Technical Briefs

Force on a Small Particle Attached to a Plane Wall in a Hiemenz Straining Flow

[+] Author and Article Information
A. B. Maynard

 School of Engineering, The University of Vermont, Burlington, VT 05405

J. S. Marshall1

 School of Engineering, The University of Vermont, Burlington, VT 05405jeffm@cems.uvm.edu


Corresponding author.

J. Fluids Eng 134(11), 114502 (Oct 24, 2012) (5 pages) doi:10.1115/1.4007742 History: Received February 27, 2012; Revised August 07, 2012; Published October 24, 2012

The force acting on a spherical particle fixed to a wall and immersed in an axisymmetric straining flow is examined for small Reynolds numbers. The steady, incompressible flow field is computed using an axisymmetric finite-volume method over conditions spanning five decades in the Reynolds number. The flow is characterized by the formation of a vortex ring structure in the wedge region formed between the particle lower surface and the plane wall. A power law expression for the dimensionless particle force is obtained as a function of the Reynolds number, which is found to hold with excellent accuracy for Reynolds numbers below about 0.1.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 2

Total number of grid elements (N) in the inner region (up to 10 diameters from the particle) plotted against the dimensionless force for R = h = 40 (squares/dashed line), R = h = 50 (circles/dash-dotted line), and R = h = 60 (triangles/solid line)

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Figure 3

Streamlines and contours of the velocity magnitude for the flow field about the spherical particle in the r-z plane, for a case with Re = 0.1. The streamlines are directed downward and radially outward in the ambient straining flow.

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Figure 4

Log-log plot of the dimensionless force F plotted versus straining-flow Reynolds number. The correlation given by Eq. 8 is plotted as a straight line.

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Figure 5

Streamlines for the two equilibrium solutions observed for Re = 1

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Figure 1

Flow domain geometry and boundary conditions




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