Civil Engineering ⇒ Topic : Surface Tension and Capillarity

Surface Tension and Capillarity :
Surface tension is defined as the tensile force acting on the surface of a liquid in contact with a gas or on the surface between two immiscible liquids such that the contact surface behaves like a membrane under tension. The magnitude of this force per unit length of the free surface will have the same value as the surface energy per unit area. It is denoted by Greek letter 6 (called sigma). In MKS units, it is expressed as kgf/m while in SI units as N/m.
The phenomenon of surface tension is explained by Fig below.

        Surface tension

Consider three molecules A, B, C of a liquid in a mass of liquid. The molecule A is attracted in all directions equally by the surrounding molecules of the liquid. Thus the resultant force acting on the molecule A is zero. But the molecule B, which is situated near the free surface, is acted upon by upward and downward forces which are unbalanced. Thus a net resultant force on molecule B is acting in the downward direction. The molecule C, situated on the free surface of liquid, does experience a resultant downward force. All the molecules on the free surface experience a downward force. Thus the free surface of the liquid acts like a very thin film under tension of the surface of the liquid act as though it is an elastic membrane under tension.

Surface Tension on Liquid Droplet :
Consider a small spherical droplet of a liquid of radius 'r'. On the entire surface of the droplet, the tensile force due to surface tension will be acting.
Let σ = Surface tension of the liquid
p = Pressure intensity inside the droplet (in excess of the outside pressure intensity)
d = Dia. of droplet.
Let the droplet is cut into two halves. The forces acting on one half (say left half) will be
(i) tensile force due to surface tension acting around the circumference of the cut portion as shown in Fig. (b) and this is equal to
= σ x Circumference
=σ x πd

            Forces on droplet
(ii) pressure force on the area πd²/4 = p x πd²/4 as shown in Fig. (c). These two forces will be equal and opposite under equilibrium conditions, i.e.,
p x πd²/4 = σ x πd
or p = σ x πd / πd²/4
= 4σ / d
Above equation shows that with the decrease of diameter of the droplet, pressure intensity inside the droplet increases.

      Forces on liquid jet
Let p = Pressure intensity inside the liquid jet above the outside pressure
σ = Surface tension of the liquid.
Consider the equilibrium of the semi jet, we have
Force due to pressure = p x area of semi jet
= p x L x d
Force due to surface tension = σ x 2L.
Equating the forces, we have
p x L x d = σ x 2L
p = σ x 2L / L x d

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