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 $k_{Ax}=$ mass transfer coefficient of component $A(molc{m}^{-2}{s}^{-1})$

$v=$ average velocity of the reacting fluid

$c=$ molar concentration active species, $molc{m}^{-3}$

$D_{AB}=$ Diffusion coefficient, $c{m}^2{s}^{-1}$

$D=$ diameter of catalyst pore, $cm$

$=$ viscosity of reacting, $gc{m}^{-1}{s}^{-1}$

$=$ density of reacting fluid, $gc{m}^{-3}$

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