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Prediction of Microdroplet Breakup Regime in Asymmetric T-Junction Microchannels

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Abstract

Splitting droplets is becoming a major functional component in increasing number of droplet microfluidic applications, and there is an increasing interest in splitting droplets into two daughter droplets with different volumes. However, designing an asymmetric droplet splitter and predicting how a droplet splits in such designs is not trivial. In this study, numerical simulations were conducted to study droplet breakup in asymmetric T-junctions of square cross-sections having different pressure gradient ratios (i.e. T-junctions with outlet branches of different lengths). The goal of the simulation is to identify the conditions where a parent droplet breaks or does not break into two smaller droplets of different sizes (so called critical condition) and to identify the important fluid and microchannel parameters in this process. Four modes of droplet breakup (primary-, transition-, bubble-, and non-breakups) are identified and an empirical correlation is introduced that can predict the breakup/non-breakup of the droplet based on the parent droplet size and the capillary number. The simulation results are then compared with experimental data to verify its accuracy and the effect of fluids properties on the proposed correlation are studied. Two major asymmetric breakup mechanisms are determined, namely “breakup with permanent obstruction” and “unstable breakup”. The numerical results show that the splitting ratio for the asymmetric breakup mechanisms depends on flow conditions and dwell time of the droplet at the junction prior to splitting. Finally, the results from two-dimensional and three-dimensional simulations were compared. It is shown that two-dimensional simulation may not accurately predict the breakup behavior for asymmetric droplet breakup and viscosity ration has a greater effect on the prediction critical condition.

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Abbreviations

Ca :

Capillary number, \( Ca=\frac{\mu \cdotp U}{\sigma } \)

D Hyd :

Hydraulic diameter, \( {D}_{Hyd}=\frac{4A}{P} \)

F s :

External force

L :

Channel length

p :

Pressure

\( \dot{Q} \) :

Volumetric flow rate

Re :

Reynolds number, \( \mathit{\operatorname{Re}}=\frac{\rho \cdot U\cdot {D}_{Hyd}}{\mu } \)

t :

Time

u :

Fluid velocity

U :

Averaged fluid velocity

V :

Volume

W :

Channel width

We :

Weber number, \( We=\frac{\rho \cdotp {U}^2\cdotp {D}_{Hyd}}{\sigma } \)

α :

Volume fraction

β :

Generic fluid property

ε :

Droplet extension

ζ :

Ratio of pressure gradient, \( \zeta =\frac{L_x}{L_n} \)

η μ :

Viscosity ratio, \( {\eta}_{\mu }=\frac{\mu_D}{\mu_C} \)

η ρ :

Density ratio, \( {\eta}_{\rho }=\frac{\rho_D}{\rho_C} \)

λ :

Length of droplet in the microchannel

μ :

Dynamic viscosity

ξ :

Splitting ratio of daughter droplet, \( \xi =\frac{V_x}{V_n} \)

ρ :

Fluid density

σ :

Surface tension

τ :

Dimensionless time, \( \tau =\frac{\sigma \cdotp t}{\mu\ W} \)

ψ :

Dimensionless constant in the formula for critical Capillary number

C :

Continuous phase

cr :

Critical condition

D :

Discrete phase

Hyd :

Hydraulic diameter

in :

Inlet

n :

Shorter outlet arm

x :

Longer outlet arm

0:

Initial state

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Acknowledgements

This publication was made possible by the NPRP award [NPRP 5-671-2-278] from the Qatar National Research Fund (a member of The Qatar Foundation). The statements made herein are solely the responsibility of the author[s]. The high performance computing resources and services used in this work is jointly provided by the IT Research Computing Group at TAMUQ and High Performance Research Computing at the Texas A&M Supercomputing Facility in College Station, Texas, USA.

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  1. Texas A&M University at Qatar, Doha, Qatar

    Way Lee Cheng

  2. Texas A&M University, College Station, TX, USA

    Reza Sadr, Jing Dai & Arum Han

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  1. Way Lee Cheng
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Correspondence to Reza Sadr.

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Cheng, W.L., Sadr, R., Dai, J. et al. Prediction of Microdroplet Breakup Regime in Asymmetric T-Junction Microchannels. Biomed Microdevices 20, 72 (2018). https://doi.org/10.1007/s10544-018-0310-8

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