Derivation of Stokeslet Green's Function

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In summary, the conversation discusses the derivation of the free-space Green's function for the velocity field generated by a point force in a fluid (the Stokeslet). The conversation also mentions the difficulty in understanding how it becomes a tensor and provides a few articles that may help with the derivation. These articles focus on different aspects of the problem, such as the asymptotic approximation of the Green's tensor, fluid-structure coupling, and parametric problems.
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KRP
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Derivation of "stokeslet"

Ok, so basically I cannot find ANYWHERE the step-by-step derivation of the free-space Green's function for the velocity field generated by a point force in a fluid (the Stokeslet).


I have not for the life of my got a clue why it somehow turns into a tensor along the way...?

help appreciated.
 
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This thread got no love in the Homework Forum. Maybe it will have better luck here in Engineering.
 
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your journey continues

Hey KRP,

Try these articles. I don't think they have EXACTLY the information you need but might be able to lead you to it - a couple mention other methods, etc.. I tried to upload the pdf's for these but the limit is 50kB. If you're interested in giving them a look, you can try to obtain them from Science Direct OR I can email them to you. I'll try to check back to see what you want to do.

Hope it helps

Uniform asymptotic approximation of the evanescent part of the Green's tensor • SHORT COMMUNICATION
Optics Communications, Volume 207, Issues 1-6, 15 June 2002, Pages 7-15
Henk F. Arnoldus and John T. Foley

FLUID–STRUCTURE COUPLING FOR AN UNBAFFLED ELASTIC PANEL IMMERSED IN A DIFFUSE FIELD • ARTICLE
Journal of Sound and Vibration, Volume 198, Issue 4, 12 December 1996, Pages 485-506
H. Nelisse, O. Beslin and J. Nicolas

Green's function for gratings: parametric problems • ARTICLE
Optics Communications, Volume 136, Issues 5-6, 1 April 1997, Pages 349-353
J. F. Bird

Short-wave asumptotic behaviour of Green's function in the problem of diffraction at a plane layer • ARTICLE
USSR Computational Mathematics and Mathematical Physics, Volume 13, Issue 3, 1973, Pages 170-186
S. I. Grinberg, E. N. Semenyaka and I. V. Sukharevskii
 

1. What is a stokeslet?

A stokeslet is a theoretical point force used in fluid dynamics to model the motion of an infinitely small particle in a fluid. It is named after George Gabriel Stokes, a mathematician and physicist who first described its properties.

2. How is a stokeslet derived?

A stokeslet can be derived using the Navier-Stokes equations, which describe the motion of fluids. By simplifying these equations for the case of an infinitely small particle, the stokeslet can be mathematically defined.

3. What are the assumptions made in the derivation of a stokeslet?

The derivation of a stokeslet assumes that the fluid is incompressible, the particle is small compared to the fluid, and the flow is steady and laminar. It also assumes that the particle is moving slowly enough that inertial forces can be neglected.

4. What is the significance of a stokeslet in fluid dynamics?

The stokeslet is a useful tool in understanding the behavior of particles in a fluid, as it allows for the calculation of fluid flow and particle motion in a simplified manner. It is also used in developing numerical methods for simulating fluid flow.

5. Can stokeslet be applied to real-life situations?

While the stokeslet is a theoretical concept, it can be applied to real-life situations in which the assumptions made in its derivation hold true. This includes microfluidics, where particles are small compared to the fluid, and in low Reynolds number flows, where inertia is negligible.

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