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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