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Numerical simulation of the droplet formation in a cross-junction microchannel using the Lattice Boltzmann Method

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Abstract

This study describes the numerical simulation of two-dimensional droplet formation and the following motion by using the Lattice Boltzmann Method (LBM) with the phase field equation. The free energy model is used to treat the interfacial force and the deformation of a binary fluid system, drawn into a cross-junction microchannel. While one fluid is introduced through the central inlet channel, the other fluid is drawn into the main channel through the two vertical inlet channels. Due to the effect of surface tension on the interface between the two fluids, the droplets of the first fluid are formed near the cross-junction. The aim in this investigation is to examine the applicability of LBM to the numerical analysis of the droplet formation and its motion in the microchannel. It was found from comparison with the experimentally visualized patterns that LBM with the free energy model can reproduce the droplet formation successfully. However because of the stability problem which is intrinsic for high surface-tension cases, it requires a very long computational time. This issue is to be resolved in the future.

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Abbreviations

c :

Reference velocity

E :

Error

e :

Discrete particle velocity

F :

Free-energy function

f i :

Distribution function of the total density

f i :

Distribution function of the total density after the collision process

g i :

Distribution function of the density difference

g i :

Distribution function of the density difference after the collision process

P αβ :

Pressure tensor

Δt :

Time step

u :

Fluid velocity

U in :

Maximum velocity at the horizontal inlet

ũ j :

Normalized velocity

u j :

Normalized exact solution

V in :

Maximum velocity at the vertical inlet

Δx:

Space step

Γ:

Mobility coefficient of the fluids

Δμ:

Chemical potential difference

ξ:

Interfacial width

ρ:

Total density of both fluids

ρ a :

Density of fluid A

ρ b :

Density of fluid B

ρ *0 :

Reference density (dimensional)

σ:

Surface tension at the interface

ν:

Kinematic viscosity of both fluids

φ:

Density difference between fluid A and B

*:

Dimensional variable

eq:

Equilibrium term

a:

Fluid A

b:

Fluid B

i :

Link number

in:

Inlet

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Authors and Affiliations

  1. Department of Mechanical Engineering, Dong-A University, 840 Hadandong, Sahagu, 604-714, Busan, Korea

    Zilu Li, Jinfen Kang, Jae Hyun Park & Yong Kweon Suh

Authors
  1. Zilu Li
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  2. Jinfen Kang
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  3. Jae Hyun Park
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  4. Yong Kweon Suh
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Corresponding author

Correspondence to Yong Kweon Suh.

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Li, Z., Kang, J., Park, J.H. et al. Numerical simulation of the droplet formation in a cross-junction microchannel using the Lattice Boltzmann Method. J Mech Sci Technol 21, 162–173 (2007). https://doi.org/10.1007/BF03161722

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  • DOI: https://doi.org/10.1007/BF03161722

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