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April 2011 - Capillary pressure and its surprising consequences on PT indications

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Written by Administrator
Friday, 01 April 2011 12:03

When performing a colour contrast PT, one of our readers was very surprised to see that cracks 7 mm (ca 0.25 inch) long, ca 1.5 mm (ca 0.06 inch) deep and, say, with a nominal width of 12 µm (ca 0.47 mil), did not give indications as straight lines, but as two large spots on both ends of the crack, while the main length of the crack gave a faint signal.

These cracks are artificial cracks; we cannot give more information, due to confidentiality concerns.

It is quite easy to explain this aspect, after getting some views of the cracks’ends. The nominal width of 12 µm (ca 0.47 mil) comes down to less than a µm (ca 0.04 mil), and different solid pollutants may even make this internal width lower.

Keep in mind that a penetrant, or any liquid, or gas, enter a discontinuity due to the capillary pressure.

The capillary pressure ∆ p is the difference in pressure across the interface between two non-miscible fluids and it is given by the Young-Laplace equation:

 

γ being the surface tension of the liquid/gas, θ being the contact angle between the liquid/gas interface and the solid surface, and r being the radius of the capillary “tube”.

It is not even necessary to calculate the pressure, as what is important is to understand that the tighter the tube, the higher the pressure, for the same liquid/gas interface. Therefore, a ratio between the central area, where width is 12 µm (ca 0.47 mil), and the ends, where width goes down to ca 1 µm (ca 0.04 mil) leads to a factor of 12. The capillary pressure in the ends is then 12 times higher than in the middle.

If the non-aqueous wet developer is sprayed from one end to the other, parallel to the crack, the developer arrives on the first end, some milliseconds before on the center of the crack, or before on the second end. The developer draws the penetrant from the first end, and the difference of capillary pressure attracts the penetrant from the middle of the crack to the end.

Same way in the second end. That is why the crack is displayed as an indication in an unusual way.

Just for readers to get a better idea of the values of capillary pressure, we can give the calculus.

Many penetrants have a surface tension in the 30/35 mN/m range. The contact angle is generally very close to zero, hence a cosine very, very close to 1.

Let us take a 32 mN/m figure as a current surface tension.
The radius is either 6 µm (ca 0.24 mil), or 0.5 µm (ca 0.02 mil), the radius being equal to half the width.
The capillary pressure in the middle of the crack is ca 11 kPa (ca 1.6 psi), while it is 128 kPa (ca 18.6 psi) in both ends. Many people are very surprised of these values when given figures for tight cracks. When using fluorescent penetrants, it is not unusual to detect cracks less than a µm (ca 0.04 mil), wide. Pressure may be higher than 128 kPa (ca 18.6 psi).

And what about water in cracks? Water has a surface tension in the 72 mN/m range, depending on temperature, as for any liquid/gas interface. The capillary pressure will be at least twice as high as that of penetrants! An explanation why it is difficult to draw water from
tight cracks: a drying oven set at 70°C (ca 158°F) is not enough. A 110°C (ca 230°F) is far better. Do not forget this when drying parts after an alkaline cleaning before penetrant application.

Last Updated ( Thursday, 19 May 2011 17:08 )