A mathematical model was formulated to describe yeast cell growth within the Ca-alginate microbead during air-lift bioreactor cultivation. Model development was based on experimentally obtained data for the intra-bead cell concentration profile, after reached the equilibrium state, as well as, total yeast cell concentration per microbed and microbead volume as function of time. Relatively uniform cell concentration in the carrier matrix indicated that no internal nutrient diffusion limitations, but microenvironmental restriction, affected dominantly the dynamics of cell growth. Also interesting phenomenon of very different rates of cell number growth during cultivation is observed. After some critical time, the growth rate of cell colonies decreased drastically, but than suddenly increased again under all other experimental condition been the same. It is interpreted as disintegration of gel network and opening new free space for growth of cell clusters. These complex phenomena are modeled using the thermodynamical, free energy formalism. The particular form of free energy functional is proposed to describe various kinds of interactions, which affected the dynamics of cell growth and cause pseudo-phase transition of hydrogel. The good agreement of experimentally obtained data and model predictions are obtained. In that way the model provides both, the quantitative tools for further technological optimization of the process and deeper insight into dynamics of cell growth mechanism.