## Wednesday, December 17, 2014

### Angle of Contact and Capillarity

Angle of contact

The angle between the two tangents drawn at the point of contact where one tangent is drawn to the solid surface into the liquid and other tangent is drawn to the liquid surface itself is called as angle of contact. The value of the angle of the contact depends on the nature of the surfaces that are in the contact and of course it also depends on the temperature.

Capillarity and Angle of Contact

Angle of contact is generally defined with respect to a capillary tube. Capillary tube is a fine tube whose length is very large when compared with its radius. Both the ends always an open state and we can insert this in a liquid.

When a capillary tube is immersed in a liquid and depending on the angle of contact the liquid can either rise or fall inside the tube. This phenomena is called capillarity. Whether the liquid is going to rise or fall depends on the nature of the liquid in the nature of the capillary tube.If the adhesive forces between the  liquid and the vessels wall is dominating then there will be a capillary rise.If the cohersive forces are dominating between the liquid and the vessel then there will be a capillary fall.

Depending on the nature of this angle of contact also will vary. If adhesive forces are dominating angle of contact is less than 90° and if the cohersive forces are dominating the angle of contact is going to be greater than 90°. If no forces are dominating then the angle of contact is equal to 90° itself. This can be experienced with the pure silver and the pure glass. If a glass capillary tube is immersed in a pure silver there will be neither rise or fall in the liquid level.

If a glass capillary tube is immersed in water because of the domination of the adhesive forces it can be noticed that the liquid level is rising. If a glass tube is immersed in mercury because of the domination of the cohersive forces with can identify the fall in the liquid level.

Applications of the capillarity

We can see the daily life applications of the capillarity it so many places. Trees are able to pump the water even to the highest parts from the ground using the root system and this root system acts basing on the capillarity.

A kerosene lamp can pump kerosene through its wick basing on the Capillarity and the same is the case with the paraffin candle.

The phenomenon of rise or fall of the liquid level in this capillary tube is called capillarity.

Expression for capillary rise

We can derive the equation further capillarity rise quite easily. Let us consider a thin capillary tube having a radius and it is immersed in the liquid beaker as shown. Being the angle of contact is less than 90° the liquid will rise up to some extend and then it stops. At the upper level and at the point of contact we can draw angle of contact as shown.

It is very clear that the cos component is  going to act in up ward direction and it pull the liquid in the upward direction.The sin component is going to act in a horizontal direction and tried to pull the liquid against the walls of the capillarity tube. As this force is never sufficient to break the capillary tube  it is not going to be any product to work.

There is simultaneous force acting in the downward direction due to the weight of the liquid that is rising in the capillarity tube. It is certain the support force is balanced by the download force and it can acquire an equilibrium.

From the equation it is very clear that the capillarity rise depends on the area of cross-section,radius of the tube as well as the acceleration due to gravity at a given place.

If the tube of higher radius is taken the liquid rise is small. If a tube of insufficient length is taken then the liquid will never overflow .There will be adjustment in the radius of the surface.The surface will become more deep and the radius will increase in the height of the capillarity tube is not sufficient.

Forces acting during the capillarity

The shape of the liquid surface is decided basing on the forces that are acting on the capillary tube. Between the same liquid molecules there is cohersive force of attraction and between the liquid molecule in the gas molecule there is a adhesive force of attraction.

The adhesive forces always tries to pull the liquid horizontally away from the liquid molecules whereas the cohercive force molecules at any given point always tries to pull it towards other liquid molecules as shown.  There is another force acting that is nothing but the weight of the liquid molecule.

In the following diagram the shape of the liquid and the corresponding forces acting is as shown.

The rise of the capillarity is independent of the shape of the tube and is also going to be independent of the angle of inclination.

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