When can Stokes' law be used for motion in a liquid?

[ManFrommars]

Hello,
Could anyone tell me what assumptions are made about conditions in the derivation of Stokes' law ( F = 6(pi)(eta)rv )? Also, how is the Ladenburg correction for motion in a fluid derived from/related to this? I have searched high and low on the net and in libraries, but I'm not coming up with anything useful for some reason... any help would be hugely appreciated!
Thanks in advance...

 

[selfAdjoint]

Stoke's law assumes that the fluid is conserved, that it has no sources where new fluid appears or sinks where fluid disappears. Then every change in the amount of a fluid in a region must come from flow across the boundary of the region.

 

[ManFrommars]

Hi, thank you for he reply. I'm not sure what you mean though... could ou possibly clarify?
Cheers

 

[selfAdjoint]

Hi, thank you for he reply. I'm not sure what you mean though... could ou possibly clarify?
Cheers

A source is a point in space where fluid is appearing, say a faucet or something like that. A sink is a point where fluid is disappearing, like a drain. Nonconserved fluids have sources and sinks. For example if you treat heat as a fluid you have this problem because for example of the specific heat of materials, so heat can appear or disappear upon change of state, without temperature changing. So heat in the atmosphere is not a conserved fluid and you aren't gauranteed that Stoke's theorem will work for that.

Think about what you have in Stoke's theorem. One side is an integral over the volume of some region, right? And the other is an integral over the bounding surface of that volume. And what are the integrands? Really look at them and try to explain to yourself what they mean physically.

 

[arildno]

Stokes' integral theorem is not the same as Stokes' law of resistance, which seems to be the subject of the original question.
Stokes' classical law for the resistance acted upon a sphere by a viscous fluid, may formally be seen as the force consistent with the first-order approximation in a perturbation series solution of the (stationary) Navier-Stokes equations with the Reynolds number as the perturbation parameter.
That is, Stokes' law is a good approximation as long as Re<<1 (strongly viscous fluids).
We use separation of variables (spherical coordinates) in the tedious derivation of the velocity field and pressure distribution.
Stokes' law follows from the calculated pressure distribution.

I haven't heard the name "Ladenburg correction" before; presumably, it is simply a higher-order perturbation solution of N-S.