Slender-body theory for the generation of micrometre-sized emulsions through tip streaming

Journal of Fluid Mechanics

Volumn 698, Issue , 2012, Pages 423-445

  Castro Hernandez E ^a   Campo Cortes F ^a   Gordillo, José Manuel ^a  

^a UNIVERSITY OF SEVILLE   (Spain)

Author keywords

drops and bubbles; low Reynolds number flows; microfluidics

Indexed keywords

BODIES OF REVOLUTION; EMULSIFICATION; MICROFLUIDICS; ORDINARY DIFFERENTIAL EQUATIONS; OSTWALD RIPENING; PARALLEL FLOW; REYNOLDS NUMBER; VELOCITY; VISCOSITY;

BOUNDARY INTEGRALS; CONCENTRATED EMULSION; DIMENSIONLESS NUMBER; DROPS AND BUBBLES; LOW REYNOLDS NUMBER FLOW; NARROW SIZE DISTRIBUTIONS; SLENDER-BODY THEORY; THIRD ORDER DIFFERENTIAL EQUATIONS;

DROPS;

BUBBLE; EMULSION; JET; NUMERICAL MODEL; REYNOLDS NUMBER; SIZE DISTRIBUTION; VISCOSITY;

EID: 84859992637     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/jfm.2012.100     Document Type: Review

References (33)

1. ABRAMOWITZ, M. & STEGUN, I. A. 1970 Handbook of Mathematical Functions. Dover.
2. ACRIVOS, A. & LO, T. S. 1977 Deformation and breakup of a single slender drop in an extensional flow. J. Fluid Mech. 86, 641-672.
3. ANNA, S. L., BONTOUX, N. & STONE, H. A. 2003 Formation of dispersions using flow focusing in microchannels. Appl. Phys. Lett. 82, 364-366.
4. BARRERO, A. & LOSCERTALES, I. G. 2007 Micro-and nanoparticles via capillary flows. Annu. Rev. Fluid Mech. 39, 89-106. (Pubitemid 46210825)
5. BASARAN, O. A. 2002 Small-scale free surface flows with breakup: drop formation and emerging applications. AIChE J. 48, 1842-1848. (Pubitemid 36172976)
6. BUCKMASTER, J. D. 1971 Pointed bubbles in slow viscous flow. J. Fluid Mech. 55, 385-400.
7. CASTRO-HERNÁNDEZ, E. 2011 Analysis of the mechanisms of generation and breakup of bubbles and droplets in gas-liquid and liquid-liquid streams. PhD thesis, Universidad de Sevilla.
8. CASTRO-HERNÁNDEZ, E., GUNDABALA, V., FERNÁNDEZ-NIEVES, A. & GORDILLO, J. M. 2009 Scaling the drop size in coflow experiments. New J. Phys. 11, 075021.
9. CASTRO-HERNÁ NDEZ, E., HOEVE, W., LOHSE, D. & GORDILLO, J. M. 2011 Microbubble generation in a co-flow device operated in a new regime. Lab on a Chip 11, 2023-2029.
10. FERNANDEZ DE LA MORA, J. 2007 The fluid dynamics of Taylor cones. Annu. Rev. Fluid Mech. 39, 217-243. (Pubitemid 46210830)
11. FERNANDEZ DE LA MORA, J. & LOSCERTALES, I. G. 1994 The current emitted by highly conducting Taylor cones. J. Fluid. Mech. 260, 155-184. (Pubitemid 279257)
12. GAÑÁN CALVO, A. M. 1998 Generation of steady liquid microthreads and micron-sized monodisperse sprays in gas streams. Phys. Rev. Lett. 80, 285-288.
13. GAÑÁN CALVO, A. M. & GORDILLO, J. M. 2001 Perfectly monodisperse microbubbling by capillary flow focusing. Phys. Rev. Lett. 87, 274501.
14. GARSTECKI, P., GITLIN, I., DILUZIO, W., WHITESIDES, G. M., KUMACHEVA, E. & STONE, H. A. 2004 Formation of monodisperse bubbles in a microfluidic flow-focusing device. Appl. Phys. Lett. 85, 2649-2651.
15. LADYZHENSKAYA, O. A. 1969 The Mathematical Theory of Viscous Incompressible Flows. Gordon & Breach.
16. LEAL, L. G. 2007 Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes. Cambridge University Press.
17. LOSCERTALES, I. G., BARRERO, A., GUERRERO, I., CORTIJO, R., MÁ RQUEZ, M. & GAÑÁN CALVO, A. M. 2002 Micro/nano encapsulation via electrified coaxial liquid jets. Science 295, 5560.
18. MAŔIN, A. G., CAMPO-CORTÉS, F. & GORDILLO, J. M. 2009 Generation of micron-sized drops and bubbles through viscous coflows. Colloids Surf. A: Physicochem. Engng Aspects 344, 2-7.
19. MAŔIN, A. G., LOSCERTALES, I. G., MÁRQUEZ, M. & BARRERO, A. 2007 Simple and double emulsions via coaxial jet electrosprays. Phys. Rev. Lett. 98, 014502.
20. POZRIKIDIS, C. 1992 Boundary Integral and Singularity Methods for Linearized Viscous Flows. Cambridge University Press.
21. RALLISON, J. M. 1984 The deformation of small viscous drops and bubbles in shear flows. Annu. Rev. Fluid Mech. 16, 45-66. (Pubitemid 14551167)
22. SHERWOOD, J. D. 1983 Tip streaming from slender drops in a nonlinear extensional flow. J. Fluid Mech. 144, 281-295. (Pubitemid 15437360)
23. SIEROU, A. & LISTER, J. R. 2003 Self-similar solutions for viscous capillary pinch-off. J. Fluid Mech. 497, 381-403. (Pubitemid 38171604)
24. STONE, H. A. 1994 Dynamics of drop deformation and breakup in viscous fluids. Annu. Rev. Fluid Mech. 26, 65-102. (Pubitemid 24987418)
25. STONE, H. A. & LEAL, L. G. 1989 Relaxation and breakup of an initially extended drop in an otherwise quiescent fluid. J. Fluid Mech. 198, 399-427.
26. STONE, H. A., STROOCK, A. D. & ADJARI, A. 2004 Engineering flows in small devices: microfluidics toward a lab-on-a-chip. Annu. Rev. Fluid Mech. 36, 381-411. (Pubitemid 38381916)
27. SURYO, R. & BASARAN, O. A. 2006 Tip streaming from a liquid drop forming from a tube in a co-flowing outer fluid. Phys. Fluids 18, 082102.
28. TAYLOR, G. I. 1964 Conical free surfaces and fluid interfaces. In Proceedings of the 11th International Congress of Applied Mechanics, Munich (ed. G. K. Batchelor), pp. 790-796. Springer.
29. TOMOTIKA, S. 1935 On the instability of a cylindrical thread of a viscous liquid surrounded by another viscous fluid. Proc. R. Soc. Lond. 150, 322-337.
30. UTADA, A. S., FERNÁNDEZ-NIEVES, A., STONE, H. A. & WEITZ, D. 2007 Dripping to jetting transitions in co-flowing liquid streams. Phys. Rev. Lett. 99, 094502.
31. WONG, H., RUMSCHITKI, D. & MALDARELLI, C. 1997 Theory and experiment on the low-Reynolds-number expansion and contraction of a bubble pinned at a submerged tip. J. Fluid Mech. 356, 93-124.
32. ZHANG, W. W. 2004 Viscous entrainment from a nozzle: singular liquid spouts. Phys. Rev. Lett. 93, 184502.
33. ZHANG, D. F. & STONE, H. A. 1997 Drop formation in viscous flows at a vertical capillary tube. Phys. Fluids 9, 2234-2242.