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Flow and mixing in a tube-in-tube millireactor with multiholes jet and twist tapes

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A novel tube-in-tube millireactor with multiholes jet and twist tapes was designed and investigated for its excellent mixing, low price, and industrialization prospects. The inner tube fluid jets into the annular space through six circular microholes with a diameter of 0.2 mm that are evenly drilled around the inner tube. This arrangement achieves good inlet dispersion. The annular reaction channel is modified by three types of twist tape, which facilitates fluid splitting, recombination, and swirling. A detailed computational study has been carried out on the millireactor to characterize flow using a verified and validated CFD model. Villermaux-Dushman reaction and impulse method residence time distribution were used to study both the micromixing and macromixing performance. The multiholes jet has excellent micro-mixing performance with a micro-mixing time of less than 1 ms, at Re > 350. The twist tapes effectively improve the macromixing so that a Pe > 100 is achieved in most of the range of Re 32 ~ 634. Local flow field visualization of the annular spaces with tapes is obtained by PIV - RIM, and the results align with the CFD model.

Graphical Abstract


A novel tube-in-tube millireactor with multiholes jet and twist tapes was designed with excellent micromixing and narrow RTD.

Micromixing time is less than 1ms, at Re > 350.

Pe > 100 in most of the studied range, V = 6 ~ 240 ml/min.

The local flow field was obtained by PIV-RIM under structure shading.

The micromixing and differential pressure between inner and outer tube are determined by \({Re}_{hole}\).

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Computational Fluid Dynamics

C j :

reactant concentration of species j, mol/L

C j,r :

molar concentration of species j in reaction r, mol/L

C j10 :

concentration of the surrounding fluid, mol/L

d hole :

microhole size, mm

d N :

hydrodynamic diameter

E(t) :

exit age distribution as a function of time, s− 1

E(θ) :

exit age distribution as a function of dimensionless time

f :

friction coefficient

L :

length of the reactor channel, mm

M :

parameter in empirical model

N :

parameter in empirical model

N in :

Molar amount of substance in the inner tube

N out :

Molar amount of substance in the outter tube



Pe :

reactor Peclet number, also known as Bodenstein number. The reciprocal is referred to as the Vessel Dispersion number


Particle Image Velocimetry


Planer Laser Induced Fluorescence

R :

 the ratio of the volume flow between the inner and outer tubes

RI :

Refraction index

Re :

Reynolds number


turbulent kinetic energy, m2/s2

t m :

characteristic micromixing time, s

t max :

maximum residence time

t min :

minimum residence time

\(\overline{t}\) :

mean residence time, s

V in :

volume flow rate in inner tube, ml/min

V out :

volume flow rate in outter tube, ml/min

X s :

segregation index

ΔP :

fluid pressure drop, Pa


turbulent dissipation rate, m2/s3.

μ :

viscosity, Pa s.

τ :

nominal space time, s.

\({\sigma ^2}\) :


\(\sigma _{\theta }^{2}\) :

dimensionless variance


  1. Besenhard MO, LaGrow AP, Hodzic A, Kriechbaum M, Panariello L, Bais G, Loizou K, Damilos S, Cruz MM, Thanh NTK, Gavriilidis A (2020) Co-precipitation synthesis of stable iron oxide nanoparticles with NaOH: New insights and continuous production via flow chemistry. Chem Eng J 399

  2. Rossetti I, Compagnoni M (2016) Chemical reaction engineering, process design and scale-up issues at the frontier of synthesis: Flow chemistry. Chem Eng J 296:56–70

    Article  CAS  Google Scholar 

  3. Bieringer T, Buchholz S, Kockmann N (2013) Future production concepts in the chemical industry: Modular - Small-Scale - Continuous. Chem Eng Technol 36(6):900–910

    Article  CAS  Google Scholar 

  4. Berton M, de Souza JM, Abdiaj I, McQuade DT, Snead DR (2020) Scaling continuous API synthesis from milligram to kilogram: extending the enabling benefits of micro to the plant. J Flow Chem 10(1):73–92

    Article  Google Scholar 

  5. Roberge DM, Ducry L, Bieler N, Cretton P, Zimmermann B (2005) Microreactor technology: A revolution for the fine chemical and pharmaceutical industries? Chem Eng Technol 28(3):318–323

    Article  CAS  Google Scholar 

  6. Hessel V (2009) Process windows - gate to maximizing process intensification via flow chemistry. Chem Eng Technol 32(11):1655–1681

    Article  CAS  Google Scholar 

  7. Gauthier DR, Sherry BD, Cao Y, Journet M, Humphrey G, Itoh T, Mangion I, Tschaen DM (2015) Highly efficient synthesis of hiv nnrti doravirine. Org Lett 17(6):1353–1356

    Article  CAS  PubMed  Google Scholar 

  8. Hessel V, Kralisch D, Kockmann N, Noel T, Wang Q (2013) Novel process windows for enabling, accelerating, and uplifting flow chemistry. Chemsuschem 6(5):746–789

    Article  CAS  PubMed  Google Scholar 

  9. Hessel V, Kralisch D, Kockmann N (2015) Novel Process Windows: Innovative gates to intensified and sustainable chemical processes. Wiley-VCH Verlag, Hoboken, pp 1–314

    Google Scholar 

  10. Roberge DM, Gottsponer M, Eyholzer M, Kockmann N (2009) Industrial design, scale-up, and use of microreactors. Chim Oggi-Chem Today 27(4):8–11

    CAS  Google Scholar 

  11. Kockmann N, Gottsponer M, Roberge DM (2011) Scale-up concept of single-channel microreactors from process development to industrial production. Chem Eng J167(2–3):718–726

    Article  Google Scholar 

  12. Schwolow S, Neumüller A, Abahmane L, Kockmann N, Röder T (2016) Design and application of a millistructured heat exchanger reactor for an energy-efficient process. Chem Eng Process 108:109–116

    Article  CAS  Google Scholar 

  13. Schwolow S, Mutsch B, Kockmann N, Röder T (2019) Model-based scale-up and reactor design for solvent-free synthesis of an ionic liquid in a millistructured flow reactor. React Chem Eng 4(3):523–536

    Article  CAS  Google Scholar 

  14. Plutschack MB, Pieber B, Gilmore K, Seeberger PH (2017) The Hitchhiker’s guide to flow chemistry. Chem Rev 117(18):11796–11893

    Article  CAS  PubMed  Google Scholar 

  15. Han S, Kashfipour MA, Ramezani M, Abolhasani M (2020) Accelerating gas-liquid chemical reactions in flow. Chem Commun 56(73):10593–10606

    Article  CAS  Google Scholar 

  16. Su Y, Lautenschleger A, Chen G, Kenig EY (2014) A numerical study on liquid mixing in multichannel micromixers. Ind Eng Chem Res 53(1):390–401

    Article  CAS  Google Scholar 

  17. Engler M, Kockmann N, Kiefer T, Woias P (2004) Numerical and experimental investigations on liquid mixing in static micromixers. Chem Eng J 101(1–3):315–322

    Article  CAS  Google Scholar 

  18. Kockmann N, Kiefer T, Engler M, Woias P (2006) Silicon microstructures for high throughput mixing devices. Microfluid Nanofluid 2(4):327–335

    Article  Google Scholar 

  19. Singh J, Kockmann N, Nigam KDP (2014) Novel three-dimensional microfluidic device for process intensification. Chem Eng Process-Process Intensif 86:78–89

    Article  CAS  Google Scholar 

  20. Dong C, Zhang JS, Wang K, Luo GS (2014) Micromixing performance of nanoparticle suspensions in a micro-sieve dispersion reactor. Chem Eng J 253:8–15

    Article  CAS  Google Scholar 

  21. Zhang JS, Wang K, Lu YC, Luo GS (2010) Characterization and modeling of micromixing performance in micropore dispersion reactors. Chem Eng Process 49(7):740–747

    Article  CAS  Google Scholar 

  22. Commenge JM, Falk L (2011) Villermaux-Dushman protocol for experimental characterization of micromixers. Chem Eng Process 50(10):979–990

    Article  CAS  Google Scholar 

  23. Suryawanshi PL, Gumfekar SP, Bhanvase BA, Sonawane SH, Pimplapure MS (2018) A review on microreactors: Reactor fabrication, design, and cutting-edge applications. Chem Eng Sci 189:431–448

    Article  CAS  Google Scholar 

  24. Silva JLd, Santana HS (2022) Residence time distribution in reactive and non-reactive flow systems in micro and millidevices. Chem Eng Sci 248:117163

  25. Kurt SK, Gelhausen MG, Kockmann N (2015) Axial dispersion and heat transfer in a milli/microstructured coiled flow inverter for narrow residence time distribution at laminar flow. Chem Eng Technol 38(7):1122–1130

    Article  CAS  Google Scholar 

  26. Klutz S, Kurt SK, Lobedann M, Kockmann N (2015) Narrow residence time distribution in tubular reactor concept for Reynolds number range of 10–100. Chem Eng Res Des 95:22–33

    Article  CAS  Google Scholar 

  27. Hopley A, Doyle BJ, Roberge DM, Macchi A (2019) Residence time distribution in coil and plate micro-reactors. Chem Eng Sci 207:181–193

    Article  CAS  Google Scholar 

  28. Gobert SRL, Kuhn S, Braeken L, Thomassen LCJ (2017) Characterization of milli- and microflow reactors: mixing efficiency and residence time distribution. Org Process Res Dev 21(4):531–542

    Article  CAS  Google Scholar 

  29. Ahmed SMR, Phan AN, Harvey AP (2017) Scale-up of oscillatory helical baffled reactors based on residence time distribution. Chem Eng Technol 40(5):907–914

    Article  CAS  Google Scholar 

  30. Siguemoto ES, Leite Reche L, Gut JAW, Palma MSA (2020) Residence time distribution of a capillary microreactor used for pharmaceutical synthesis. Chem Eng Technol 43(3):429–435

    Article  CAS  Google Scholar 

  31. Boskovic D, Loebbecke S (2008) Modelling of the residence time distribution in micromixers. Chem Eng J 135:S138–S146

    Article  CAS  Google Scholar 

  32. Kurnia JC, Chaedir BA, Sasmito AP (2020) Laminar convective heat transfer in helical tube with twisted tape insert. Int J Heat Mass Transf 150:119309

  33. Ahmad S, Abdullah S, Sopian K (2020) A review on the thermal performance of nanofluid inside circular tube with twisted tape inserts. Adv Mech Eng 12(6):1687814020924893

  34. Piriyarungrod N, Eiamsa-ard S, Thianpong C, Pimsarn M, Nanan K (2015) Heat transfer enhancement by tapered twisted tape inserts. Chem Eng Process-Process Intensif 96:62–71

    Article  CAS  Google Scholar 

  35. Huang F, Chen P, Wang J, Li Z, Gao Z, Derksen JJ (2020) Refractive index-matched PIV experiments and CFD simulations of mixing in a complex dynamic geometry. Ind Eng Chem Res 59(16):7982–7992

    Article  CAS  Google Scholar 

  36. Xiong Q-Q, Chen Z, Li S-W, Wang Y-D, Xu J-H (2018) Micro-PIV measurement and CFD simulation of flow field and swirling strength during droplet formation process in a coaxial microchannel. Chem Eng Sci 185:157–167

    Article  CAS  Google Scholar 

  37. Liu Z, Zhang L, Pang Y, Wang X, Li M (2017) Micro-PIV investigation of the internal flow transitions inside droplets traveling in a rectangular microchannel. Microfluid Nanofluid 21:12

    Article  Google Scholar 

  38. Wright SF, Zadrazil I, Markides CN (2017) A review of solid–fluid selection options for optical-based measurements in single-phase liquid, two-phase liquid–liquid and multiphase solid–liquid flows. Exp Fluids 58(9):1–39

  39. Li W, Xia F, Zhao S, Guo J, Zhang M, Li W, Zhang J (2019) Mixing performance of an inline high-shear mixer with a novel pore-array liquid distributor. Ind Eng Chem Res 58(44):20213–20225

    Article  CAS  Google Scholar 

  40. Ansys I (2018) ANSYS fluent theory guide, release 19.1. ANSYS Inc, Canonsburg

    Google Scholar 

  41. Li W, Xia F, Qin H, Zhang M, Li W, Zhang J (2019) Numerical and experimental investigations of micromixing performance and efficiency in a pore-array intensified tube-in-tube microchannel reactor. Chem Eng J 370:1350–1365

    Article  CAS  Google Scholar 

  42. Sung MK, Mudawar I (2008) Effects of jet pattern on single-phase cooling performance of hybrid micro-channel/micro-circular-jet-impingement thermal management scheme. Int J Heat Mass Transf 51(19–20):4614–4627

    Article  CAS  Google Scholar 

  43. Sagot B, Antonini G, Christgen A, Buron F (2008) Jet impingement heat transfer on a flat plate at a constant wall temperature. Int J Therm Sci 47(12):1610–1619

    Article  Google Scholar 

  44. Baydar E (1999) Confined impinging air jet at low Reynolds numbers. Exp Thermal Fluid Sci 19(1):27–33

    Article  Google Scholar 

  45. Nawani S, Subhash M (2021) In A review on multiple liquid jet impingement onto flat plate. International Conference on Technological Advancements in Materials Science and Manufacturing (ICTAMSM), India, Feb 19–20; India, pp 11190–11197

  46. Fogler HS (2016) Elements of chemical reaction engineering (5th). Pearson Education Inc, Boston

  47. Ham JH, Platzer B (2004) Semi-empirical equations for the residence time distributions in disperse systems - Part 1: continuous phase. Chem Eng Technol 27(11):1172–1178

    Article  CAS  Google Scholar 

  48. Krupa K, Nunes MI, Santos RJ, Bourne JR (2014) Characterization of micromixing in T-jet mixers. Chem Eng Sci 111:48–55

    Article  CAS  Google Scholar 

  49. Villermaux J, Falk L (1994) A generalized mixing model for initial contacting of reactive fluids. Chem Eng Sci 49(24):5127–5140

    Article  CAS  Google Scholar 

  50. Bałdyga J (1994) A closure model for homogeneous chemical reactions. Chem Eng Sci 49(12):1985–2003

    Article  Google Scholar 

  51. Baldyga J, Bourne J (1989) Simplification of micromixing calculations. I. Derivation and application of new model. Chem Eng J 42(2):83–92

    Article  CAS  Google Scholar 

  52. Baldyga J, Bourne J (1988) Calculation of micromixing in homogeneous stirred tank reactors. Chem Eng Res Des 66(1):33–38

    CAS  Google Scholar 

  53. Villermaux J, David R (1983) Recent advances in the understanding of micromixing phenomena in stirred reactors. Chem Eng Commun 21(1–3):105–122

    Article  CAS  Google Scholar 

  54. Villermaux J, Devillon JC (1972) Représentation de la coalescence et de la redispersion des domaines de ségrégation dans un fluide par un modèle d’interaction phénoménologique. Proceedings of the Second International Symposium on Chemical Reaction Engineering, 1–13

  55. Su Y, Chen G, Yuan Q (2011) Ideal micromixing performance in packed microchannels. Chem Eng Sci 66(13):2912–2919

    Article  CAS  Google Scholar 

  56. Rahimi M, Valeh-e-Sheyda P, Parsamoghadam MA, Azimi N, Abidi H (2014) LASP and Villermaux/Dushman protocols for mixing performance in microchannels: Effect of geometry on micromixing characterization and size reduction. Chem Eng Process 85:178–186

    Article  CAS  Google Scholar 

  57. Rahimi M, Aghel B, Hatamifar B, Akbari M, Alsairafi A (2014) CFD modeling of mixing intensification assisted with ultrasound wave in a T-type microreactor. Chem Eng Process 86:36–46

    Article  CAS  Google Scholar 

  58. Fang JZ, Lee DJ (2001) Micromixing efficiency in static mixer. Chem Eng Sci 56(12):3797–3802

    Article  CAS  Google Scholar 

  59. Mielke E, Plouffe P, Mongeon SS, Aellig C, Filliger S, Macchi A, Roberge DM (2018) Micro-reactor mixing unit interspacing for fast liquid-liquid reactions leading to a generalized scale-up methodology. Chem Eng J 352:682–694

    Article  CAS  Google Scholar 

  60. Schikarski T, Trzenschiok H, Peukert W, Avila M (2019) Inflow boundary conditions determine T-mixer efficiency. Reaction Chem Eng 4(3):559–568

    Article  CAS  Google Scholar 

  61. Levenspiel O (1998) Chemical reaction engineering. Wiley, Hoboken

    Google Scholar 

  62. Adeosun JT, Lawal A (2009) Numerical and experimental studies of mixing characteristics in a T-junction microchannel using residence-time distribution. Chem Eng Sci 64(10):2422–2432

    Article  CAS  Google Scholar 

  63. Kumar V, Shirke V, Nigam KDP (2008) Performance of Kenics static mixer over a wide range of Reynolds number. Chem Eng J 139(2):284–295

    Article  CAS  Google Scholar 

  64. Galaktionov OS, Anderson PD, Peters GWM, Meijer HEH (2003) Analysis and optimization of kenics static mixers. Int Polym Proc 18(2):138–150

    Article  CAS  Google Scholar 

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This research is funded by Jiangsu Seven Continents Green Chemical Co., Ltd.

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Authors and Affiliations



Conceptualization; methodology; CFD simulation, validation, formal analysis, writing—original draft preparation, writing-review and editing, Hanyang Liu.; supervision, Junan Jiang, Ning Yang; project administration, Rijie Wang. All authors have read and agreed to the published version of the manuscript.

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Correspondence to Rijie Wang.

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Supplementary Information

Below is the link to the electronic supplementary material.

Supporting information is available on the mesh independence and algorithm reliable verification, refractive index matching PIV, and The Villermaux–Dushman system.


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Liu, H., Jiang, J., Yang, N. et al. Flow and mixing in a tube-in-tube millireactor with multiholes jet and twist tapes. J Flow Chem 12, 353–369 (2022).

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