Multicomponent diffusivity matrix activity-based

Writing the diffusive flux of a component i in terms of activity gradients of all independent components in an N-component system, the flux equation is 

Similar to binary systems, the intrinsic diffusivity matrix is expected to be much less dependent on the composition of the system, which is the main advantage of using the activity-based diffusivity matrix. To solve the above equation, it is necessary to know the relations between the activity of every component and all concentrations. 

The set of diffusion equations based on the activity-based diffusivity matrix is expected to be complicated and solvable only numerically. Because of its complexity, no attempt has been made using this formulation to obtain the intrinsic diffusivity matrix. 

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