We simulate model B of mesoscopic dynamic with the Flory-Huggins free energy for the homopolymer blend. We concentrate the study on the rescaling of the spatial coordinates in the model. We show that the commonly used rescaling of the spatial coordinates, by the function vanishing at the spinodal, leads to the unphysical freezing of the domains. We study the evolution of the system in two different processes: One is the growth process induced by the temperature quench to the metastable or unstable region of the phase diagram and the second is the quench-jump process in which we first allow the system to separate below the spinodal and next heat it up below or above the spinodal. The proper rescaling avoiding the unphysical pinning of the domain growth at the spinodal is proposed. (C) 2004 American Institute of Physics.