Quantitative Descriptions of Mass and Heat Transport

Mass Transfer Let N a be the flux (mol A/time area) of A from the bulk fluid through the boundary layer to the surface of the catalyst particle. Let kc be the mass-transfer coefficient, based on concentration, between the bulk fluid and the external surface of the catalyst particle. The dimensions of kc are length/time, and kc will depend on the velocity of the fluid relative to the catalyst particle. The flux of A arriving at the external surface of the catalyst particle is given by 

The rate at which A reaches the external surface of the whole catalyst particle is 

In this expression, Ag is the external (geometric) surface area of the catalyst particle. If the catalyst particle were a sphae with radius/ ,Ag = 4jr/f. If Aisareactant,CA3 Ca,sand the flux of A is directed from the bulk fluid toward the particle, i.e., opposite to the radial direction. 

At steady state, there is no accumulation or depletion of A inside the catalyst particle. Therefore, the rate at which A reaches the surface of the particle through the boundary layer must be equal to the rate at which A is consumed by reaction in the whole catalyst particle. Let / A,p be the rate at which A reacts in the whole catalyst particle. Then, 

This equation shows that the concentration difference between the bulk fluid and the surface of the catalyst particle is directly proportional to the rate at which A is consumed in the catalyst particle. The faster the reaction, the larger the concentration difference. 

---