Re: Capillary siphon modeling


Tao wrote:
> Hi,
>
> I need to use a capillary to transport fluid by siphon. The inside
> diameter
> of the capillary is 100 micron meter. These are what I noticed:
>
> 1). The height difference between the two end of the capillary has
> to
> large enough to form a flow. I guess it is either due to friction or
> surface
> tension. The pressure has to be larger enough to form a droplet.

Both, actually...
Viscosity in fluids provides a drag that is also proportional to the
length of the tube and the flow velocity.

The droplet produces a 'back pressure' through surface tension (aka
surface energy).

> 2). The flow rate is not proportional to time. The size of the
> droplet formed
> at the tip affects the flow rate.

....because the surface tension of the droplet of the emergent fluid
reduces the overall pressure drop through the tube.

> 3). The flow rate is not proportional to the height difference.

The height difference produces only hydrostatic pressure. It is the
total pressure drop that drives fluid through the tube.

> I wonder if there is any analytical solution or modeling for such
> phenomenal?
> I searched but can't find any.

You will probably have to work one out for yourself. Most mechanical
engineers (those with 'expertise' in fluid flow) do not concern
themselves with capillary tubes but with pipes (where 'end effects' can
be neglected and where 'rules of thumb' are used to accommodate the
effects of pipe geometry on fast flows).

> Any help is highly appreciated.

Look up "surface tension," "viscous resistance," "fluid friction
concepts," and related ideas here:
http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

This is more appropriately a problem for a physical chemist.

Tom Davidson
Richmond, VA

.

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