Surface Tension

When a capillary tube is dipped in a liquid, the liquid rises (or falls) inside the tube. This phenomenon is called capillary action. The height 'h' to which the liquid rises (or falls) is given by the balance between the force due to surface tension and the weight of the liquid column. The horizontal component `Sdl sinθ` adds to zero when summed over the entire periphery. The force F due to the pressure of the air outside the surface ABCD is `Pπr²` where P is the atmospheric pressure. This force acts vertically downward. The pressure at EF is equal to the atmospheric pressure P. This is because EF is in the same horizontal plane as the free surface outside the tube and the pressure there is P. The force due to the liquid below EF is, therefore, `Pπr²` in vertically upward direction. Thus, F and F cancel each other and the force `F = 2πr S cosθ` balances the weight W in equilibrium. If the height raised in the tube is h and if we neglect the weight of the liquid contained in the meniscus, the volume of the liquid raised is `πr²h`.

The pressure inside a bubble is P' = P_0 + 2S/r, where P_0 is the atmospheric pressure, S is the surface tension, and r is the radius of the bubble.

The force exerted by the film on the wire is F = 2 * (length of contact) * (surface tension). The factor of 2 arises because the soap film has two surfaces.

The height h to which a liquid rises in a capillary tube is given by h = (2S cosθ) / (rρg), where S is the surface tension, θ is the contact angle, r is the radius of the capillary tube, ρ is the density of the liquid, and g is the acceleration due to gravity.

The surface energy released when two drops merge is calculated by finding the difference in surface energy before and after merging. Surface energy is given by the product of surface area and surface tension. If two drops of radius 'r' merge to form a drop of radius 'R', then volume is conserved, which gives 8/3 πr^3 = 4/3 πR^3, implying R = 2^(1/3)r. The released surface energy = 8π r 2S − 4 × 2 2/3 π r 2S

Surface tension arises from the cohesive forces between liquid molecules. At the surface, molecules experience a net inward force, causing the surface to behave like a stretched elastic membrane. This property is responsible for phenomena like capillary action and the formation of spherical droplets.