[Corribus]

Can anyone out there with expertise in fluid dynamics give me a good explanation of what the Reynold's Number practically means?  The Wikipedia definition on the topic isn't very helpful to me.  In particular I'm interested in what the Reynold's Number might be for polyethylene at room temperature.

[curiouscat]

Don't think I'm an expert; but I can try.

In particular I'm interested in what the Reynold's Number might be for polyethylene at room temperature.

Well, if it isn't flowing isn't Re, almost by definition, zero?

If it is flowing in some way, we need the flow rate and then we can evaluate Re.

Essentially, it characterizes flow. So somewhat meaningless to talk of Re for, say, diesel, unless we talk of a certain geometry and flow rate.

The wikipedia article seems quite comprehensive and has more than I would think of saying; is there any particular point you are confused about?

Alternatively, what is your application and then maybe we can help better.

[curiouscat]

In a more practical sense the places Re will most often arise (for a chemist) is to decide whether flow in a pipe will be laminar or turbulent. The particular value of Re decides that in an empirical sense.

Also, to decide pumping capacity, piping design etc. one needs to calculate pressure drops and most empirical correlations will use Re in some way.

Alternatively, for heat transfer correlations too Re is important.

[Corribus]

Some people model diffusion (of a gas, say) through a polymer by the Stokes-Einstein equation, which treats the amorphous polymer as a very viscous fluid.  However the Stokes-Einstein equation is only applicable for fluids with low Reynold's Number.

When I use the Stokes Einstein equation to do some diffusion constant estimations, I'm getting some strange results.  I am wondering if the non-applicability of the Stokes Einstein eqn is the reason, and hence Reynold's Number comes into play.

I'm doing a lot with fluid mechanics these days.  I probably should just invest in a good textbook.

[curiouscat]

Have you tried estimating your Re?

[Corribus]

No.  Problem is that these are composite materials, so it's hard to get an idea of what the viscosity is, short of measuring it, of course.  But that sort of defeats the purpose of trying to estimate the diffusivity.

I thought I'd ask about (neat) polyethylene first because it'd be simpler, even if it's not necessarily a good model for what I really need.

[curiouscat]

I thought I'd ask about (neat) polyethylene first because it'd be simpler, even if it's not necessarily a good model for what I really need.

Which is fine. So based on measured diffusion flux and estimated pore size you can get Re. I think.

[Corribus]

Well unfortunately diffusion flux is my unknown.   That's why I'm using Stokes-Einstein.

[curiouscat]

Well unfortunately diffusion flux is my unknown.   That's why I'm using Stokes-Einstein.

Hmm....I'm confused.

You said:

"When I use the Stokes Einstein equation to do some diffusion constant estimations,"

You can either know the constant and use it to estimate the flux or know the flux and use it to estimate the constant.

Which way are you working?

[Corribus]

Sorry, I tossed that out right before leaving for a wedding.  I see in my haste I got myself mixed up.

I need the diffusion constant.  I don't have any experimental data.  I want to estimate the diffusion constant and there are some references which use the Stokes-Einstein equation to do it.  However when I apply the SE equation with some diffusants, I am getting values that are several of orders of magnitudes off from published experimental values.

This is why I want to know whether the SE is really applicable in a highly viscous "fluid" like a polymer at room temperature.

[curiouscat]

Is the polymer your diffusant or the medium that something else is diffusing through?

You mentioned a gas passing through a polymer before? Shouldnt the viscosity of the gas matter and not the polymer?

[curiouscat]

Can you give some specifics? What gas etc.?

[Corribus]

Polymer is the diffusing medium.  Ex: carbon dioxide gas.  If I do the SE calculation, I arrive at a diffusion constant that is 6 orders of magnitude off of the experimental value.

[Enthalpy]

Did I see recently a Reynolds number that was NOT fluid mechanics?

Anyway, in fluid mechanics, this number compares the effect of viscosity and momentum. It tells if a flow is more likely turbulent or laminar, by comparison with a "critical Reynolds number".

Fluid mechanics is essentially experimental, and its theory rudimentary. A handful of cases are documented with curves allowing to make predictions by hand, the rest is finite elements methods, with all the necessary caution. In this context, a dozen of dimensionless numbers have been defined besides the most famous Reynold's, with the aim of reducing the number of variables when plotting experimental curves used to predict other cases. Then, empirical relations mix observed fractional powers of these numbers. There is little more than that.

So this number is not related just with a material, but with the conditions of a flow. It's used at extrusion, injection... of polymers, which is usually done with heat, not at room temperature.

[Enthalpy]

I'm doing a lot with fluid mechanics these days.  I probably should just invest in a good textbook.

In German, I recommend "Technische Fluidmechanik" from Sigloch, here and elsewhere:
http://www.amazon.de/Technische-Fluidmechanik-Herbert-Sigloch/dp/3540220089
but apparently it is not translated, too bad.

Most books put unusable differential equations, solve an infinite rotating cylinder, a laminar tube, and stop there... Sigloch gives the methods and experimental diagrams and formulas for many practical usable cases.