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Zeitschrift für angewandte Mathematik und Physik

, Volume 66, Issue 1, pp 149–169 | Cite as

Stokes flow in a two-dimensional micro-device combined by a cross-slot and a microfluidic four-roll mill

  • Jing Guan
  • Jinxia Liu
  • Xiaoduan Li
  • Jun Tao
  • Jingtao WangEmail author
Article

Abstract

The flow structures in a novel microfluidics device (CS-MFRM) combining a cross-slot (CS) and a microfluidics four-roll mill (MFRM) have been investigated through a two-dimensional boundary element method. By changing the volume flow rates at various inlets of a CS-MFRM, diverse flow structures can be generated. Some of them are proposed to be employed to achieve some functions in the fabrication process of anisotropic particles. The stagnant points and eddies in those flows are particularly discussed since they are critical to trap and/or rotate droplets. Energy consumption of eddies generated in branches in some flow structures is also investigated in this paper.

Mathematics Subject Classification (2000)

76D07 76T25 

List of symbols

μ

The viscosity of continuous phase

λ

The viscosity ratio of the droplet to the continuous phase

G

Shear rate

p

Pressure

u

Velocity vector

f

Surface stress

Sij

Fundamental solution of the two-dimensional Stokes equations

Tijk

Associated stress kernel of the fundamental solution

Q

Volume flow rate in a channel

w0

Half width of a channel

rc

Radius of central circular cavity

Keywords

Boundary element method Microchannels Stagnation points Flow branches Stokes eddies 

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  • Jing Guan
    • 1
  • Jinxia Liu
    • 2
  • Xiaoduan Li
    • 2
  • Jun Tao
    • 2
  • Jingtao Wang
    • 2
    • 3
    Email author
  1. 1.School of ScienceTianjin UniversityTianjinPeople’s Republic of China
  2. 2.School of Chemical Engineering and TechnologyTianjin UniversityTianjinPeople’s Republic of China
  3. 3.State Key Laboratory of Chemical EngineeringTianjin UniversityTianjinPeople’s Republic of China

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