Derive an expression for capillary rise for a liquid having a concave meniscus.
Answers
Explanation:
When one end of capillary tube of radius r is immersed into a liquid of density ρ which wets the sides of the capillary tube (water and capillary tube of glass), the shape of the liquid meniscus in the tube becomes concave upwards. R = radius of curvature of liquid meniscus.
Explanation:
Consider a capillary tube of radius r partially immersed into a wetting liquid of density ρ. Let the capillary rise be h and be the angle of contact at the edge of contact of the concave meniscus and glass figure. If R is the radius of curvature of the meniscus then from the figure, r=R cosθ.
Analysing capillary capillary action using Laplace's law for a spherical membrane Surface tension T is the tangential force per unit length acting along the contact line. It is directed into the liquid making an angle with the capillary wall. We ignore the small volume of the liquid in the meniscus. The gauge pressure within the liquid at a depth h, i.e., at the level of the free liquid surface open to the atmosphere, is
p−P0=ρ gh ...(1)
By Laplace's law for a spherical membrane, this gauge pressure is
P−P0=R2T ...(2)
∴ hρ g=R2T=r2T cosθ
∴ h=rρ g2T cosθ ...(3)
Thus, narrower the capillary tube, the greater is the capillary rise.
From Eq. (3),
= 2T cosθhρ rg ...(4)
Equations (3) and (4) are also valid for capillary depression h of a non-wetting liquid. In this case, the meniscus is convex and is obtuse. Then, cosθ is negative but so is h, indicating a fall or depression of the liquid in the capillary. T is positive in both cases.