Mass transfer in dilute turbulent and non‐turbulent systems with rapid irreversible reactions and equal diffusivities

Abstract Studies of mass transfer with rapid, homogeneous, irreversible reactions between dilute species with equal difusivities are carried out with a device which reduces the system of mass transfer‐reaction equations to the equations for mass transfer in the absence of reaction. A relationship which gives the rate of transfer into stagnant, laminar, or turbulent reacting systems is developed. Under some conditions the reaction increases the transfer rates by a constant factor, while under other conditions the reaction increases the individual or over‐all mass transfer coefficients by a constant factor. Calculations of concentration profiles, conversion, etc. are carried out for the Graetz problem with a homogeneous reaction between a dilute species in the fluid and a dilute species diffusing from the tube wall. Reaction completion times for various stagnant elements in infinite media are given. Although the flux into a turbulent reacting fluid is related to the time average behavior in the absence of reaction, the time average concentrations depend also upon the relative intensity of the concentration fluctuations in the absence of reaction. This latter dependence is obtained from a relationship of Hawthorne, et al. Surfaces on which the time average composition is stoichiometric and the reactant concentrations are proportional to the relative intensity of the concentration fluctuations in the absence of reaction are obtained for turbulent flow in a tube with a homogeneous reaction between the fluid and wall. Distances for almost complete reaction are estimated. The time average conversion is related to the accomplished mixing for the case in which two dilute reactants are turbulently mixed. In a uniform, stoichiometric mixture the fractional conversion equals the accomplished mixing. Calculations are carried out for uniform, nonstoichiometric mixtures.