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.
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e-mail: pswei@mail.nsysu.edu.tw
e-mail: hcy2126@cc.hwh.edu.tw
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Analytical Solution of a Creeping Flow Impinging on a Spherical Cap-Shaped Bubble on a Flat Solid Surface
P. S. Wei,
P. S. Wei
Professor
Fellow ASME
Department of Mechanical and Electro-Mechanical Engineering,
e-mail: pswei@mail.nsysu.edu.tw
National Sun Yat-Sen University
, Kaohsiung, Taiwan, ROC
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C. Y. Ho
C. Y. Ho
Associate Professor
Mechanical Engineering Department,
e-mail: hcy2126@cc.hwh.edu.tw
Hwa Hsia College of Technology and Commerce
, Taipei, Taiwan, ROC
Search for other works by this author on:
P. S. Wei
Professor
Fellow ASME
Department of Mechanical and Electro-Mechanical Engineering,
National Sun Yat-Sen University
, Kaohsiung, Taiwan, ROCe-mail: pswei@mail.nsysu.edu.tw
C. Y. Ho
Associate Professor
Mechanical Engineering Department,
Hwa Hsia College of Technology and Commerce
, Taipei, Taiwan, ROCe-mail: hcy2126@cc.hwh.edu.tw
J. Appl. Mech. May 2006, 73(3): 516-523 (8 pages)
Published Online: September 19, 2005
Article history
Received:
May 4, 2005
Revised:
September 19, 2005
Citation
Wei, P. S., and Ho, C. Y. (September 19, 2005). "Analytical Solution of a Creeping Flow Impinging on a Spherical Cap-Shaped Bubble on a Flat Solid Surface." ASME. J. Appl. Mech. May 2006; 73(3): 516–523. https://doi.org/10.1115/1.2126696
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