= Arno de Klerk
{c}
\b[<Arno de Klerk>] researches chemical conversion processes, including <catalysis> and hydrocarbon oxidation. His University of Alberta profile records qualifications in <chemical engineering> and <analytical chemistry> and describes work connecting conversion chemistry with reactor behavior.<Arno de Klerk at the University of Alberta>[Official profile, About and Research]{ref} Measuring what reactants actually reach a liquid-phase reaction is one link between those subjects.
\Image[https://apps.ualberta.ca/profile/photo/deklerk]
{title=Arno de Klerk, portrait identified by the University of Alberta directory}
{source=https://apps.ualberta.ca/directory/person/deklerk}
With <Muhammad N. Siddiquee>, de Klerk coauthored a 2016 study of in situ liquid-phase <oxygen> measurement during oxidation. The primary abstract explains why oxygen availability affects <reaction rate> and product selectivity.<In Situ Measurement of Liquid Phase Oxygen during Oxidation by Muhammad N. Siddiquee and Arno de Klerk>[Industrial & Engineering Chemistry Research 55, pp. 6607–6618, byline and Abstract]{ref} The contribution concerns quantifying the reaction environment rather than equating gas supplied to a vessel with dissolved reactant available everywhere inside it.
An original well-mixed balance illustrates the issue. Let liquid oxygen concentration be $c$, its equilibrium value at the gas boundary be $c^*$, the volumetric transfer coefficient be $k_La$, and a stipulated first-order consumption coefficient be $k$. Then
$$
\frac{dc}{dt}=k_La(c^*-c)-kc,
\qquad
c_{\mathrm{ss}}=\frac{k_La}{k_La+k}c^*.
$$
For $k_La=2\,\mathrm{h^{-1}}$ and $k=8\,\mathrm{h^{-1}}$, the steady dissolved concentration is only $0.2c^*$. Doubling the transfer coefficient gives $c_{\mathrm{ss}}=c^*/3$ even though the intrinsic consumption coefficient is unchanged. A changed measured oxidation rate need not imply changed intrinsic <chemical kinetics>.
This is a deliberately simplified <interphase mass transfer> model, not reconstructed experimental data. Spatial gradients, changing products and chain reactions can require a richer description. Direct measurements of liquid composition make it possible to test which interpretation of a reactor's behavior is consistent with the observations.
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