If the transport, ie the diffusion is much slower than the transfer across the interface, the process is said to be diffusion controlled. When this is the case, it can be considered that exchanges at the interface are such that the interface is in equilibrium.
The quantity I/II is essential in the models to predict the growth rate. By equating the amount of solute brought via diffusion to that incorporated in the B-rich phase the velocity of the interface can be expressed as a function of omega and D. This means that a straighforward MT-DATA calculation and the knowledge of the diffusion coefficient give me the growth rate.