Mass Conservation in the Solid Phase

We here introduce a process of diffusion and reaction in the solid phase similar to that in the fluid phase. By drawing an analogy to the analysis of the fluid phase, we have the following equation of mass conservation for the ath component  

The material time derivative of a function (p with respect to the mean velocity v (x,t) is given by 

The velocity gradient L, the stretch tensor D and the spin tensor are defined by 

Adopting a procedure similar to that used in (5.29), the diffusion equation of the ath component in the solid phase can be derived as follows 

The diffusion in the solid phase is referred to as the matric diffusion. Matric diffusion for a fractured rock is presented by Rasilainen (1997) however, there are always small scale fractures even in the intact part. Pure matric diffusion is rarely observed under normal temperature/stress/chemical states and therefore the diffusion velocity in the solid phase can be ignored ( v 1). 

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