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Modeling of Newtonian droplet formation in power-law non-Newtonian fluids in a flow-focusing device

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Abstract

Droplet formation in a flow-focusing device was modeled using the open source CFD package, OpenFOAM, with the VOF model for two-phase flow. Predictions using the interFoam solver and a power-law non-Newtonian model were first validated against experimental data in the literature. Then, the formation of Newtonian fluid droplets in power-law fluids was modeled during tubing, squeezing, dripping and jetting. The effects of the continuous phase rheological parameters on the droplet formation were investigated by changing the power law index (n) and the consistency coefficient (K). The results show that the droplet length and the spacing between two droplets decrease as n or K increase. However, the formation frequency and droplet velocity in the main channel increase as n or K increase. The results also show that n has a greater effect than K on the droplet formation. A method was developed to calculate the capillary number of the power-law continuous phase in the squeezing and dripping regimes including the influences of n and K. For a given dispersed phase flow rate, the formation frequency is inversely proportional to the droplet volume. A scaling law was also developed to predict the formation frequency since the droplet volume is found to vary linearly with the non-dimensional droplet length. The present work is useful for controlling droplet formation and designing microfluidic devices in areas where non-Newtonian fluids are used as the continuous phase.

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Abbreviations

a, a’, b, b’, ε, ε’, ω, ω’ :

fitting parameters

C α :

compression factor

d :

spacing between two droplets, μm

d h :

channel hydraulic diameter, μm

f :

droplet formation frequency, Hz

f σ :

surface tension, N∙m−3

g :

gravitational acceleration, m∙s−2

K :

consistency coefficient of power-law fluids, Pa∙sn

L :

droplet length, μm

Lblock, Lsqueeze :

droplet length increase, μm

L d :

characteristic length, μm

L e :

channel flow development length, μm

M w :

unit tangential vector

n :

power-law index of power-law fluids

N :

normal vector

N w :

unit normal vector

p :

pressure, Pa

Q c :

continuous flow rate, μL/h

Q d :

dispersed flow rate, μL/h

r :

final droplet radius, μm

S :

cross sectional area, μm2

t :

time, s

u :

velocity vector, m∙s−1

u c :

average velocity of the continuous phase, m∙s−1

u r :

interface-compression velocity, m∙s−1

v :

droplet velocity, m∙s−1

V :

droplet volume, m3

W c :

channel width, μm

α :

volume fraction

γ :

rate-of-strain tensor, s−1

μ :

volume-averaged viscosity, Pa∙s

ρ :

volume-averaged density, kg∙m−3

κ :

interfacial curvature

σ :

surface tension coefficient, N∙m−1

θ w :

contact angle, °

∆ρ :

density difference, kg∙m−3

∆t :

time step, s

∆x :

mesh spacing, μm

*:

dimensionless parameter

c:

continuous phase

d:

dispersed phase

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Funding

This study was funded by the National Natural Science Foundation of China (No. 51706125).

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Authors and Affiliations

  1. Institute of Thermal Science and Technology, Shandong University, 17923 Jingshi Road, Jinan, 250061, China

    Qi Chen, Jingkun Li & Xuefang Li

  2. Department of Energy and Power Engineering, Tsinghua University, 30 Shuangqing Road, Beijing, 100084, China

    Yu Song & David M Christopher

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  1. Qi Chen
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Chen, Q., Li, J., Song, Y. et al. Modeling of Newtonian droplet formation in power-law non-Newtonian fluids in a flow-focusing device. Heat Mass Transfer 56, 2711–2723 (2020). https://doi.org/10.1007/s00231-020-02899-6

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  • DOI: https://doi.org/10.1007/s00231-020-02899-6

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