International audienceCFD simulations are performed to study the micro-mixing in a T-mixer with square bends by using the Villermaux-Dushman reaction. The calculated segregation indices are compared with previously published data and it is shown that whilst the trend is capture the simulation overpredict the extent of miccromixing. This paper provides guidance on the computational requirements needed to obtain accurate results in such laminar flows and shows the complex species fields that develop within the reactor

Aubin, Joelle

Avila, M

Fletcher, D.

Poux, M

Xuereb, C

English

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CFD Modelling of Micromixing in a T-mixer with
Square Bends
D. Fletcher, M Avila, M Poux, C Xuereb, Joelle Aubin
To cite this version:
D. Fletcher, M Avila, M Poux, C Xuereb, Joelle Aubin. CFD Modelling of Micromixing in a T-mixer
with Square Bends. 16th European Conference on Mixing, Sep 2018, Toulouse, France. ￿hal-02373262￿
 16
th
 European Conference on Mixing – Mixing 16  9-12 September 2018, Toulouse, France 
 
CFD Modelling of Micromixing in a T-mixer with Square Bends  
D.F. Fletcher
1
, M. Avila
2
, M. Poux
2
, C. Xuereb
2
, Joelle Aubin
2
  
 
1
 School of Chemical and Biomolecular Engineering, The University of Sydney, NSW 2006, Australia; 
david.fletcher@sydney.edu.au 
2
 Laboratoire de Génie Chimique, Université de Toulouse, CNRS, INPT, UPS, Toulouse, France; 
marco.avilalopez@ensiacet.fr; martine.poux@ensiacet.fr; Catherine.Xuereb@ensiacet.fr; 
joelle.aubincano@ensiacet.fr 
 
 
Abstract: CFD simulations are performed to study the micro-mixing in a T-mixer 
with square bends by using the Villermaux-Dushman reaction. The calculated 
segregation indices are compared with previously published data and it is shown that 
whilst the trend is capture the simulation overpredict the extent of miccromixing. 
This paper provides guidance on the computational requirements needed to obtain 
accurate results in such laminar flows and shows the complex species fields that 
develop within the reactor. 
 
Keywords: micromixing, microchannel, CFD, segregation 
 
Introduction  
Micromixing, i.e. mixing at the molecular-scale, controls the outcome of many chemically-
reacting systems and crystallization applications [1]. In turbulent flow simulations there are now well-
established approaches to take this into account via modelling of the effects of small-scale turbulence 
probabilistically rather than directly simulating it [2]. However, in laminar conditions the flow must be 
fully resolved down to the smallest scales.  
Many experimental studies have been performed to characterize micromixing in various 
micro-scale devices using the Villermaux-Dushman competing reactions [3,4] but the status of 
computational modelling of micromixing in laminar flows has been less well studied and no coherent 
advice is available on the best methodology to follow. Here we use the experimental data of 
Commenge and Falk [5] to validate a CFD model of micromixing in a T-junction with square bends 
and to demonstrate the complexity of this very simple system. 
 
Computational Model 
 In the following sections, we describe the reactions and reaction kinetics, the methodology for 
quantification of micromixing via the degree of segregation and the CFD model.  
Reactions and reaction rates  
The Villermaux-Dushman reaction system comprises parallel competing reactions composed 
of a neutralisation reaction (R1) and a redox reaction (R2). It was used initially to study micromixing 
in a stirred tank [6] and was subsequently extended to the study of continuous flow in microreactors 
by Falk and Commenge [7]. Details of the experimental method are given in Guichardon and Falk [8] 
and a detailed study of the reaction kinetics is given in Guichardon et al. [9]. 
Reaction (R1) is almost instantaneous whilst Reaction (R2) is very fast with a rate of the same 
order of magnitude as the micromixing process. The reactions used are: 
 
     
                                                                                                                                                     
 
   
                                                                                                                                             
 
It is the competition between these two reactions that allows the degree of micromixing to be 
determined. In addition to the above reactions, the iodine formed in reaction (R2) can react with iodide 
ions as follows: 
 
    
    
                                                                                                                                                                
 
where reaction (R3) is very fast compared with reaction (R2) and is therefore in equilibrium. 
 16
th
 European Conference on Mixing – Mixing 16  9-12 September 2018, Toulouse, France 
 
The literature contains a variety of reaction rates with many CFD articles giving incorrect 
and/or inconsistent values. Here we have adopted the following reaction set based on its consistency 
with the literature cited above. The rates of reaction (R1) and (R2) are given by 
 
        
         
                 
                                                                                               
  
        
            
                                                                                                                                            
 
for which Guichardon et al. [9] determined: 
                                                                                                                                  
                                                                                                                        
 
where   is the ionic strength of the mixture given by   
 
 
   
 
     
   where       the charge number of 
species  ,     is the molar concentration of ion   and the sum is taken over all ions in the solution [7].  
For reaction R3, the equilibrium condition is expressed in terms of the equilibrium constant 
which is given by: 
   
   
   
 
   
  
        
                                                                                                                                                   (4) 
where Palmer et al. [10] determined the equilibrium constant as: 
         
   
 
                                                                                                                               
 
The value of    for a temperature of 20°C is 787 l mol
–1
, giving the following reaction rates:    
          
              and            
                                                                                       
 
Quantification of micromixing 
The above system is widely used to quantify micromixing via the use of the segregation index, 
  , which is 0 when the flow is perfectly mixed and 1 when it is completely segregated [11]. When 
micromixing is poor reaction (R2) is favoured, whereas when micromixing is fast almost all the H
+
 
ions are consumed by reaction (R1), so there is little or no I2 formed. From reaction (R2), two moles of 
H
+
 are required for every mole of I2 generated. Therefore, for continuous flow mixers, the selectivity 
of the iodide reaction, YI, is defined via: 
   
           
  
   
        
  
              
      
            
    
                                     (7)         
 
where    denotes the molar flow rate and    denotes the volumetric flowrate. Note it is often implicitly 
assumed that the inlet flow rates of both streams are the same, in which case equation (7) reduces to: 
    
         
      
      
                                           (8) 
 
The segregation index is given by 
                                      (9) 
 
where     is the selectivity of iodide when there is total segregation. In this case the mixing time is 
very long, and the two reactions (R1) and (R2) can be assumed to be infinitely fast and the selectivity 
is controlled only by the relative concentrations of     
     and       
     so that: 
    
     
    
     
           
    
                                                                                                                                
Geometry and Operating Conditions 
 The geometry and operating conditions are chosen to replicate the study of Falk and 
Commenge [7]. The geometry of the mixer and operating conditions are given in Figure 1. The 
concentration of    
  is measured by spectrophotometry at 353 nm following the Beer-Lambert law: 
   
   
  
  
 
            (11) 
 16
th
 European Conference on Mixing – Mixing 16  9-12 September 2018, Toulouse, France 
 
where OD is the measured optical density (or light absorption),  is the molar extinction coefficient of 
  
  ions at 353 nm and l is the optical path length, taking values of 26047 L mol
-1
 cm
-1
 and 5mm, 
respectively. 
 
 
 
Reynolds 
number 
60 - 300 
Inlet 1 [H+] = 0.03 [mol/L] 
Inlet 2 [H2BO3
⁻ ] = 0.09 [mol/L] 
 [I+] = 0.032 [mol/L] 
 [IO3
-] = 0.006 [mol/L] 
Yst 0.286 
D ~10-9 m2/s 
Fluid 
properties 
Water at 25 C 
 
Figure 1: Geometry and operating conditions used in the study. 
CFD Model 
 
Simulations were performed for both steady and transient, three-dimensional flow using the 
following equations for conservation of mass, momentum and species: 
 
                                                                                                                                                                         
 
     
  
                                                                                                          (12) 
 
      
  
                        
   
   
                                                                                                       
 
These equations were solved using ANSYS Fluent 19. Initial simulations were performed in 
unsteady mode but the flow was found to be steady and so this approach was abandoned as it offered 
no advantage. The equations are very stiff, so the in-built Stiff Chemistry solver with Direct 
Integration was employed together with the pseudo-transient solver for the mass, momentum and 
species equations. Typically, the pseudo-timestep used for the species equations was 1000 times larger 
than that used for the momentum equation. However, this approach still required more than 50,000 
iterations to obtain an acceptable atomic balance over the system, running on 72 cores for the finest 
mesh. Second order upwind differencing was applied to the convective terms of all equations. 
 
Results 
Simulations were made using two different hexahedral meshes in which cubic elements were 
employed with 20 and 40 cells across the duct. Given that the meshes are regular and all the schemes 
used (convection, diffusion, pressure) are second order Richardson extrapolation can be used to 
estimate a grid independent result. The results are shown in Figure 2 below. It is evident that mesh 
independence is much easier at higher Reynolds numbers, where there is more rapid mixing and 
reaction (R1) dominates. At the lowest Reynolds number of 60, even with the very fine mesh there is 
still some remaining mesh dependence. Agreement with the experimental data is good in that the trend 
is well predicted but there is a tendency to predict better micromixing than is observed in the 
experiments. It is evident that at the high Reynolds number no amount of mesh refinement is going to 
change this. 
Figure 3 shows the exit concentrations of the I species used in the calculation of the 
segregation index for the extremes of the Reynolds numbers considered. At Re = 300 the 
concentration is almost constant (<0.8%), whereas for Re = 30 the pattern is complex and mirrors the 
Dean vortices responsible for mixing.  
Conclusions  
CFD simulations have been successfully performed to study micromixing in a T-mixer with 
square bends. The simulations are computationally very costly requiring very fine meshes and 
 16
th
 European Conference on Mixing – Mixing 16  9-12 September 2018, Toulouse, France 
 
>200,000 iterations to obtain convergence. The results capture the experimental trend but over predict 
the degree of micromixing. The complexity of the concentration distribution is highlighted. 
 
 
Figure 2: Comparison of the simulated segregation index with the data for concentration set 1 of 
Commenge and Falk [5]. 
 
 
 
 
                      (a)  Re = 60                      (b) Re = 300 
Figure 3: Exit concentrations of the I species used in equ. (8) to determine the segregation index. 
 
Acknowledgements 
 We thank Prof. Jean-Marc Commenge and Dr. Laurent Falk for supplying us with the raw 
data. The authors acknowledge the University of Sydney for providing High Performance Computing 
resources that have greatly contributed to the research results reported here 
(http://sydney.edu.au/research_support). 
 
References  
[1] Baldyga J., Bourne J.R., (1999), Turbulent Mixing and Chemical Reactions, Wiley.  
[2] Tsai K., Gillis P.A., Sen S., Fox R.A., (2002), ASME J. Fluids Engng., 124:102-107. 
[3] Reckamp J.M., Bindels A., Duffield S., Liu Y.C., Ricci E., Susanne F., Rutter A., (2017), Org. 
Process Res. Dev., 21:816-820. 
[4] Guo X., Fan Y., Luo L., (2013), Chem. Eng. J., 227:116-127. 
[5] Commenge J.-M., Falk L., (2011), Chem. Eng. Proces., 50:979-990. 
[6] Assirelli M., Bujalski W., Eaglesham E., Nienow A.W., (2004), Chem. Eng. Sci., 60:2333-2339. 
[7] Falk L., Commenge J.-M., (2010), Chem. Eng. Sci., 65:405-411. 
[8] Guichardon P., Falk L., (2000), Chem. Eng. Sci., 55:4233-4243. 
[9] Guichardon P., Falk L., Villermaux J., (2000). Chem. Eng. Sci., 55:4245-4253. 
[10] Palmer D.A., Ramette R.W., Mesmer R.E., (1984), J. Solut. Chem., 13:673-682. 
[11] Fournier M.-C., Falk L., Villermaux J., (1996), Chem. Eng. Sci., 51:5053-5064. 


CFD Modelling of Micromixing in a T-mixer with Square Bends

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CFD Modelling of Micromixing in a T-mixer with Square Bends

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