Concentration non-uniformities and averages in flow-through spectrophotometric measurements

The use of a spectrophotometer in a flow-through configuration to measure an `averagedʹ solute concentration, under conditions where local non-uniformities in concentration are present, is investigated in a tubular flow system. Various definitions of an `averagedʹ concentration are possible, and which of these, if any, most closely approximates the one that is actually measured is studied. Numerical solutions of the convection–diffusion equation without reaction are compared to experimental results using different analytes under a range of steady laminar-flow conditions. The cross-sectionally averaged concentration from numerical simulations is found to underestimate measurements consistently, whereas a flux-weighted averaged concentration yields surprisingly good agreement with measured values.