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

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Abstract

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.

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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.

Abbreviations

α :

Fluid volume function

Ca:

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

L III :

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

c:

Continuous phase

co:

Coalescence

d:

Dispersed phase

ds:

Dispersed phase with scalars

r:

Real

s:

Liquid slug

sup:

Superficial

I:

Droplet I

II:

Droplet II

III:

Droplet III

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Funding

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).

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Authors

Contributions

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.

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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). https://doi.org/10.1007/s41981-023-00258-0

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  • DOI: https://doi.org/10.1007/s41981-023-00258-0

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