Hele-Shaw Flow

I am beginning to add some post which I encounter in class or research which will catalog some various topics and discussion. This particular post is concerned with Hele-Shaw Flow.

According to Cohen and Kundu [1, 2], Hele-Shaw flow is defined as the flow between objects which are short distances apart or between very small gaps such as tribology or the theory of flows in mechanical bearings. The Hele-Shaw flow occurs for low Reynolds numbers, also known as creeping flow, and remarkably, produces inviscid-like flow visualization. Since the Reynolds number is defines as a length scale times the fluid density times the speed of the fluid divided by the kinematic viscosity or

\( \mathrm{Re} = \dfrac{\rho U h}{ \mu} = \dfrac{U h}{ \nu} \)

the Reynolds number value becomes very small if the distance of the gap is small, \( h \), and even smaller if the fluid speed is slow, \( U \). Experimentalist can get the number even lower by using large dynamic viscosity property fluids, \( \nu \). When an object is place in the gap and fills that space then it has been observed to mimic potential flow theory values around an object [3].

In progress...

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References:

[1] I. M. Cohen & P. K. Kundu. Fluid Mechanics. (2nd ed.). Academic Press, San Diego, CA. 2002

[2] I. M. Cohen & P. K. Kundu. Fluid Mechanics. (4th ed.). Academic Press, Burlington, MA. 2008

[3] P. A. A. Narayana & K. N. Seetharamu. Engineering Fluid Mechanics. Alpha Science International, Ltd, Middlesex, UK. 2005