Calculating Film Thickness on Rotating Cylinders with Fluid Gap?

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Discussion Overview

The discussion revolves around calculating the film thickness of a fluid on two rotating cylinders that do not touch but are positioned close together. The context includes aspects of fluid dynamics, particularly concerning roll coating and the application of the Navier-Stokes equations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Experimental/applied

Main Points Raised

  • One participant proposes that the problem can be approached using the Navier-Stokes equations, although they express concern about the complexity of manual calculations.
  • Another participant requests clarification on the setup, indicating confusion about the arrangement of the cylinders and the fluid dynamics involved.
  • A later reply suggests that simulating the problem numerically using the Navier-Stokes equations would be challenging due to the nature of viscous free surface flow and the need for appropriate boundary conditions.
  • This participant also recommends using commercial Computational Fluid Dynamics software, such as Fluent 6.0, to tackle the problem more effectively.
  • Another suggestion is to conduct experimental measurements of fluid variables to determine the thickness through integral conservation laws.

Areas of Agreement / Disagreement

Participants express differing views on the feasibility of solving the problem analytically versus using numerical simulations or experimental methods. No consensus is reached on the best approach to calculate the film thickness.

Contextual Notes

The discussion highlights the complexity of the fluid dynamics involved, particularly regarding boundary conditions and the nature of the flow. There are unresolved aspects concerning the specific arrangement of the cylinders and the fluid behavior.

Samy1977
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I am trying to solve a problem concering roll coating. This is 2 rotating cylinders whith different speeds. The two cylinders are in the same horizontal plane. They don't touch each other, but are close together. On one cylinder there is a fluid. When the fluid goes through the gap, the point where the cylinders are closest to each other, both cylinders take some of the fluid. Is it possible to calculate how thick the film is on each cylinder??

I have looked a month at this problem now. I think it can be done with the Navier-Stokes formulas, but they could be too difficult to calculate manualy. I know it abolutely has something to do with the speed of the cylinders, and probably the gap between them.
 
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Sorry but I cannot imagine your problem. Do you mind posting a picture of it?. It can be done in .bmp and clicking below in Manage Attachments. I don't know if the cylinders are concentric, parallel, and I don't understand what you mean with the closest point and "both cylinders take some of the fluid".
 
stage.bmp]The problem[/URL]

At the top you see how the cylinders are located to each other. In the close up, the red is the fluid. One cylinder has all the fluid first, then it is divided between the two cylinders. I want to "know"/calculate the thickness one cylinder 1. Between the two blue arrows.
Hope it is clearer now. Sorry about the description, it is a bit difficult to describe.
 
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Wow!

I'm sorry. To be honest, I think your problem is very difficult to be solved in a classical way. I will explain that:

Making your own numerical simulation with the N-S equations will be a serious challenge. It's a viscous free surface flow. The free surfaces flow are heavier to simulate, because you need a boundary condition between the fluid and the air.

My advice, if you want to listen it, is to use a commercial simulation software of Computational Fluid Dynamics. Surely Fluent 6.0 can solve your problem.

Your question is not trivial at all. :bugeye:

Another posibility would be to measure experimentally some fluid variables and to obtain the thickness by means of integral conservation laws.
 
Thanks, that is what I thought. I had to verify.
 

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