Kinetic Study of Leuco‐Indigo Carmine Oxidation and Investigation of Taylor and Dean Flow Superposition in a Coiled Flow Inverter

Abstract

In two‐phase capillary flow, Taylor and Dean vortices can enhance mass transfer according to recent studies. By utilizing a colorimetric method based on the consecutive oxidation of leuco‐indigo carmine it is possible to visualize the superposition of Taylor and Dean vortices in a gas‐liquid system. A kinetic study is performed in order to estimate the enhancement factor. Depending on the flow conditions, three different flow regimes are identified with different intensities of Taylor and Dean vortices affecting the oxygen distribution within the liquid phase. A dimensionless number is derived that describes this transition in flow regimes.

Numerical simulation and benchmarking of drops and bubbles

“…In order to prevent a too detailed description of the optimisation procedure we discuss here only the results for the found parameter values providing the closest match with the experimental references. The value of the estimated reaction constants were k 1 = k 2 = 8 • 10 5 L mol s −1 , which are matching reasonably with the experimentally expected values of Krieger et al [31] simulated process and the experimentally measured one, since the concentration distributions are matching each other at all three time levels. In particular, the prediction of the dynamics of the intermediate species C is the most crucial since the concentration values of this species is the lowest and has the most significant spatial distribution forming a ring shape of a thickness and radial location which is possible to predict only with the right prediction of the overall reactive transport phenomena.…”

“…Another simplification introduced into the model is related to the assumption of constant material properties which however is strongly justified due to the fact that the chemical species are present at only very low concentrations and therefore have a negligible influence on the otherwise constant material properties. The material properties are listed in Table 1.9 which provides the viscosities µ, densities ρ of the present g/l phases, the interfacial tension σ and diffusion coefficients D i [31] of the chemical species in the liquid phase. The presence of the gas phase was not considered in the transport equation of species (only in the preceding multiphase flow simulation), instead a Dirichlet boundary condition according to Henry law has been used for the Oxygen species concentration and zero flux for all other species.…”

Arduino‐based slider setup for gas–liquid mass transfer investigations: Experiments and CFD simulations

“…Since dissolved oxygen cannot be measured with the current setup, this calculation is based on the assumption that the absorbed oxygen is fully converted to keto‐indigo carmine and/or intermediate: with , n IM , and n KIC as molar amount of consumed oxygen, intermediate and keto‐indigo carmine, respectively. Enhancement of mass transfer due to the reaction has been found negligible in a previous study . As a result, the amount of consumed oxygen is expected to follow a linear trend until saturation effects become relevant and oxygen accumulates in the liquid phase.…”

“…The approach will be similar to the grid‐adaptation technique near the interface, which is utilized in order to efficiently capture the hydrodynamics of gas–liquid slug flow. Another aspect is that the kinetic parameters used for the numerical simulations were determined assuming first‐order kinetics regarding both reactants . By adjusting the kinetic parameters based on the numerical results, the match between experiments and simulations can be further improved (see Supporting Information).…”

“…After obtaining the steady flow‐field, we solved the coupled reaction‐transport equation with an operator splitting approach; this allowed us to adopt different time‐step sizes for the reaction and transport phenomena. The consecutive redox reactions (described in Krieger et al) are solved with a highly accurate numerical scheme which is based on the methods introduced by Shampine and Gordon . The transport Equation for the species is discretized by Q 1 FE.…”