Microfluidics and Nanofluidics

, Volume 19, Issue 5, pp 1101–1108

Numerical analysis of mixing performance in sinusoidal microchannels based on particle motion in droplets

Research Paper

DOI: 10.1007/s10404-015-1628-7

Cite this article as:
Özkan, A. & Erdem, E.Y. Microfluid Nanofluid (2015) 19: 1101. doi:10.1007/s10404-015-1628-7


This numerical study was conducted to analyze and understand the parameters that affect the mixing performance of droplet-based flow in sinusoidal microfluidic channels. Finite element analysis was used for modeling fluid flow and droplet formation inside the microchannels via tracking interface between the two heterogeneous fluids along with multiple particle trajectories inside a droplet. The solutions of multiphase fluid flow and particle trajectories were coupled with each other so that drag on every single particle changed in every time step. To solve fluid motion in multiphase flow, level set method was used. Parametric study was repeated for different channel dimensions and different sinusoidal channel profiles. These results were compared with mixing in droplets inside a straight microchannel. Additionally, tracking of multiple particles inside a droplet was performed to simulate the circulating flow profile inside the droplets. Based on the calculation of the dispersion length, particle trajectories, and velocities inside droplets, it is concluded that having smaller channel geometries increases the mixing performance inside the droplet. This also shows that droplet-based fluid flow in microchannels is very suitable for performing chemical reactions inside droplets as it will occur faster. Moreover, narrower and sinusoidal microchannels showed better dispersion length difference compared to straight and wider microchannels.


Droplet-based microfluidics Dispersion length Mixing performance Microfluidics Droplet formation Level set method 

List of symbols

\({d}_{{\text {effective}}}\)

Effective droplet diameter

\({F}_{{\text {drag}}}\)

Drag force on spherical particle

\({F}_{{\text {st}}}\)

Surface tension force


Length of the droplet


Flow velocity

\({u}_{{\text {rel}}}\)

Relative velocity of particle



\({t}_{{\text {corr.}}}\)

Corresponding time for maximum dispersion length occurrence




Particle 1


Particle 2


Particle radius

\({r}_{{\text {i}}}\)

Inner radius of sinusoidal channel

\({r}_{{\text {c}}}\)

Central radius of sinusoidal channel

\({r}_{{\text {o}}}\)

Outer radius of sinusoidal channel

\({l}_{{\text {diff,3D}}}\)

Three-dimensional dispersion length

\({l}_{{\text {diff,max}}}\)

Maximum dispersion length difference between particles


Level set function

\(\epsilon , \gamma\)

Numerical stabilization parameters of level set function




Dynamic viscosity

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringBilkent UniversityAnkaraTurkey