Question

Why do some liquids rise and some liquids dip in a capillary tube? Explain.

Answer 1

Hint: For a solid-liquid pair having acute $\left( { < {{90}^0}} \right)$ angle of contact, liquid rises up into a capillary tube made of that solid. For a solid-liquid pair having an obtuse $\left( { > {{90}^0}} \right)$ angle of contact, liquid depressed into a capillary tube made of that solid. The risen or depression of liquid inside a capillary tube depends on the surface tension of the liquid.

Complete answer:
First of all, we will define some related terms as follows:
Force of cohesion: It is the force between two molecules of similar nature. It is very strong is case of solids, weaker in case of liquids, and weakest in case of gas
Force of adhesion: It is the force between two molecules of different nature. Due to this force water wets a paper.

Angle of contact: For a pair of solid and liquid, it is the angle between tangent to the liquid surface drawn at the point of contact and the solid surface inside the liquid.
The height $\left( h \right)$ of liquid risen or depressed in a capillary tube is given by Jurin’s equation.
$h = \dfrac{{2T\cos \theta }}{{r\rho g}}$ …… (1)
Where $T$ is the surface tension, $\theta $ is the angle of contact, $r$ is the radius of the capillary tube, $\rho $is the density of the liquid and $g$ is the acceleration due to gravity.

Case I: Rise of liquid in capillary tube
The liquid which gets curved up, towards the solid, will have an acute angle $\left( {\theta < {{90}^0}} \right)$ of contact for the given pair of solid and liquid. This happens when the force of cohesion is less than the force adhesion. In such a case the liquid molecules will stick with the solid, thus making the solid wet.

If such a liquid is put in the solid tube, it will have a meniscus concave upwards. For $\theta < {90^0}$, $\cos \theta $ is positive and hence the value of $h$ (from equation 1) will be positive meaning that the liquid shall rise inside the capillary tube.Water is an example of this type of liquid. The angle of contact for water and glass lies between ${0^0}$ and ${8^0}$.

Case II: Fall of liquid in a capillary tube
This is the exact opposite case of the above discussion. When the force of cohesion is greater than the force of adhesion, the liquids have an obtuse angle $\left( {\theta > {{90}^0}} \right)$ of contact for the given pair of solid and liquid. In such cases liquids do not wet the solids.

Such liquids will have a meniscus convex upwards when put in the solid tube. For $\theta > {90^0}$, $\cos \theta $ is negative and hence the value of $h$ (from equation 1) will be negative meaning that the liquid shall get depressed inside the capillary tube.

Note: For angle of contact $\theta = {90^0}$, $\cos {90^0} = 0$ and therefore $h = 0$ i.e., the liquid shall neither rise nor depress inside the capillary tube. In this case the force of cohesion and adhesion are equal to each other. Example: Silver plate dipped in water or water put in a silver.