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Divergent streamlines and free vortices in Newtonian fluid flows in microfluidic flow-focusing devices

Published online by Cambridge University Press:  28 September 2012

M. S. N. Oliveira ,
F. T. Pinho  and
M. A. Alves
M. S. N. Oliveira*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Strathclyde, Glasgow G1 1XJ, UK Faculdade de Engenharia, Universidade do Porto, Centro de Estudos de Fenómenos de Transporte, Rua Dr Roberto Frias, 4200-465 Porto, Portugal
F. T. Pinho
Affiliation:
Faculdade de Engenharia, Universidade do Porto, Centro de Estudos de Fenómenos de Transporte, Rua Dr Roberto Frias, 4200-465 Porto, Portugal
M. A. Alves
Affiliation:
Faculdade de Engenharia, Universidade do Porto, Centro de Estudos de Fenómenos de Transporte, Rua Dr Roberto Frias, 4200-465 Porto, Portugal
*
†Email addresses for correspondence: monica.oliveira@fe.up.pt, monica.oliveira@strath.ac.uk
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Abstract

The appearance of divergent streamlines and subsequent formation of free vortices in Newtonian fluid flows through microfluidic flow-focusing geometries is discussed in this work. The micro-geometries are shaped like a cross-slot but comprise three entrances and one exit. The divergent flow and subsequent symmetric vortical structures arising near the centreline of the main inlet channel are promoted even under creeping flow conditions, and are observed experimentally and predicted numerically above a critical value of the ratio of inlet velocities (VR). As VR is further increased these free vortices continue to grow until a maximum size is reached due to geometrical constraints. The numerical calculations are in good agreement with the experimental observations and we probe numerically the effects of the geometric parameters and of inertia on the flow patterns. In particular, we observe that the appearance of the central recirculations depends non-monotonically on the relative width of the entrance branches and we show that inertia enhances the appearance of the free vortices. On the contrary, the presence of the walls in three-dimensional geometries has a stabilizing effect for low Reynolds numbers, delaying the onset of these secondary flows to higher VR. The linearity of the governing equations for creeping flow of Newtonian fluids was invoked to determine the flow field for any VR as a linear combination of the results of three other independent solutions in the same geometry.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows Micro-/Nano-fluid dynamics: Microfluidics Vortex Flows: Vortex dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 711 , 25 November 2012 , pp. 171 - 191
Copyright
Copyright © Cambridge University Press 2012

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