Microscopic Equation of Change for Kinetic Energy

Step 7. Manipulate the equation of change for specific entropy, via definitions of convective and molecular entropy fluxes, to identify all terms that correspond to entropy generation. These terms appear as products of fluxes and forces. 

Step 8. Postulate Unear relations between these fluxes and forces that obey the Curie restriction, and demonstrate that entropy generation can be expressed as a positive-definite quadratic form. 

Step 9. Use matrix concepts for positive-definite quadratic forms and the Onsager reciprocal relations to develop expressions for the diffusional mass flux of component i and the molecular flux of thermal energy in binary mixtures. 

Step 10. Use the expression for diffusional mass flux in binary mixtures to derive the Stokes-Einstein diffusion equation for liquid-phase diffusivities. 

Step 11. Use the equation of change for internal energy and the molecular flux of thermal energy to develop the appropriate thermal energy balance for multicomponent reactive mixtures. 

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