Jerzy Bałdyga

Interaction between chemical reactions and mixing on various scales

Abstract The way in which reagents are mixed can have a large influence on the product distribution of a chemical reaction. This has been analysed earlier when micromixing is the limiting mixing step. Additional segregation at a larger scale has only been treated in detail when the local turbulent dispersion of a feed stream was relevant. Here additional segregation due to the finite disintegration rate of large concentration eddies is represented by a feasible structure to describe the environment within which micromixing and chemical reaction take place. The resulting model contains one time constant each for micro- and mesomixing. Their estimation is discussed and applied to predicting the yields of fast complex reactions in plug-flow static mixers and in a semibatch stirred tank reactor under conditions where neither macromixing nor turbulent dispersion were limiting. The comparison with measured yields is good for micromixing and fairly satisfactory for inertial-convective mesomixing. Further research on this step is needed.

Simplification of Micromixing Calculations. I. Derivation and Application of New Model

Abstract The micromixing model reported by us in 1984 consists of a set of partial differential equations to express unsteady diffusion and reaction in deforming laminated structures formed by engulfment in a turbulent fluid. This engulfment—deformation—diffusion (EDD) model has been widely applied to interpret experiments showing an effect of mixing on the product distribution of the reactions between 1-naphthol and diazotized sulphanilic acid. Theoretical arguments and recent experimental results show how the EDD model can be simplified by neglecting deformation and diffusion provided that Sc ⪡ 4000 and F ⪡ 1. The new E model retains fluid engulfment as the rate-determining step in micromixing and contains no arbitrary parameters. Application to two complex reactions has shown that engulfment is also product determining, i.e. the product distribution does not depend on deformation and diffusion. The new E model consists of a set of ordinary differential equations; it is one to two orders of magnitude faster to compute and a wider choice of software is available for its numerical implementation. Micromixing calculations have been simplified and accelerated.

Particle formation by mixing with supercritical antisolvent at high Reynolds numbers

Abstract A precipitation process is considered in which completely miscible solution and supercritical antisolvent are passed through premixing and diluting zones of a turbulent flow. The influence of flow velocity on particle size and nuclei concentration is discussed in terms of mixing and precipitation time constants and their supersaturation dependencies. The proposed model allowed the major process parameters such as supersaturation profile, mixed fluid fraction and mean particle size to be calculated and compared with experimental data. For the crystallization system paracetamol/ethanol/CO 2 studied, the supersaturation profile becomes established at Re ≅10 4 . The particle size and shape are defined, firstly, by increase of supersaturation and relative volume of mixed (on molecular scale) fluid with increase of flow velocity and, secondly, by decrease of residence time available for nucleation with increase of flow velocity. These competitive processes can result in minimum particle size at a defined flow rate.

Turbulent micromixing in chemical reactors - a review *

Abstract The idea of micromixing, its definition and measures are outlined. The concepts of mixing environments and mixing earliness are presented. The paper concentrates on the effects of turbulent mixing of incompressible fluids in single-phase systems on the course of chemical reactions. The processes of turbulent micromixing are discussed in detail: the fluid mechanical interpretation of turbulent micromixing (effect of fluid element deformation on the acceleration of molecular diffusion, engulfing of environment, inertial—convective disintegration of large eddies and local intermittency) is presented. It is concluded that stretching of material elements and vortices, accompanied by molecular diffusion results in the growth of the mixing zones. The groth of the zone mixed on the molecular scale is a characteristic feature of micromixing and should be included in micromixing modelling. The characteristic time constants for the consecutive stages of mixing are presented and compared with the characteristic time for chemical reaction — the numerical criteria are outlined. The two approaches, i.e. eulerian and lagrangian, are described; it is shown that each requires different methods of description and generates specific problems (closure problem, problem of environment). The applications of the micromixing theory to the most important fields of industrial practice, such as complex reactions, precipitations and polymerizations, are outlined.

Turbulent mixer model with application to homogeneous, instantaneous chemical reactions

Abstract A method to evaluate the decay of concentration variance in turbulent mixers is presented. The turbulent mixer model links together macromixing (large-scale convective motions and turbulent dispersion) with successive stages of micromixing process (inertial-convective disintegration of large eddies, formation of laminated structures within energy dissipating vortices and molecular diffusion within deforming laminated structures). A beta probability density function is used for an inert scalar type composition variable formed with reagents concentrations difference in order to estimate conversion of instantaneous reactions in the system. The results calculated from the model for the multijet mixers and reactors are compared with experimental results available in the literature.

Interactions between mixing on various scales in stirred tank reactors

Abstract Fast, competitive-consecutive reactions exhibit product distributions which are influenced by micro- and macroscale concentration gradients in a reactor. If a reaction is run many times under identical conditions in a semi-batch reactor, except that different feed rates are used, the product distribution is constant at low feed rates, but indicates increasing non-uniformity of composition at higher feed rates. Competition between micromixing and reaction determines product distribution at low feed rates. The additional inhomogeneity appearing at higher feed rates signals a mixing constraint at scales larger than microscopic. The relevant scale is not the macroscopic one of the whole vessel, but rather a mesoscale reflecting the interaction of the plume of fresh feed with its surroundings. Dispersion of this plume has been calculated for homogeneous turbulence, as well as when the mean plume velocity and the turbulence properties in its vicinity were spatially varying. Micromixing and chemical reaction could then be calculated in the concentration field resulting from turbulent dispersion. The relative importance of meso- and micromixing could be expressed by the ratio of their time constants. The description of simultaneous meso- and micromixing developed here successfully predicted product distributions from fast diazo-coupling reactions which had been measured at two scales, two feed points, three concentration levels and various stirrer speeds. The model requires knowledge of the reaction kinetics and the flow field, but does not, however, contain any arbitrary parameters.

The use of a new model of micromixing for determination of crystal size in precipitation

Abstract The course of the precipitation process and the size distribution of the solid particles obtained depend significantly on the intensity of mixing in the crystallizer. The authors have used a new model of micromixing, based on the spectral interpretation of mixing in the isotropic, homogeneous turbulent field to evaluate the influence of the intensity of mixing on the rate of precipitation and on the particle size of the product obtained in a stirred vessel with ideal macromixing The results obtained from the model are in good agreement with the experimental results obtained for the precipitation of BaSO 4 .

Effects of agitation and scale-up on drop size in turbulent dispersions: allowance for intermittency

Abstract Experimental and theoretical work has recently shown that classical drop size correlations have significant limitations. In particular, that work indicated a slow drift towards smaller drops when agitation is maintained, as well as smaller drops and faster break-up when scaling up at constant power per unit volume. Moreover, the exponent on Weber number fell below −0.6. It was considered that the phenomenon of turbulent intermittency was the mechanism causing the limitations. Here, these ideas are explored farther using equations for stable drop size and drop break-up in intermittent turbulence, the latter being modelled by a multifractal spectrum. These equations are then successfully applied to new drop size measurements for two geometrically similar stirred tanks having different scales, giving further support for the need to consider the phenomenon of intermittency when modelling mixing processes in stirred tanks in the turbulent regime.

The effect of micromixing on parallel reactions

The literature gives little guidance on the factors (e.g. choice of reactor, sequence of adding reagents, imperfect mixing) determining the product distribution of parallel reactions. By considering two irreversible, second-order reactions between three substances, it is shown here how the sequence of adding reagents to a semi-batch reactor will influence the yield when the mixing is perfect as well as when segregation is complete. A mixing model is then applied to predict yields when segregation is partial. Such calculations were made for three mixing sequences when chemically equivalent quantities of the three reagents were employed and when one of the two reactions was instantaneous. The yield then depended upon the mixing sequence, the volume ratio of reagent solutions and the Damkiihler number (this is a ratio of characteristic times for micromixing and chemical reaction). Sodium hydroxide, ferric sulphate and ethyl chloroacetate solutions were contacted in the sequences corresponding to cases 1 and 3 of the modelling. The alkali reacted competitively and the extents of the two parallel reactions were measured after it had been fully consumed. The independent variables were stirrer speed, volume ratio of the two reagent solutions and the concentration level at constant stoichiometric ratio. The effects of these operating variables on the product distribution were well predicted. The stoichiometry of the precipitation of ferric ions in alkaline solution is probably more complex than considered in the modelling and the parallel reactions used here need improvement or possibly replacement. A similar comparison was made between measured and predicted yields of nitrobenzene during the competitive nitration of benzene and toluene. Twelve out of 13 yields measured by Tolgyesi (1965) were satisfactorily predicted.

THE EFFECTS OF MICROMIXING AND THE MANNER OF REACTOR FEEDING ON PRECIPITATION IN STIRRED TANK REACTORS

The effect of micromixing on the course of a precipitation process involving instantaneous irreversible chemical reaction (of the type: A + B → C) between two ionic solutions snd subsequent crystallization of the product is considered. It is demonstrated that the micromixing intensity and the manner of reactor feeding (batch or continuous, premixed or unpremixed feed system) are major factors affecting the precipitation process and the resulting size distribution of precipitated particles. The method of prediction of these effects is based on a micromixing model, which is related to the theory of turbulent mixing in an isotropic, homogeneous turbulent field.