Skip to main content
SpringerLink
Log in

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

  • Research Paper
  • Published:
Microfluidics and Nanofluidics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

Abbreviations

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 /σ

c s :

Speed of sound

D :

Diameter of the drop

e i :

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

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

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

*:

Non-dimensional quantities

eq:

Equilibrium

References

  • Anna SL, Bontoux N, Stone HA (2003) Formation of dispersions using ‘flow focusing’ in microchannels. Appl Phys Lett 82(3):364–366

    Article  Google Scholar 

  • Chen S, Doolen GD (1998) Lattice Boltzmann method for fluid flows. Ann Rev Fluid Mech 30:329–364

    Article  MathSciNet  Google Scholar 

  • Christopher GF, Anna SL (2007) Microfluidic methods for generating droplet streams. J Phys D 40:R319–R336

    Article  Google Scholar 

  • 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 78:036317

    Article  Google Scholar 

  • Cramer C, Fischer P, Windhab EJ (2004) Drop formation in a co-flowing ambient fluid. Chem Eng Sci 59:3045–3058

    Article  Google Scholar 

  • De Menech M, Garstecki P, Jousse F, Stone HA (2008) Transition from squeezing to dripping in a microfluidic T-shaped junction. J Fluid Mech 595:141–161

    MATH  Google Scholar 

  • Garstecki P, Stone HA, Whitesides GM (2005) Mechanism for flow-rate controlled breakup in confined geometries: a route to monodisperse emulsions. Phys Rev Lett 94:164501

    Article  Google Scholar 

  • 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 6:437–446

    Article  Google Scholar 

  • Gu X, Gupta A, Kumar R (2009) Lattice Boltzmann simulation of surface impingement at high density ratio. J Thermophys Heat Trans (in print)

  • Guillot P, Colin A (2005) Stability of parallel flows in a microchannel after a T-junction. Phys Rev E 72:066301

    Article  Google Scholar 

  • Gunstensen AK, Rothman DH, Zaleski S, Zanetti G (1991) Lattice Boltzmann model of immiscible fluids. Phys Rev A 43:4320–4327

    Article  Google Scholar 

  • Gupta A, Kumar R (2008) Lattice Boltzmann simulation to study multiple bubble dynamics. Int J Heat Mass Transf 51:5192–5203

    Article  MATH  Google Scholar 

  • Gupta A, Murshed SMS, Kumar R (2009) Droplet formation and stability of flows in a microfluidic T-junction. Appl Phys Lett 94:161407

    Google Scholar 

  • Husny J, Cooper-White JJ (2006) The effect of elasticity on drop creation in T-shaped microchannels. J Non-Newton Fluid Mech 137:121–136

    Article  Google Scholar 

  • Inamuro T, Tajima S, Ogino F (2004) Lattice Boltzmann simulation of droplet collision dynamics. Int J Heat Mass Transf 47:4649–4657

    Article  MATH  Google Scholar 

  • Latva-Kokko M, Rothman DH (2005) Diffusion properties of gradient-based lattice Boltzmann models of immiscible fluids. Phys Rev E 71:056702

    Article  Google Scholar 

  • Lishchuk SV, Care CM, Halliday I (2003) Lattice Boltzmann algorithm for surface tension with greatly reduced microcurrents. Phys Rev E 67:036701

    Article  Google Scholar 

  • Lishchuk SV, Halliday I, Care CM (2008) Multicomponent lattice Boltzmann method for fluids with a density contrast. Phys Rev E 77:036702

    Article  Google Scholar 

  • Shan X, Chen H (1993) Lattice Boltzmann model for simulating flows with multiple phases and components. Phys Rev E 47:1815–1819

    Article  Google Scholar 

  • Swift M, Osborne W, Yeomans J (1995) Lattice Boltzmann simulation of nonideal fluids. Phys Rev Lett 75:830–833

    Article  Google Scholar 

  • Thorsen T, Roberts RW, Arnold FH, Quake SR (2001) Dynamic pattern formation in a vesicle-generating microfluidic device. Phys Rev Lett 86(18):4163–4166

    Article  Google Scholar 

  • Tice JD, Lyon AD, Ismagilov RF (2004) Effects of viscosity on droplet formation and mixing in microfluidic channels. Anal Chim Acta 507:73–77

    Article  Google Scholar 

  • Umbanhowar PB, Prasad V, Weitz DA (2000) Monodisperse emulsion generation via drop break off in a coflowing stream. Langmuir 16:347–351

    Article  Google Scholar 

  • 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 22:4144–4152

    Article  Google Scholar 

  • 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 34:852–864

    Article  Google Scholar 

  • Xu JH, Li SW, Tan J, Luo GS (2008) Correlations of droplet formation in T-junction microfluidic devices: from squeezing to dripping. Microfluid Nanofluid 5:711–717

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, 48109, USA

    Amit Gupta

  2. Department of Mechanical, Materials and Aerospace Engineering, University of Central Florida, Orlando, FL, 32816, USA

    Ranganathan Kumar

Authors
  1. Amit Gupta
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ranganathan Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ranganathan Kumar.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gupta, A., Kumar, R. Effect of geometry on droplet formation in the squeezing regime in a microfluidic T-junction. Microfluid Nanofluid 8, 799–812 (2010). https://doi.org/10.1007/s10404-009-0513-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10404-009-0513-7

Keywords

Search

Navigation