LAUSR

Abstract One of the challenges in mathematical modelling of microchips is the lack of available data for dispersion coefficients of biomolecules. The main focus of this study was to determine the hydrodnamic dispersion coefficients of the model substrates, 4-Nitrophenyl-β- d -glucopyranoside (pNPG_1) and 4-Nitrophenyl-β- d -glucuronide (pNPG_2) for β-glucosidase and β-glucoronidase. The substrate solutions were pumped through the silica porous gel inside the S-shaped PDMS microreactor at flow rates of 1, 3 and 5 µl/min. The output flow was collected with respect to time and quantified by UPLC. The general mathematical model was derived for the coupled dynamics of convective–diffusive mass transfer and a computational algorithm was developed for the numerical solutions of the derived partial differential equations in MATLAB. The hydrodynamic dispersion coefficients of pNPG_1 were determined as 0.370 × 10 −6 , 3.638 × 10 −6 and 11.680 × 10 −6  m 2 /s, while as 0.368 × 10 −6 , 1.515 × 10 −6 and 3.503 × 10 −6 m 2 /s for pNPG_2 at respective flow rates. Furthermore, the relations between dispersion coefficients and flow rates were investigated. Obtained hydrodynamic dispersion coefficients can be used for modelling of pNPG reactions which may also be adapted to other enzyme related reactions within life sciences.