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Old Mar 2nd 2016, 09:24 AM   #1
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Join Date: Mar 2016
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Washburn equation dependence over time variable?

Hello everyone,
This is my first post and a warm greetings to all!!

I work on pore scale modeling and use OpenFOAM for carrying out numerical analysis.

I recently came across "Washburn equation" and most of the posts/ papers (along with the original paper of Washburn's) relate flow length of fluid within a capillary tube(dl) proportional to the square root of time.

I don't understand the logic behind that.

From my point of view,
change in volume due to capillary flow= force applied/ flow resistance.
(or)
change in volume due to capillary flow=
Poiseuille
relation.

(
Poiseuille
relation states: pressure gradient/ flow resistance)

When we talk about the pressure gradient between inlet and outlet and flow resistance it is seen over the entire length(L) of the tube.

But what i observed from original Washburn's paper and also from many papers is that they combine channel length(L) with the flow length(dl) that is to be determined. That is, both are independent and the capillary flow length is only dependent over time and not the square root of time.

Is my analysis correct or am I wrong? The most confusing part is that my numerical analysis also is closer to my theory than to Washburn's theory.

Could anyone illuminate over this area,

Thanks;
Saideep
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dependence, equation, fluid dynamics, physics, time, variable, washburn



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