Encapsulation of Droplets Using Cusp Formation behind a Drop Rising in a Non-Newtonian Fluid
Abstract
:1. Introduction
2. Experimental Set-Up and Test Fluids
3. Experimental Observations: Different Regimes
4. Droplet Formation
4.1. Tail Size
4.2. Emission Period and Wavelength
4.3. Droplet Size
5. Discussion
5.1. Tail Appearance and Breakup
5.2. Volume Loss
6. Conclusions and Perspectives
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
- Wu, L.; Chen, P.; Dong, Y.; Feng, X.; Liu, B.F. Encapsulation of single cells on a microfluidic device integrating droplet generation with fluorescence-activated droplet sorting. Biomed. Microdevices 2013, 15, 553–560. [Google Scholar] [CrossRef] [PubMed]
- Teh, S.Y.; Lin, R.; Hung, L.H.; Lee, A.P. Droplet microfluidics. Lab Chip 2008, 8, 198–220. [Google Scholar] [CrossRef] [PubMed]
- Theberge, A.B.; Courtois, F.; Schaerli, Y.; Fischlechner, M.; Abell, C.; Hollfelder, F.; Huck Wilhelm, T.S. Microdroplets in Microfluidics: An Evolving Platform for Discoveries in Chemistry and Biology. Angew. Chem. Int. Ed. 2013, 49, 5846–5868. [Google Scholar] [CrossRef] [PubMed]
- Mark, D.; Haeberle, S.; Roth, G.; Von Stetten, F.; Zengerle, R.L. Microfluidic Lab-on-a-Chip Platforms: Requirements, Characteristics and Applications. In Microfluidics Based Microsystems; Kakaç, S., Kosoy, B., Li, D., Pramuanjaroenkij, A., Eds.; Springer: Dordrecht, The Netherlands, 2010; pp. 305–376. ISBN 978-90-481-9029-4. [Google Scholar]
- Garstecki, P.; Fuerstman, M.J.; Stone, H.A.; Whitesides, G.M. Formation of droplets and bubbles in a microfluidic T-junction—Scaling and mechanism of break-up. Lab Chip 2006, 6, 437–446. [Google Scholar] [CrossRef] [PubMed]
- De Menech, M.; Garstecki, P.; Jousse, F.; Stone, H. Transition from squeezing to dripping in a microfluidic T-shaped junction. J. Fluid Mech. 2008, 595, 141–161. [Google Scholar] [CrossRef]
- Arigo, M.T.; McKinley, G.H. An experimental investigation of negative wakes behind spheres settling in a shear-thinning viscoelastic fluid. Rheol. Acta 1998, 37, 307–327. [Google Scholar] [CrossRef]
- Bisgaard, C.; Hassager, O. An experimental investigation of velocity fields around spheres and bubbles moving in non-Newtonian liquids. Rheol. Acta 1982, 21, 537–539. [Google Scholar] [CrossRef]
- Broadbent, J.; Mena, B. Slow flow of an elastico-viscous fluid past cylinders and spheres. Chem. Eng. J. 1974, 8, 11–19. [Google Scholar] [CrossRef]
- Caswell, B.; Manero, O.; Mena, B. Recent developments on the slow viscoelastic flow past spheres and bubbles. Rheol. Rev 2004, 197–223. [Google Scholar]
- Chhabra, R.P. Bubbles, Drops and Particles in Non-Newtonian Fluids; CRC Press: Boca Raton, FL, USA, 1993. [Google Scholar]
- Manero, O.; Mena, B. On the slow flow of viscoelastic fluids past a circular cylinder. J. Non-Newton. Fluid Mech. 1981, 9, 379–387. [Google Scholar] [CrossRef]
- Mena, B.; Manero, O.; Leal, L.G. The influence of rheological properties on the slow flow past spheres. J. Non-Newton. Fluid Mech. 1987, 26, 247–275. [Google Scholar] [CrossRef]
- Herrera-Velarde, J.R.; Zenit, R.; Chehata, D.; Mena, B. The flow of non-Newtonian fluids around bubbles and its connection to the jump discontinuity. J. Non-Newton. Fluid Mech. 2003, 111, 199–209. [Google Scholar] [CrossRef]
- Rodrigue, D.; De Kee, D. Bubble velocity jump discontinuity in polyacrylamide solutions: A photographic study. Rheol. Acta 1998, 37, 307–327. [Google Scholar] [CrossRef]
- Rodrigue, D.; De Kee, D.; Chan Man Fong, C. Bubble velocities: further developments on the jump discontinuity. J. Non-Newton. Fluid Mech. 1998, 79, 45–55. [Google Scholar] [CrossRef]
- Zenit, R.; Feng, J.J. Hydrodynamic Interactions Among Bubbles, Drops, and Particles in Non-Newtonian Liquids. Annu. Rev. Fluid Mech. 2018, 50, 505–534. [Google Scholar] [CrossRef]
- Astarita, G.; Apuzzo, G. Motion of gas bubbles in non-Newtonian liquids. AIChE J. 1965, 11, 815–820. [Google Scholar] [CrossRef]
- Pilz, C.; Brenn, G. On the critical bubble volume at the rise velocity jump discontinuity in viscoelastic liquids. J. Non-Newton. Fluid Mech. 2007, 145, 124–138. [Google Scholar] [CrossRef]
- Ortiz, S.L.; Lee, J.S.; Figueroa-Espinoza, B.; Mena, B. An experimental note on the deformation and breakup of viscoelastic droplets rising in non-Newtonian fluids. Rheol. Acta 2016, 55, 879–887. [Google Scholar] [CrossRef]
- Soto, E.; Goujon, C.; Zenit, R.; Manero, O. A study of velocity discontinuity for single air bubbles rising in an associative polymer. Phys. Fluids 2006, 18, 121510. [Google Scholar] [CrossRef]
- Fraggedakis, D.; Pavlidis, M.; Dimakopoulos, Y.; Tsamopoulos, J. On the velocity discontinuity at a critical volume of a bubble rising in a viscoelastic fluid. J. Fluid Mech. 2016, 789, 310–346. [Google Scholar] [CrossRef]
- Hassager, O. Negative wake behind bubbles in non-Newtonian liquids. Nature 1979, 279, 402–403. [Google Scholar] [CrossRef] [PubMed]
- Lister, J.R.; Stone, H.A. Capillary breakup of a viscous thread surrounded by another viscous fluid. Phys. Fluids 1998, 10, 2758–2764. [Google Scholar] [CrossRef]
- De Gennes, P.G.; Brochard-Wyart, F.; Quéré, D. Capillary and Wetting Phenomena—Drops, Bubbles, Pearls, Waves; Alex, R., Translator; Springer: Berlin/Heidelberg, Germany, 2002. [Google Scholar]
- Deblais, A.; Velikov, K.P.; Bonn, D. Pearling instabilities of a viscoelastic thread. Phys. Rev. Lett. 2018, 120, 194501. [Google Scholar] [CrossRef] [PubMed]
- Clasen, C.; Eggers, J.; Fontelos, M.A.; Li, J.; McKinley, G. The beads-on-string structure of viscoelastic threads. J. Fluid Mech. 2006, 556, 283–308. [Google Scholar] [CrossRef]
- Skelland, A.H.P.; Raval, V.K. Drop size in power law non-Newtonian systems. Can. J. Chem. Eng. 1972, 50, 41–44. [Google Scholar] [CrossRef]
- Kitamura, Y.; Takahashi, T. Breakup of jets in power law non-Newtonian–Newtonian liquid systems. Can. J. Chem. Eng. 1982, 60, 732–737. [Google Scholar] [CrossRef]
- Teng, H.; Kinoshita, C.M.; Masutani, S.M. Prediction of droplet size from the breakup of cylindrical liquid jets. Int. J. Multiph. Flow 1995, 21, 129–136. [Google Scholar] [CrossRef]
- Barnes, H.A.; Hutton, J.F.; Walters, K. An Introduction to Rheology; Elsevier: New York, NY, USA, 1989. [Google Scholar]
- Ghannam, M.T.; Esmail, M.N. Rheological properties of aqueous polyacrylamide solutions. J. Appl. Polym. Sci. 1998, 69, 1587–1597. [Google Scholar] [CrossRef]
- Palacios-Morales, C.; Zenit, R. The formation of vortex rings in shear-thinning liquids. J. Non-Newton. Fluid Mech. 2013, 194, 1–13. [Google Scholar] [CrossRef]
- Mendoza-Fuentes, A.J.; Manero, O.; Zenit, R. Evaluation of drag correction factor for spheres settling in associative polymers. Rheol. Acta 2010, 49, 979–984. [Google Scholar] [CrossRef]
- Esteban, B.; Riba, J.-R.; Baquero, G.; Puig, R.; Rius, A. Characterization of the surface tension of vegetable oils to be used as fuel in diesel engines. Fuel 2012, 102, 231–238. [Google Scholar] [CrossRef]
- Hu, R.Y.Z.; Wang, A.T.A.; Hartnett, J.P. Surface tension measurement of aqueous polymer solutions. Exp. Therm. Fluid Sci. 1991, 4, 723–729. [Google Scholar] [CrossRef]
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Poryles, R.; Zenit, R. Encapsulation of Droplets Using Cusp Formation behind a Drop Rising in a Non-Newtonian Fluid. Fluids 2018, 3, 54. https://doi.org/10.3390/fluids3030054
Poryles R, Zenit R. Encapsulation of Droplets Using Cusp Formation behind a Drop Rising in a Non-Newtonian Fluid. Fluids. 2018; 3(3):54. https://doi.org/10.3390/fluids3030054
Chicago/Turabian StylePoryles, Raphaël, and Roberto Zenit. 2018. "Encapsulation of Droplets Using Cusp Formation behind a Drop Rising in a Non-Newtonian Fluid" Fluids 3, no. 3: 54. https://doi.org/10.3390/fluids3030054