Abstract
In droplet microfluidic devices with suction-based flow control, the microchannel geometry and suction pressure at the outlet govern the dynamic properties of the two phases that influence the droplet generation. Therefore, it is critical to understand the role of geometry along with suction pressure in the dynamics of droplet generation to develop a predictive model. We conducted a comprehensive characterization of droplet generation in a flow focusing device with varying control parameters. We used these results to formulate a scaling argument and propose a governing parameter, called as modified capillary number (CaL), that combines normalized droplet volume with geometrical parameters (length of dispersed and continuous phase channels) and flow parameters (interfacial tension, phase viscosity and velocity) in a power law relationship. CaL effectively captures the transition from squeezing to dripping regimes of droplet generation, providing essential insights into the design requirements for suction-driven droplet generation. These findings are key to standardize microfluidic flow-focusing devices that can achieve the desired droplet generation behavior with optimal pressure consumption.
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Data availability
Experimental data presented in his study is available upon request to the authors.
Abbreviations
- Ca:
-
Capillary number
- CaL :
-
Modified capillary number
- μ C :
-
Viscosity of continuous phase
- μ D :
-
Viscosity of dispersed phase
- G :
-
Characteristic rate of strain
- n :
-
Characteristic size of neck
- V :
-
Droplet volume
- v D :
-
Velocity of dispersed phase
- v C :
-
Velocity of continuous phase
- γ :
-
Interfacial tension
- λ :
-
Viscosity ratio
- φ :
-
Flow rate ratio
- Q D :
-
Dispersed phase flow rate
- Q C :
-
Continuous phase flow rate
- R D :
-
Hydraulic diameter of dispersed phase inlet
- R D :
-
Hydraulic diameter of continuous phase inlet
- d :
-
Droplet diameter
- d L :
-
Droplet length
- w :
-
Channel width
- ϵ :
-
Shear rate
- ω :
-
Droplet velocity/average cont. phase velocity
- C λ :
-
Correction factor
- α :
-
Ratio of effective cross-section area of channels
- t n :
-
Time between initiation and breakup
- ∆P D :
-
Pressure drop in dispersed phase channel
- ∆P C :
-
Pressure drop in continuous phase channel
- P atm :
-
Absolute atmospheric pressure
- P j :
-
Absolute pressure at the junction
- L D :
-
Length of dispersed phase channel
- L C :
-
Length of continuous phase channel
- L :
-
Length ratio
- δW S :
-
Work done per unit area
- δα :
-
Work done by stretching
- δH :
-
Work done by bending
- δD :
-
Work done by torsion
- ∆A :
-
Surface element
- B :
-
Bending moments
- \( \vartheta \) :
-
Torsion moment
- VDrop :
-
Observed droplet volume
- \(\overline{{\text{V}} }\) Drop :
-
Scaled droplet volume
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Acknowledgements
This project was partially funded by support from the Indian Institute of Science (IISc) Bangalore, DBT Biodesign Bioengineering Initiative (BT/PR13926/MED31/97/2010) and Rao Biomedical Research Fund (RBRF02). We also acknowledge use of the photolithography facilities at the Center for Nano Science and Engineering (CeNSe), funded by the Department of Information Technology, Gov. of India.
Funding
This article is funded by Bioengineering and Biodesign Initiative at IISc, BT/PR13926/MED31/97/2010, Rao Biomedical Research Fund, RBRF02.
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JP and RR designed the project. JP conducted the experiments, analysis and wrote the manuscript. Both authors reviewed the manuscript.
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Supplementary file 2: The supplementary software S1 for suction pressure control is available at: https://doi.org/10.5281/zenodo.10031121 (ZIP 450 KB)
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Panwar, J., Roy, R. Modified capillary number to standardize droplet generation in suction-driven microfluidics. Microfluid Nanofluid 28, 23 (2024). https://doi.org/10.1007/s10404-024-02714-2
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DOI: https://doi.org/10.1007/s10404-024-02714-2