A sophomore chemical engineering student has just been introduced to the concept of mass transfer coefficient. Mass transfer coefficient is an empirical parameter often used in mass transfer analysis when mass transfer occurs between a solid surface and a flowing fluid past it$.$ Based on this, he speculates that a relation of the form shown below must exist for chemical reactants flowing through a porous catalyst pores:

$k_{Ax}=f(v,c,,D_{AB},,D)$

where

Use dimensionless analysis method to obtain the form of the relationship between the fundamental variables $($if such a relationship exists$).$