilibrium phenomenological theory of mass and heat transfer, presented in previous works, is applied here in combination with the classical equilibrium phenomenological theory to model absorption of the ammonia bubble. The modeling tool is a non-empirical linear Phenomenological Hydro-Gaso-Dynamical (PhHGD) approach, outlined in the second section of this paper. First results refer to the elucidation of the problem of the ammonia bubble absorption, where from the following we are to be learned: (i) absorption process in the ammonia/water medium is a mass phenomenon and not a surface one; (ii) an intensive way of improving absorption is emphasized, which seeks to promote the i.p.a. effect appearance; this would replace the extensive way currently used, based on increasing gas-liquid interaction area; to this extent, the bubble absorber is hereby proposed for efficient absorption; (iii) the i.p.a. effect existence offers an additional chance for a satisfactory explanation of the Marangoni effect. The PhHGD code is extended to a refined analytical study of absorption, which may constitute a first data base for the bubble absorber. The paper also presents experimental results of ammonia bubble absorption in water, which are in good agreement with the predictions of the PhHGD approach.