Abstract
A new technique of visualization of diffusion-convection phenomena at a solid-liquid interface using the luminol chemiluminescent reaction catalyzed by immobilized peroxidase has been previously described (Dimicoli, J.L., M. Nakache, and P. Peronneau, 1982, Biorheology, 19:281-300). We propose now a theoretical model that predicts quantitatively the light fluxes, JL, corresponding to the transfer J of the hydrogen peroxide substrate at the liquid-solid interface in a cylindrical tube for continuous flow experiments. A simple phenomenological relation, J alpha J1/mL (1 less than m less than 3) was first established for each point of the wall. Then, numerical integration showed that, independent of the laminar or turbulent character of the flow, J1/mL was proportional to (S1 Kideal)/(1 + Kideal/ET), where S1 is the bulk substrate concentration, Kideal is the ideal transport coefficient, and ET (in cm.S-1) a phenomenological first-order enzymatic rate constant per unit of wall surface. This relation proved to be satisfactory for all experimental conditions since a single mean value of ET takes into account the experimental data collected for a given enzymated tube in a large range of Reynolds number values (Re) (500 less than Re less than 9,000) and of distances from the entrance of the tube (chi greater than 0.3 cm). This quantitative analysis using a pseudo-first-order approximation interprets the observed great dependence of JL on Re(JL alpha Ren', with n' usually greater than 1/3 for laminar flows) and on S1 (JL alpha S1m). It predicts also that the laminar-to-turbulent transition can be evidenced for interfacial enzymatic activity, ET greater than 2.10(-4) cm.S-1, as observed with most of the tubes prepared by covalent binding of peroxidase on the acrylamide gel wall. The experiment had to be carried out at a pH value of 8, which corresponds to the fastest rate of the chemiluminescent reaction. The predicted entrance effects were also observed experimentally for the first time in an immobilized enzyme system. This technique appears therefore to be a valuable tool for the quantitative analysis of diffusion-convection phenomena at a liquid-solid interface with a good spatial resolution with a great range of flow rate.