Capillary Tube

Figure 1.9 : Capillary Tube

 

As shown in Fig. 1.9, if a small open tube is inserted into a container with water, we see that water raises into the tube. We now get a liquid-gas-solid interface. In this case, attraction or adhesion between solid and water is strong and is able to overcome the mutual cohesion between liquid molecules. That is why water rises into the tube. The liquid is said to wet the surface.

The height of the liquid column is related to surface tension, tube radius, specific weight of the liquid and angle of contact $\theta$ between liquid and the tube. The vertical force due to surface tension , $2 \pi R \sigma cos \theta$ and weight of the fluid, $\gamma \pi R^2 h$ will balance each other.

$$\gamma \pi R^2 h = 2 \pi R \sigma cos \theta$$ or

$${h} = {{2 \sigma cos\theta} \over {\gamma R}}$$ (1.25)

It is seen that if the tube radius is small the capillary rise, h is pronounced. That is narrower the tube more the height to which the fluid rises in it. But whether the fluid rises in the capillary tube or not is decided by the contact angle, $\theta$ shown in the figure. It is the angle between the solid and the liquid surfaces. When this angle is less than $90^0$ the surface tension is such as to pull the fluid through the tube. There is a meniscus (concave upwards). The liquid is said to wet the surface. But when the angle is greater than $90^0$ as happens with mercury the liquid level is actually depressed. Now the liquid does not wet the surface.

(c) Aerospace, Mechanical & Mechatronic Engg. 2005
University of Sydney