Analytical Solution of a Creeping Flow Impinging on a Spherical Cap-Shaped Bubble on a Flat Solid Surface

[+] Author and Article Information
P. S. Wei1

Department of Mechanical and Electro-Mechanical Engineering,  National Sun Yat-Sen University, Kaohsiung, Taiwan, ROCpswei@mail.nsysu.edu.tw

C. Y. Ho

Mechanical Engineering Department,  Hwa Hsia College of Technology and Commerce, Taipei, Taiwan, ROChcy2126@cc.hwh.edu.tw


To whom correspondence should be addressed.

J. Appl. Mech 73(3), 516-523 (Sep 19, 2005) (8 pages) doi:10.1115/1.2126696 History: Received May 04, 2005; Revised September 19, 2005

In this study, a general, analytical solution of a steady creeping or Stokes flow impinging on a stationary spherical cap-shaped bubble on a solid flat surface is provided. The phenomena usually take place in bubble∕pore formation in materials and manufacturing processing and MEMS, boiling heat transfer, and nucleation and growth of gas bubbles in tissues of animals and human, etc. In view of high capillary pressure and small liquid pressure, the shape of the bubble in a microscale can be considered as a spherical cap on a surface. In this model, shear stresses associated with the no-slip condition, interfacial mass transport such as condensation and evaporation are absent on the bubble surface. An analytical solution of the Stokes equations for zero Reynolds number flow in a toroidal coordinate system is found by decomposing the flow into a stagnation flow and a flow disturbed by the bubble and applying the separation-of-variables method. The stream function can be expressed in terms of a difference in Legendre functions of the first kind. The effects of impinging velocity and contact angle of the bubble on the flow pattern and pressure distribution are provided.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Physical model and coordinate system

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Figure 2

Relationship between toroidal and cylindrical coordinate systems

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Figure 3

Streamlines around a bubble in different shapes of spherical cap, (a) ηc=1, and (b) ηc=0.5, on flat solid surface for dimensionless height of domain H=10

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Figure 4

Streamlines around a spherical cap-shaped bubble with cap coordinate ηc=0.5 on flat solid surface for different dimensionless heights of domain: (a) H=5 and (b) H=20

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Figure 5

(a) Shapes and (b) pressure distributions around bubble surface

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Figure 6

The locus for the location of zero tangential velocity on the cap for different cap shapes




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