This paper deals with experimental investigation, mathematical modelling and numerical simulation of the crystallization processes induced by counter diffusion method of a precipitant agent in a lysozyme protein solution. Novel mathematical strategies are introduced to simulate the experiments and in particular to take into account the kinetics of the growth process and the motion of the crystals due to the combined effect of gravitational force and viscous drag if the sedimenting process is allowed (protein chamber free of gel). Comparison between experimental observations and numerical simulations in the presence of convection and sedimentation and without them provides a validation of the model. The crystal formation in gel results modulated in space. If the gel matrix is not present, convective cells arise in the protein chamber due to local inversions in the density distribution associated to nucleation phenomena. As time passes, these vortex cells migrate towards the top of the protein chamber exhibiting a different wave number according to the distance from the gel interface. The sedimentating particles produce a wake due to depletion of protein from the surrounding liquid. The models and the experiments may represent a useful methodology for the determination of the parameters and conditions that may lead to protein crystallization.