Constructing Integral and Microscopic Descriptions of the Mass Transfer Equation

9-4 CONSTRUCTING INTEGRAL AND MICROSCOPIC DESCRIPTIONS OF THE MASS TRANSFER EQUATION 

The open-system mass balance for component i with nnits of mass per time is stated qnalitatively as 1 = 2 H- 3 where 1 is the accnmnlation rate process or the unsteady-state contribution, 2 is the net rate of inpnt dne to mass flux acting across the snrface that surrounds the control volume, and 3 is the rate of production of component i due to multiple chemical reactions. In mathematical terms  

This is the integral form of the mass transfer equation within an arbitrary control volume V (f). Notice that there is a term of the form / pi(n Vsurface) dS in the accumulation rate process and in the net rate of input due to mass flux acting across the time-varying surface S(t). These terms are present because the surface that bounds the control volume is in motion. The fact that they cancel provides quantitative support for the claim that the final form of the mass transfer equation is independent of the characteristics of the control volume. All surviving terms in the mass balance. 

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