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
Your Session has timed out. Please sign back in to continue.



Grahic Jump Location
Figure 1

Flow domain geometry and boundary conditions

Grahic Jump Location
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)

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
Figure 5

Streamlines for the two equilibrium solutions observed for Re = 1




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In