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Equilibrium Position of a Buoyant Drop in Couette and Poiseuille Flows at Finite Reynolds Numbers

Published online by Cambridge University Press:  16 October 2012

M. Bayareh  and
S. Mortazavi
M. Bayareh*
Affiliation:
Department of Mechanical Engineering, Young Researchers Club, Lamerd Branch, Islamic Azad University, Lamerd, Iran
S. Mortazavi
Affiliation:
Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran
*
*Corresponding author ([email protected])
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Abstract

The equilibrium position of a deformable drop in Couette and Poiseuille flows is investigated numerically by solving the full Navier-Stokes equations using a finite difference/front tracking method. The objective of this work is to study the motion of a non-neutrally buoyant drop in Couette and Poiseuille flows with different density ratios at finite Reynolds numbers. Couette flow: The equilibrium position of the lighter drops is higher than the heavier drops at each particle Reynolds number. Also, the equilibrium position height increases with increasing the Reynolds number at a fixed density ratio. At this equilibrium distance from the wall, the migration velocity is zero, while the velocity of the drop in the flow direction and rotational velocity of the drop is finite. It is observed that the equilibrium position is independent of the initial position of the drops and depends on the density ratio and the shear Reynolds number. Poiseuille flow: When the drop is slightly buoyant, it moves to an equilibrium position between the wall and the centerline. The equilibrium position is close to the centerline if the drop lags the fluid but close to the wall if the drop leads the fluid. As the Reynolds number increases, the equilibrium position of lighter drops moves slightly closer to the wall and the equilibrium position of heavier drops moves towards the centerline.

Keywords

Couette flowPoiseuille flowFinite difference methodFront tracking methodDensity ratioReynolds number
Type
Articles
Information
Journal of Mechanics , Volume 29 , Issue 1 , March 2013 , pp. 53 - 58
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2012

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References

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