Skip to main content


Log in

Effects of two-phase periodic velocity on droplet coalescence inside microchannels

  • Full Paper
  • Published:
Journal of Flow Chemistry Aims and scope Submit manuscript


A novel method based on periodic change of two-phase velocity for the droplet coalescence in microchannels is proposed. The feasibility of the method is justified by investigating the droplet coalescence in several combinations of the velocity pairs. Once the droplet pairs have been generated, the frequency of the droplet coalescence can be divided into a liquid slug of continuous phase dominated region and a real velocity ratio dominated region. Since the liquid slug between the droplet pairs and the real velocity ratio of the droplet pairs are determined by the flow rate ratios, the critical value of the flow rate ratio is determined to distinguish whether the frequency of the droplet coalescence is liquid slug dominated or real velocity ratio dominated. Compared with the traditional passive method, the droplet pairs are alternatively generated by the periodic change of the two-phase velocity. The velocity gradient of the droplet pairs can be generated spontaneously which avoids the introduction of an expansion structure. The mixing performance inside the coalesced droplet is improved due to the reorganized inner circulation when the droplets is coalesced. The quantitative mixing of the reagents can be achieved to satisfy special application needs by a precise control of the volume of the droplet pairs.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Data Availability

The data that support the findings of this study are available on request from the corresponding author, [Jin-yuan Qian], upon reasonable request.


α :

Fluid volume function


Capillary number

f co :

Droplet coalescence frequency, s1

F :

Surface tension, mN/m

k :

Curvature of the two-phases interface

L :

Length of the droplet, μm

L s :

Liquid slug between the droplet pairs, μm

L I :

Length of the droplet I, μm

L II :

Length of the droplet II, μm


Length of the droplet III, μm

n :

The normal vector of the unit surface at the free surface

p :

Pressure, MPa

Q c :

Continuous phase flow rate, μL/s

Q d :

Dispersed phase flow rate, μL/s

(Q d/Q c)I :

Flow rate ratio for the generation of droplet I

(Q d/Q c)II :

Flow rate ratio for the generation of droplet II

t :

Droplet flow time, ms

T :

Droplet formation time, ms

v :

Velocity vector

v II/v I :

Real velocity ratio of the droplet pairs in one period

w :

Continuous phase channel width, μm

μ :

Viscosity, Pa·s

ρ :

Density, kg/m3

σ :

Interfacial tension, mN/m

θ w :

Contact angle between the liquid–liquid phases and the wall


Continuous phase




Dispersed phase


Dispersed phase with scalars




Liquid slug




Droplet I


Droplet II


Droplet III


  1. Abiev RS (2021) Mathematical model of gas-liquid or liquid-liquid Taylor flow with non-Newtonian continuous liquid in microchannels. J Flow Chem 11:525–537.

    Article  CAS  Google Scholar 

  2. Li Y, Qiu Z, Cui D, Wang Z, Zhang J, Ji Y (2021) Numerical investigation on the thermal-hydraulic performance of helical twine printed circuit heat exchanger. Int Commun Heat Mass Transf 128:105596.

    Article  CAS  Google Scholar 

  3. Guan F, Blacker AJ, Hall B, Nikil K, Wen J, Zhang M (2021) High-pressure asymmetric hydrogenation in a customized flow reactor and its application in multi-step flow synthesis of chiral drugs. J Flow Chem 11:763–772.

    Article  CAS  Google Scholar 

  4. Qian J, Li X, Gao Z, Jin Z (2019) Mixing efficiency and pressure drop analysis of liquid-liquid two phases flow in serpentine microchannels. J Flow Chem 9:187–197.

    Article  CAS  Google Scholar 

  5. Zhao Y, Cheng Y, Shang L, Wang J, Xie Z, Gu Z (2015) Microfluidic synthesis of barcode particles for multiplex assays. Small 11:151–174.

    Article  CAS  PubMed  Google Scholar 

  6. Pati AR, Mandal S, Dash A, Barik K, Munshi B, Mohapatra SS (2018) Oil-in-water emulsion spray: a novel methodology for the enhancement of heat transfer rate in film boiling regime. Int Commun Heat Mass Transf 98:96–105.

    Article  Google Scholar 

  7. Mashaghi S, Abbaspourrad A, Weitz DA, van Oijen AM (2016) Droplet microfluidics: a tool for biology, chemistry and nanotechnology. Trac-Trends Anal Chem 82:118–125.

    Article  CAS  Google Scholar 

  8. Jia Y, Ren Y, Hou L, Liu W, Deng X, Jiang H (2017) Sequential coalescence enabled two-step microreactions in triple-core double-emulsion droplets triggered by an electric field. Small 13:1702188.

    Article  CAS  Google Scholar 

  9. Varma VB, Ray A, Wang Z, Wang Z, Ramanujan RV (2016) Droplet merging on a lab-on-a-chip platform by uniform magnetic fields. Sci Rep 6:37671.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  10. Xu B, Wong T, Zhang D, Shen X (2019) Experimental and numerical investigation on a simple droplet coalescence design in microchannels. Heat Mass Transf 55:1553–1562.

    Article  CAS  Google Scholar 

  11. Leibacher I, Reichert P, Dual J (2015) Microfluidic droplet handling by bulk acoustic wave (BAW) acoustophoresis. Lab Chip 15:2896–2905.

    Article  CAS  PubMed  Google Scholar 

  12. Deng N, Mou C, Wang W, Ju X, Xie R, Chu L (2014) Multiple emulsion formation from controllable drop pairs in microfluidics. Microfluid Nanofluid 17:967–972.

    Article  Google Scholar 

  13. Jeong H, Lee B, Jin SH, Lee C (2019) Hydrodynamic control of droplet breakup, immobilization, and coalescence for a multiplex microfluidic static droplet array. Chem Eng J 360:562–568.

    Article  CAS  Google Scholar 

  14. Zhang Y, Xia H, Wu J, Zhang J, Wang Z (2019) Synchronized generation and coalescence of largely dissimilar microdroplets governed by pulsating continuous-phase flow. Appl Phys Lett 114:73701.

    Article  CAS  Google Scholar 

  15. Ma P, Liang D, Zhu C, Fu T, Ma Y (2020) An effective method to facile coalescence of microdroplet in the symmetrical T-junction with expanded convergence. Chem Eng Sci 213:115389.

    Article  CAS  Google Scholar 

  16. Lai Y, Hsu M, Yang J (2010) Enhanced mixing of droplets during coalescence on a surface with a wettability gradient. Lab Chip 1:3149–3156.

    Article  CAS  Google Scholar 

  17. Deng N, Sun S, Wang W, Ju X, Xie R, Chu L (2013) A novel surgery-like strategy for droplet coalescence in microchannels. Lab Chip 13:3653–3657.

    Article  CAS  PubMed  Google Scholar 

  18. Yeh S, Fang W, Sheen H, Yang J (2013) Droplets coalescence and mixing with identical and distinct surface tension on a wettability gradient surface. Microfluid Nanofluid 14:785–795.

    Article  CAS  Google Scholar 

  19. Yeh S, Sheen H, Yang J (2015) Chemical reaction and mixing inside a coalesced droplet after a head-on collision. Microfluid Nanofluid 18:1355–1363.

    Article  CAS  Google Scholar 

  20. Akartuna I, Aubrecht DM, Kodger TE, Weitz DA (2015) Chemically induced coalescence in droplet-based microfluidics. Lab Chip 15:1140–1144.

    Article  CAS  PubMed  Google Scholar 

  21. Ma R, Zhang Q, Fu T, Zhu C, Wang K, Ma Y, Luo G (2018) Manipulation of microdroplets at a T-junction: Coalescence and scaling law. J Ind Eng Chem 65:272–279.

    Article  CAS  Google Scholar 

  22. Abiev RSh, Svetlov SD, Ponyaev AI (2020) Microdispersant for droplet generation. Russian Federation Patent 2718617

  23. Abiev RSh, Ponyaev AI (2020) Micro-disperser with periodic structure with variable pitch for generation of drops. Russian Federation Patent 2732142

  24. Hung L, Choi KM, Tseng W, Tan Y, Shea KJ, Lee AP (2006) Alternating droplet generation and controlled dynamic droplet fusion in microfluidic device for CdS nanoparticle synthesis. Lab Chip 6:174.

    Article  CAS  PubMed  Google Scholar 

  25. Yagodnitsyna AA, Kovalev AV, Bilsky AV (2016) Flow patterns of immiscible liquid-liquid flow in a rectangular microchannel with T-junction. Chem Eng J 303:547–554.

    Article  CAS  Google Scholar 

  26. Li Q, Angeli P (2017) Experimental and numerical hydrodynamic studies of ionic liquid-aqueous plug flow in small channels. Chem Eng J 328:717–736.

    Article  CAS  Google Scholar 

  27. Qian J, Li X, Wu Z, Jin Z, Zhang J, Sundén B (2019) Slug formation analysis of liquid-liquid two-phase flow in T-junction microchannels. J Therm Sci Eng Appl 11:051017.

    Article  CAS  Google Scholar 

  28. Qian J, Li X, Gao Z, Jin Z (2019) Mixing efficiency analysis on droplet formation process in microchannels by numerical methods. Processes 7:33.

    Article  CAS  Google Scholar 

  29. Cao Z, Wu Z, Sundén B (2018) Dimensionless analysis on liquid-liquid flow patterns and scaling law on slug hydrodynamics in cross-junction microchannels. Chem Eng J 344:604–615.

    Article  CAS  Google Scholar 

  30. Garstecki P, Fuerstman MJ, Stone HA (2006) Whitesides GM (2006) Formation of droplets and bubbles in a microfluidic T-junction—scaling and mechanism of break-up. Lab Chip 6:437–446.

    Article  CAS  PubMed  Google Scholar 

Download references


This research was supported by National Natural Science Foundation of China (No.52175067), Zhejiang Key Research & Development Project (No.2021C01021) and Natural Science Foundation of Zhejiang Province (No.LY20E050016).

Author information

Authors and Affiliations



Wen-qing Li and Xiao-juan Li designed the research. Xiao-juan Li, Wen-qing Li, and An-qi Guan processed the corresponding data. Wen-qing Li and Xiao-juan Li wrote the first draft of the manuscript. An-qi Guan, Zhi-jiang Jin and Jin-yuan Qian helped to organize the manuscript. Zhi-jiang Jin and Jin-yuan Qian revised and edited the final version.

Corresponding author

Correspondence to Jin-yuan Qian.

Ethics declarations

Conflict of interest

There are no conflicts to declare.

Additional information

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, Wq., Li, Xj., Guan, Aq. et al. Effects of two-phase periodic velocity on droplet coalescence inside microchannels. J Flow Chem 13, 63–72 (2023).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: