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The effect of weak-inertia on droplet formation phenomena in T-junction microchannel

Meccanica volume 51, pages 819–834 (2016)Cite this article

Abstract

We present droplet formation in a T-junction microfluidic device in five different regimes of squeezing, dripping, transition, jetting and parallel. Droplet is created as a result of interaction of two immiscible liquids. Effects of Capillary number (Ca) and Reynolds number (Re) are investigated which changes the regime of droplet formation and creates rotational flow inside droplet, respectively. Simulations were done with the open source code Gerris using volume of fluid method and adaptive mesh refinement techniques in order to track interface properly. Two kinds of jetting regimes, i.e., stable and unstable, were simulated in this work. For higher Re number the parallel regime is observed so Re number is limited to 25. This study shows that the results of Re > 1 have some differences compared with those of Re < 1. Using the effect of inertial forces, transition regime is limited to a range of Ca number. Simulations indicate that new vortices are created due to effect of inertial forces at a moment after droplet detachment, while it is fully creeping flow for Re < 1. The vortices which have appeared at the tail of droplet will become weaker with time. Also, at the downstream, two rotational flows were observed in droplet for both Re > 1 and Re < 1 which are due to wall shear stresses. Droplets with rotational flow can increase diffusivity, which is motivation of this work.

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Abbreviations

C :

Tracer for multi-fluid interface

\( \tilde{c} \) :

Spatial filter

D :

Deformation tensor

L :

Droplet length

m :

Local normal to the interface

n :

Normal vector at the interface

p :

Pressure

Q :

Flow rate ratio = \( {\raise0.7ex\hbox{${Q_{c} }$} \!\mathord{\left/ {\vphantom {{Q_{c} } {Q_{d} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${Q_{d} }$}} \)

R :

Radius of curvature of interface

u :

Velocity vector

w:

Channel width

x :

Position vector

κ :

Radius of curvature of the interface

μ :

Dynamic viscosity

λ :

Viscosity ratio = \( {\raise0.7ex\hbox{${\mu_{d} }$} \!\mathord{\left/ {\vphantom {{\mu_{d} } {\mu_{c} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\mu_{c} }$}} \)

θ :

Angle

ρ :

Density

∇:

Gradient of parameters

Δ:

Difference operator

Bo:

Bond number = gravitational/interfacial forces

Ca:

Capillary number = \( {\raise0.7ex\hbox{${u_{c} \mu_{c} }$} \!\mathord{\left/ {\vphantom {{u_{c} \mu_{c} } \gamma }}\right.\kern-0pt} \!\lower0.7ex\hbox{$\gamma $}} \)

Re:

Reynolds number of the continuous phase = \( {\raise0.7ex\hbox{${u_{\text{c}} \rho_{\text{c}} {\text{w}}}$} \!\mathord{\left/ {\vphantom {{u_{\text{c}} \rho_{\text{c}} {\text{w}}} {\mu_{\text{c}} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\mu_{\text{c}} }$}} \)

Red :

Reynolds number of the dispersed phase = \( {\raise0.7ex\hbox{${u_{\text{d}} \rho_{\text{d}} {\text{w}}}$} \!\mathord{\left/ {\vphantom {{u_{\text{d}} \rho_{\text{d}} {\text{w}}} {\mu_{\text{d}} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\mu_{\text{d}} }$}} \)

α :

Determine volume fraction

δ :

Dirac delta function

σ :

Surface tension

γ :

Interfacial tension = |σ c  − σ d |

c:

Continuous phase

d:

Dispersed phase

t:

Time

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Authors and Affiliations

  1. Graduate Student of Mechanical Engineering, Babol University of Technology, Babol, Islamic Republic of Iran

    Milad Azarmanesh

  2. Faculty of Mechanical Engineering, Babol University of Technology, P.O. Box 484, Babol, Islamic Republic of Iran

    Mousa Farhadi

Authors
  1. Milad Azarmanesh
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  2. Mousa Farhadi
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Correspondence to Milad Azarmanesh.

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Azarmanesh, M., Farhadi, M. The effect of weak-inertia on droplet formation phenomena in T-junction microchannel. Meccanica 51, 819–834 (2016). https://doi.org/10.1007/s11012-015-0245-6

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  • DOI: https://doi.org/10.1007/s11012-015-0245-6

Keywords

  • Droplet formation
  • T-junction
  • Reynolds number
  • Microchannel
  • VOF