Table 1-3 Fick's Law for Binary Mixtures of A and B Reference velocity Mass units Molar units PD AB JA = -PDABVWA (A) JA = WA (B) MA V (M) j(M) = -CMADAB VXA (C) A J(M) - -CDAB VXA (D54 - -CDABVXA 1-2. Diffusion Relative to Volume-Average Velocity A reference frame sometimes chosen for the analysis of diffusion is the volume-average veloc- ity, v. For a binary mixture it is given by v () = NAVA + NBVB where VA and VB are the partial molar volumes of species A and B, respectively. The total molar con- centration is related to the partial molar volumes and mole fractions by C = (XAVA + XBVB) . The molar flux of A relative to the volume-average velocity, JO, is defined as J = NA - CAV(). The objective is to derive the form of Fick's law that applies when using v. (a) Show that JOVA + JO VB = 0 J = CV BJ(M) (b) Use the results in part (a) to show that JO - -DAB VCA which indicates that the "natural" driving force in this reference frame is the gradient in molar con- centration; compare with Eqs. (A) and (D) of Table 1-3