Excess Pressure inside Liquid Drop and inside Liquid Bubble | Physics Grade XI

Fluid Mechanics

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Excess Pressure inside Liquid Drop and inside Liquid Bubble | Physics Grade XI

Excess Pressure inside Liquid Drop and inside Liquid Bubble

Excess pressure inside a Liquid Drop

Excess pressure inside a liquid drop

Consider a drop of liquid R as shown in the figure. The molecules lying on the surface of the liquid drop due to surface tension will experience a resultant force acting inwards perpendicular to the surface. As a result, the pressure inside the drop must be greater than the pressure outside it. The excess pressure inside the drop will provide a force acting outwards perpendicular to the surface, to balance the resultant force due to surface tension.

Let T be the surface tension and P be the excess pressure inside the drop. Suppose due to excess pressure, there be an increase in the radius of the drop by quantity dR. In such case we can write, work done by excess pressure,
W = Force * displacement = (Excess pressure * area) * displacement
or, W = P * 4πR2 * dR …….. (i)

Increase in surface area of the drop = Final surface area – Initial surface area
= 4π (R + dR)2 - 4πR2
= 4π [ R2 + 2. R. dR + dR2] - 4πR2
= 8πR dR [since dR2 is very small, it is neglected]
 
Increase in surface energy = Increase in surface area * surface tension
= 8πR dR * T
 
From equation (i) and (ii), we get
P * 4πR2 * dR = 8πR dR * T
.: P = 2T/R
or, Pin – Pout = 2T/R
 
Excess pressure inside Liquid Bubble or Soap Bubble
     P = 2 * 2T/R = 4T/R
 
Angle of Contact: The angle θ which the tangent to the liquid surface at the point of contact makes with the solid surface inside the liquid is called angle of contact or capillary angle.
 
Capillarity: The very fine bore is known as capillary tube.

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