Gravity-induced swirl of nanoparticles in microfluidics

Research Paper

DOI: 10.1007/s11051-013-1611-8

Cite this article as:
Zhao, C., Oztekin, A. & Cheng, X. J Nanopart Res (2013) 15: 1611. doi:10.1007/s11051-013-1611-8


Parallel flows of two fluids in microfluidic devices are used for miniaturized chemistry, physics, biology and bioengineering studies, and the streams are often considered to remain parallel. However, as the two fluids do not always have the same density, interface reorientation induced by density stratification is unavoidable. In this paper, flow characteristics of an aqueous polystyrene nanofluid and a sucrose-densified aqueous solution flowing parallel in microchannels are examined. Nanoparticles 100 nm in diameter are used in the study. The motion of the nanoparticles is simulated using the Lagrangian description and directly observed by a confocal microscope. Matched results are obtained from computational and empirical analysis. Although solution density homogenizes rapidly resulting from a fast diffusion of sucrose in water, the nanofluid is observed to rotate for an extended period. Angular displacement of the nanofluid depends on the ratio of gravitational force to viscous force, Re/Fr2, where Re is the Reynolds number and Fr is the Froude number. In the developing region at the steady state, the angular displacement is related to y/Dh, the ratio between distance from the inlet and the hydraulic diameter of the microfluidic channel. The development of nanofluid flow feature also depends on h/w, the ratio of microfluidic channel’s height to width. The quantitative description of the angular displacement of nanofluid will aid rational designs of microfluidic devices utilizing multistream, multiphase flows.


Microfluidics Density stratification Nanoparticles Angular displacement Miscible fluids 

List of symbols

x, y, z (μm)

Spatial coordinates

h (μm)

Microfluidic channel height

w (μm)

Microfluidic channel width

l (μm)

Microfluidic channel length

Dh (μm)

Microfluidic channel hydraulic diameter

Lp (μm)

Developing length

ρ (kg m−3)

Density of the fluid

μ (Pa s)

Viscosity of the fluid

p (Pa)

Static pressure

\( \overline{\overline{\tau }} \) (Pa)

Stress tensor

\( \vec{g} \) (m s−2)

Gravitational acceleration

\( \vec{u} \) (m s−1)

Fluid phase velocity


Local mass fraction of each species

Di,m (m2 s−1)

Diffusion coefficient of species i in the mixture

\( \rho_{\text{P}} \) (kg m−3)

Density of the particles

dp (μm)

Particle diameter

\( \vec{u}_{\text{p}} \) (m s−1)

Particle velocity

\( \dot{m}_{\text{p}} \) (kg s−1)

Mass flow rate of the particles

\( \Updelta t \) (s)

Time step

\( C_{\text{D}} \)

Drag coefficient

\( F_{\text{D}} \) (kg m s−2)

Drag force

T (K)

Absolute temperature of the fluid


Boltzmann constant

di,j (Pa)

Deformation tensor


Froude number


Reynolds number

\( Re_{\text{p}} \)

Relative Reynolds number

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Materials Science and Engineering and Bioengineering ProgramLehigh UniversityBethlehemUSA
  2. 2.Department of Mechanical Engineering and MechanicsLehigh UniversityBethlehemUSA

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