how to non$-$dimensionalize and solve this question?

$R_{V,A}=\frac{-k_{\text{c}\text{a}\text{t}}{C}_{E0}{C}_A}{K_m+C_A}$

Where $k_{\text{c}\text{a}\text{t}}=0\mathrm{.}02s^{-1}$ and $K_m=48M.$ ref In order to carry out the reaction, we will utilize

spherical beads loaded with VAO covalently attached to and uniformly distribution within a

hydrogel scaffold. The solubility of Vanillylamine is $16\mathrm{.}1\frac{g}{L}$ and its molar mass is $153\mathrm{.}18$ g$/$mol$.$ The VAO concentration in the hydrogel is $1$mol$/$L

For the purposes of this problem:

The reaction only takes place within the beads.

The diffusivity of vanillin$/$vanillylamine in water is $D_A=1{10}^{-13}{m}^{{?}^{{?}^{?}}}\frac{2}{s}$

Assume that the vanillylamine concentration with the reactor is uniform everywhere

$($well$-$mixed$)$

i$.$ Simplify and non$-$dimensionalize the governing differential equation and boundary

conditions. What dimensionless group$($s$)$ appear?

ii$.$ Obtain a solution for the ODE. Comment on how the radius of the beads impacts the

utilization of the catalyst by plotting the solution for several bead radii values. Hint: In this

case the beads can range from $0\mathrm{.}05-1mm$ in diameter.