JEE Physics Mechanical Properties Of Fluids Notes Set 03

Surface Tension

Surface tension T is the force per unit length on a line in the surface (or the surface energy per unit area). It arises from cohesion, is reduced by heating and by detergents, and explains the spherical shape of drops, floating needles and insects walking on water. The work done in increasing the area is \( W=T\Delta A \), and a soap film has two surfaces, so \( W=2T\Delta A \). The weight a needle of length l can float is \( 2Tl \).

Excess pressure: \( \dfrac{2T}{r} \) in a liquid drop or an air bubble in a liquid (one surface) and \( \dfrac{4T}{r} \) in a soap bubble (two surfaces). Two bubbles in contact have a common surface of radius \( \dfrac{r_1r_2}{r_2-r_1} \). When n drops of radius r coalesce into one drop of radius R, \( R=n^{1/3}r \) and energy is released. Splitting a drop needs energy.

Capillarity

The angle of contact is acute for wetting liquids (water on glass; the liquid rises in a tube) and obtuse for non-wetting liquids (mercury on glass; the liquid falls). The height of rise is \( h=\dfrac{2T\cos\theta}{r\rho g} \), inversely proportional to the radius, and the mass of liquid raised is proportional to r. In a freely falling or orbiting vessel the effective g is zero, so the liquid fills the tube; on the moon the height is six times larger. For two limbs of a U-tube, the difference of levels is \( \dfrac{2T}{\rho g}\left(\dfrac1{r_1}-\dfrac1{r_2}\right) \).