Diffusion molar flux

In the DGM, the solid phase is modeled as giant dust molecules held motionless in space with which the diffusing gas molecules collide. The constitutive equations governing the diffusion molar flux intensities Nf for both MTPM and DGM are the generalized Maxwell-Stefan equations... 

Here is the (diffusive) mass flux of species A (mass transfer by diffusion per unit time and per unit area normal to the direction of mass transfer, in kg/s m ) and is the (diffusive) molar flux (in kmol/s m ). The mass flux of a species at a location is propoitional to the density of the mixture at that location. Note that p = Px + Pb density and C = Q + is the molar concentration of the binary mixture, and in general, they may vary throughout the mixture. Therefore, pd(pjp) dp or Cd(C /C) + dC - But in the special case of constant mixture density p or constant molar concentration C, the relations above simplify to... 

It is sometimes convenient to cast the governing set of equations into a q — 1 dimensional matrix form. Starting out from the diffusive molar fluxes, as given by the last term on the RHS of (2.298), yield ... 

The first Tick law corresponds to the following equation for the diffusion molar flux density = - A A Ttie second Pick law is then based on the volume mass balance ... 

Relative contributions of the migration and diffusion molar flux densities at steady state... 

The fact that electroneutrality applies throughout the electrolyte Imposes a strong constraint, which In turn creates a link between the diffusion molar flux densities of the two Ions (algebraic normal components) at all points in the electrolyte ... 

Eq. 4.20 can be inverted to develop a direct formulation of the diffusive molar flux vector as [73]... 

Let s use Fontana s classical model of concentration polarization [1] shown in Figure 4.6. This model suggests that the ionic concentration in the bulk of solution is higher than that on the electrode surface. Therefore, Cb > Co meaning that the diffusion direction of hydrogen cations is towards the electrode surface where anodic and cathodic reactions take place. Hence, the diffusion molar flux is determined by Pick s first law equation under steady-state conditions. It can be assumed that no other mass transfer phenomenon is present... 

Assume that the mass transfer is due to diffusion and that the diffusion molar flux (Jx) is the chemical rate of the mass transfer under steady-stale condition. Subsequently, the diffusion process can be described by Pick s first law. Thus, eq. (4.18) becomes... 

Now, the diffusion molar flux (Tick s first law of diffusion) is... 

Consider the electrolyte hydrodynamic flow condition shown in Figure 7.17. This is amass transfer found in electrowinning and electrorefining cells, in which the electrolyte motion is upwards on the anode surface due to the generation of oxygen bubbles, which enhances the mass transfer. The reader can observe in this model that the electrolyte motion is more intense at the top than at the bottom of the electrode as indicated by the arrows. If the current flows, then the electrolyte motion increases and descends to the bottom of the cathode. This is the case in which a significant convective molar flux is superimposed on the Pick s diffusion molar flux. The concentration gradient in the fluid adjacent to the vertical electrode (plate) surface causes a variation in the fluid density and the boundary layer (tf ) develops upwards from laminar to turbulent conditions [2,7]. 

This model has been successfully used by Chin and Sabde [25] for crevice cathodic protection using numerical analysis based on the dilute solution theory and reduction reaction of dissolved oxygen and Aa+, Cl, and OH ions at the crevice surface. Hence, the Nemst-Plank equation, eq. (4.2), can be generalized as a differentiable and continues scalar diffusion molar flux function... 

Note that the diffusive molar flux given by Ficks s law can also be expressed in terms of fhe diffusion velocity of the species relative to the mixture molar average velocity. 

Tables 3.1.3A, 3.1.3B value of /, in region k diffusive molar flux vector of species 1 (4.2.63) temperature gradient driven molar flux vector of species 1 (4.2.62) z-components of flux vectors /, and /s, y-component of flux vector /J z-components of flux vectors /, /J, / and... 

Starting out from the diffusive molar fluxes, as given by the last term on the RHS... 

Instantaneous diffusive molar flux of species s in mixture (kmol/m s)... 

Therefore, as soon as a current exists, the membrane will be charged and the proton concentration remains constant. The charge of protons equals to the fixed charges. The diffusive molar flux for the protons can be written as... 

---