# Viscosity

Viscosity describes a fluid's resistance to flow. Liquids such as water that flow easily, have a lower viscosity than do liquids such as ketchup. Viscosity has little effect on the ability of a penetrant material to enter a defect but it does have an effect on the speed at which the penetrant fills a defect. The equations for the fill times of a  cylindrical void and an elliptical void are shown below:

Cylindrical Void:

$t=\frac{2l^{2}\mu}{r\cos(\theta)s_{LG}}$

Elliptical Void:

$t=\left(\frac{2l^{2}\mu}{s_{LG}\cos(\theta)}\right)\left(\frac{a^{2}+b^{2}}{(a+b)ab}\right)$

Where: t= Fill time
l = defect depth
μ = viscosity
r = radius of the crack opening
s LG = liquid-gas surface tension
θ = contact angle
a = flaw width
b = flaw length

From these equations, it can be seen that fill time is directly proportional to penetrant viscosity. While it has no real bearing on this discussion, it should be noted that the two equations do not take into account entrapped gas that could be present in a closed end capillary.

Reference:

• Deutsch, S. A, Preliminary Study of the Fluid Mechanics of Liquid Penetrant Testing, Journal of Research of the National Bureau of Standards, Vol. 84, No. 4, July - August 1979, pp. 287-291.