Name: Angle of Contact
Uploaded: 2019-07-19
Duration: 6 min 57 s
Description: What is the contact angle? Which factor does the contact angle depend on? Why does the contact angle for the same liquid on different surfaces differ? Let's...

Question

What is capillarity? Establish a relation among the height

h

of water column in a glass capillary tube, the internal radius

r

of the tube and the surface tension

T

of water.

Accepted Answer

If a tube of a very narrow bore (called capillary) is dipped in a liquid, it is found that the liquid in the capillary either ascends or descends relative to the surrounding liquid. This phenomenon is called capillarity.

In order to calculate the height to which a liquid will rise in a capillary, consider a glass capillary of radius $R$ dipped in water as shown in Fig. shown. As the meniscus is concave and nearly spherical, the pressure below the meniscus will be $[p_{0} - (2 T / r)]$ as atmospheric pressure and $p_{0}$ as the radius of the meniscus. Now as liquid flows from higher to lower pressure and at the same level in a liquid pressure must be the same (this is because a liquid cannot sustain tangential stress), so the liquid will ascend in the capillary till hydrostatic pressure of the liquid compensates for the decrease in pressure. i.e.

$p_{0} = [p_{0} - \frac{2 T}{r}] + h ρ g$ or $h = \frac{2 T}{r ρ g}$ ...(1)

But from the figure shown it is clear that the radius of the meniscus $r$ is related to the radius of capillary through the relation.

$(R / r) = \cos θ$ , i.e., $r = R / \cos θ$ ...(2)

where $θ$ is the angle of contact. So substituting the value of from Eqn. $(2)$ in $(1)$ , we get

$h = \frac{2 T}{r ρ g} = \frac{2 T \cos θ}{R ρ g}$ ...(3)

What is capillarity? Establish a relation among the height $h$ of water column in a glass capillary tube, the internal radius $r$ of the tube and the surface tension $T$ of water.

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