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Microfluidics and Nanofluidics

, Volume 8, Issue 6, pp 799–812 | Cite as

Effect of geometry on droplet formation in the squeezing regime in a microfluidic T-junction

  • Amit Gupta
  • Ranganathan Kumar
Research Paper

Abstract

In the surface tension-dominated microchannel T-junction, droplets can be formed as a result of the mixing of two dissimilar, immiscible fluids. This article presents results for very low Capillary numbers and different flow rates of the continuous and dispersed phases. Through three-dimensional lattice Boltzmann-based simulations, the mechanism of the formation of “plugs” in the squeezing regime has been examined and the size of the droplets quantified. Results for \( Re_{\text{c}} \ll 1\) show the dependence of flow rates of the two fluids on the length of the droplets formed, which is compared with existing experimental data. It is shown that the size of plugs formed decreases as the Capillary number increases in the squeezing regime. This article clearly shows that the geometry effect, i.e., the widths of the two channels and the depth of the assembly, plays an important role in the determination of the length of the plugs, a fact that was ignored in earlier experimental correlations.

Keywords

Microfluidics Capillary number Lattice Boltzmann Multiphase flow 

List of symbols

a

Acceleration

a

Index for velocity-space discretization

\( \bar{b} \)

Dimensionless length of the emerging droplet

c

Lattice unit length

C

Color field

Ca

Capillary number = μ c U c

cs

Speed of sound

D

Diameter of the drop

ei

Lattice speed of particles moving in direction i

f

Particle distribution function

F

Force

I

Unit tensor

L

Droplet length

n

Normal vector at the interface

N

Number of links at each lattice point

p

Pressure

p

Momentum

Q

Flow rate/ratio

r

Radius of the drop

Re

Reynolds number = UD/ν

t

Time

U

Velocity

V

Droplet volume

w

Width of the channel/weight along link

Greek symbols

β

Parameter controlling the width of the interface

γ

Lattice weights

δαβ

Kronecker delta

κ

Curvature

λ

Viscosity ratio

ρ

Density

σ

Surface tension

μ

Dynamic viscosity

ν

Kinematic viscosity

τ

Relaxation time

φ

Angle

Gradient

Γ

Height-to-width ratio

Λ

Dispersed-to-continuous channel width ratio

Ω

Collision operator

Subscripts

B

Blue fluid

c

Continuous phase

d

Dispersed phase

eff

Effective

ext

External

growth

Growth

i

Index

in

Inside the drop

out

Outside the drop

R

Red fluid

Spur

Spurious

x

x-component

y

y-component

Superscripts

*

Non-dimensional quantities

eq

Equilibrium

References

  1. Anna SL, Bontoux N, Stone HA (2003) Formation of dispersions using ‘flow focusing’ in microchannels. Appl Phys Lett 82(3):364–366CrossRefGoogle Scholar
  2. Chen S, Doolen GD (1998) Lattice Boltzmann method for fluid flows. Ann Rev Fluid Mech 30:329–364CrossRefMathSciNetGoogle Scholar
  3. Christopher GF, Anna SL (2007) Microfluidic methods for generating droplet streams. J Phys D 40:R319–R336CrossRefGoogle Scholar
  4. Christopher GF, Noharuddin NN, Taylor JA, Anna SL (2008) Experimental observations of the squeezing-to-dripping transition in T-shaped microfluidic junctions. Phys Rev E 78:036317CrossRefGoogle Scholar
  5. Cramer C, Fischer P, Windhab EJ (2004) Drop formation in a co-flowing ambient fluid. Chem Eng Sci 59:3045–3058CrossRefGoogle Scholar
  6. De Menech M, Garstecki P, Jousse F, Stone HA (2008) Transition from squeezing to dripping in a microfluidic T-shaped junction. J Fluid Mech 595:141–161zbMATHGoogle Scholar
  7. Garstecki P, Stone HA, Whitesides GM (2005) Mechanism for flow-rate controlled breakup in confined geometries: a route to monodisperse emulsions. Phys Rev Lett 94:164501CrossRefGoogle Scholar
  8. Garstecki P, Fuerstman MJ, Stone HA, Whitesides GM (2006) Formation of droplets and bubbles in a microfluidic T-junction—scaling and mechanism of break-up. Lab Chip 6:437–446CrossRefGoogle Scholar
  9. Gu X, Gupta A, Kumar R (2009) Lattice Boltzmann simulation of surface impingement at high density ratio. J Thermophys Heat Trans (in print)Google Scholar
  10. Guillot P, Colin A (2005) Stability of parallel flows in a microchannel after a T-junction. Phys Rev E 72:066301CrossRefGoogle Scholar
  11. Gunstensen AK, Rothman DH, Zaleski S, Zanetti G (1991) Lattice Boltzmann model of immiscible fluids. Phys Rev A 43:4320–4327CrossRefGoogle Scholar
  12. Gupta A, Kumar R (2008) Lattice Boltzmann simulation to study multiple bubble dynamics. Int J Heat Mass Transf 51:5192–5203zbMATHCrossRefGoogle Scholar
  13. Gupta A, Murshed SMS, Kumar R (2009) Droplet formation and stability of flows in a microfluidic T-junction. Appl Phys Lett 94:161407Google Scholar
  14. Husny J, Cooper-White JJ (2006) The effect of elasticity on drop creation in T-shaped microchannels. J Non-Newton Fluid Mech 137:121–136CrossRefGoogle Scholar
  15. Inamuro T, Tajima S, Ogino F (2004) Lattice Boltzmann simulation of droplet collision dynamics. Int J Heat Mass Transf 47:4649–4657zbMATHCrossRefGoogle Scholar
  16. Latva-Kokko M, Rothman DH (2005) Diffusion properties of gradient-based lattice Boltzmann models of immiscible fluids. Phys Rev E 71:056702CrossRefGoogle Scholar
  17. Lishchuk SV, Care CM, Halliday I (2003) Lattice Boltzmann algorithm for surface tension with greatly reduced microcurrents. Phys Rev E 67:036701CrossRefGoogle Scholar
  18. Lishchuk SV, Halliday I, Care CM (2008) Multicomponent lattice Boltzmann method for fluids with a density contrast. Phys Rev E 77:036702CrossRefGoogle Scholar
  19. Shan X, Chen H (1993) Lattice Boltzmann model for simulating flows with multiple phases and components. Phys Rev E 47:1815–1819CrossRefGoogle Scholar
  20. Swift M, Osborne W, Yeomans J (1995) Lattice Boltzmann simulation of nonideal fluids. Phys Rev Lett 75:830–833CrossRefGoogle Scholar
  21. Thorsen T, Roberts RW, Arnold FH, Quake SR (2001) Dynamic pattern formation in a vesicle-generating microfluidic device. Phys Rev Lett 86(18):4163–4166CrossRefGoogle Scholar
  22. Tice JD, Lyon AD, Ismagilov RF (2004) Effects of viscosity on droplet formation and mixing in microfluidic channels. Anal Chim Acta 507:73–77CrossRefGoogle Scholar
  23. Umbanhowar PB, Prasad V, Weitz DA (2000) Monodisperse emulsion generation via drop break off in a coflowing stream. Langmuir 16:347–351CrossRefGoogle Scholar
  24. Van der Graaf S, Nisisako T, Schroën CGPH, van der Sman RGM, Boom RM (2006) Lattice Boltzmann simulations of droplet formation in a T-shaped microchannel. Langmuir 22:4144–4152CrossRefGoogle Scholar
  25. Wu L, Tsutahara M, Kim LS, Ha MY (2008) Three-dimensional lattice Boltzmann simulations of droplet formation in a cross-junction microchannel. Int J Multiph Flow 34:852–864CrossRefGoogle Scholar
  26. Xu JH, Li SW, Tan J, Luo GS (2008) Correlations of droplet formation in T-junction microfluidic devices: from squeezing to dripping. Microfluid Nanofluid 5:711–717CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of Aerospace EngineeringUniversity of MichiganAnn ArborUSA
  2. 2.Department of Mechanical, Materials and Aerospace EngineeringUniversity of Central FloridaOrlandoUSA

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