Gas chromatography $($GC$)$ is one of the important techniques used to determine chemical compounds and their concentrations. GC is frequently used in the food industry for flavorings, steroids, enzymes, various metabolites, and in pharmacological studies for active ingredient determinations. For example, a GC uses a very long silica capillary tube $($column$)$ to which polysiloxane polymer or other absorbent materials have been added. After the sample is introduced, each unknown compound is absorbed or desorbed by the absorbent material; these compounds are also carried by a carrier inert gas $($usually hydrogen, helium, or nitrogen$).$ At the other end of the column, there is a detector $($e$.$g$.,$ a flame ionization detector$)$ that gives electrical signals based on the concentration of the chemical compound. The identification of the chemical is based on the retention time $($or the time between injection and detection$).$ The length and type of the tube, absorbent coatings $($stationary phase$),$ temperature, carriers, and detectors can be optimized for different chemical substances.

In a GC used to determine the amount of ammonia in samples, a $30$m x $250$ micrometers $($diameter$)$ capillary column and dry nitrogen gas as the carrier are used. The column temperature is $50\backslash$deg C$.$ Determine which type of diffusion is more dominant in the GC: Knudsen diffusion or Fickian diffusion.

If the Knudsen number $($Kn$)<=1,$ the diffusion is normal Fickian diffusion.

If the Knudsen number $($Kn$)>=100,$ the diffusion is Knudsen diffusion.

Data:

$-$ Atomic diffusion volume: Nitrogen $=17\mathrm{.}9$ m$^3,$ Ammonia $=14\mathrm{.}9$ m$^3$

$-$ Atmospheric pressure: $101\mathrm{.}3$ kN$/$m$^2$

$-($M$\_\{$N$2\}=28$ kg$/$kmol

$-($M$\_\{$NH$3\}=17$ kg$/$kmol

$-($R $=8314$ kg$.$m$^2/$s$^2-$kgmol K

$-$ Dynamic viscosity of nitrogen: $1\mathrm{.}88$ x$10^-5,$N s$/$m$^2)$

$-$ Dynamic viscosity of ammonia: $1\mathrm{.}09$ xtimes $10^-5,$N s$/$m$^2)$