Contact Angle : Definition and Its Various Cases

Have you noticed how the water beads up on a freshly waxed car or crawls on clean glass? The general observations all relate to what's called the contact angle. The contact angle is the angle formed where a liquid meets a solid surface and indicates how well the liquid wets that surface. It's an equally important parameter for a variety of natural and industrial processes, from plants' ability to uptake water to the efficiency of waterproof coatings. The contact angle can explain and help to control the behaviour of liquids on various surfaces.

In this article, we will cover the concept of Contact Angle. This concept is the part of chapter Properties of Solids and Liquids which is a crucial chapter in Class 11 physics. It is not only essential for board exams but also for competitive exams like the Joint Entrance Examination (JEE Main), National Eligibility Entrance Test (NEET), and other entrance exams such as SRMJEE, BITSAT, WBJEE, VITEEE and more. Over the last ten years of the JEE Main AND NEET (from 2013 to 2023), a total of three questions have been asked on this concept.

The shape of the Liquid Meniscus

When a capillary tube is dipped in a liquid, the liquid surface becomes curved near the point of contact. The curved surface of the liquid is called the meniscus of the liquid. This curved surface is due to the resultant of two forces i.e. the force of cohesion and the force of adhesion.

If liquid molecule A is in contact with a solid (i.e. wall of capillary tube) then forces acting on molecule A are

• Force of adhesion (Fa)

This is force due to solid molecules on liquid molecules.

Here it will act outwards at a right angle to the wall of the tube.

• Force of cohesion (Fc)

This is the force due to liquid molecules on liquid molecules.

Here it will act at an angle 45⁰ to the vertical and towards the liquid.

So the resultant force (FN) will be given by

F→N=F→a+F→c

And If FN makes an angle α with Fa

Then,

tan⁡α=FcSin(135)Fa+FcCos(135)=Fc2Fa−Fc

As we know the free surface of the liquid adjusts itself at a right angle to this resultant force.

So by knowing the direction of the resultant force, we can find out the shape of the meniscus.

Shape of Liquid Meniscus in various Cases

Case I- When Fc=2Fa

As shown in the below figure,

The resultant force acts vertically downwards.

Hence the liquid meniscus must be horizontal.

Example-Pure water in a silver-coated capillary tube.

Case II- When $F_c<\sqrt{2} F_a$

As shown in the below figure,

The resultant force is directed outside the liquid. Hence the liquid meniscus must be concave upward.

Example-Example: Water in a glass capillary tube.

Case III- When Fc>2Fa

As shown in the below figure,

The resultant force is directed inside the liquid. Hence the liquid meniscus must be convex upward.

Example: Mercury in a glass capillary tube.

Now, after knowing about the shape of the liquid meniscus and its different types of cases coming to the main part of this story which is the angle of contact.

The Angle of Contact (θ)

The angle of contact between a liquid and a solid is defined as the angle enclosed between the tangents to the liquid surface and the solid surface inside the liquid.

While drawing tangent keep the following things in mind.

1. Both the tangents are drawn at the point of contact of the liquid with the solid.

2. Tangent to the liquid surface should be away from the solid surface.

3. Tangent to the solid surface should be towards the liquid surface.

Its value lies between 0^o and 180^o

• When Fc=2Fa then θ=90∘

i.e. plane meniscus.
In this case, Liquid does not wet the solid surface

• When Fc<2Fa then θ<90∘ then θ<90∘

i.e. concave meniscus.
In this case, Liquid wets the solid surface

• When Fc>2Fa then θ>90∘

i.e. Convex meniscus.
In this case, Liquid does not wet the solid surface.

On increasing the temperature, the angle of contact decreases.

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Solved Example Based on Contact Angle

Example 1: The meniscus of the liquid is due to

1) the force of cohesion

2) the force of adhesion

3) Both a and b

4) None of these

Solution:

The meniscus of the liquid is due to both the force of cohesion and the force of adhesion.

Hence, the answer is option (3).

Example 2: Choose the correct option.
1) Viscosity of liquids increases with temperature
2) Viscosity of gases increases with temperature
3) Surface tension of liquids decreases with temperature.
4) For angle of contact θ=0∘, liquid neither rises hor falls on capillary.

Solution:

For contact angle θ=90∘, liquid neither rises nor falls. The viscosity of gases increases with temperature.

Hence, the answer is option (1).

Example 3: If the angle of contact is greater than 90∘, which of the following is true?

1) Adhesive force = Cohesive force

2) Adhesive force < Cohesive force

3) Adhesive force > Cohesive force

4) None of these

Solution: If the angle of contact is greater than 90∘, then Adhesive force < Cohesive force.

Hence, the answer is option (2).

Example 4: Wax is coated on the inner wall of a capillary tube and the tube is then dipped in water. then, compared to the unwaxed capillary, the angle of contact θ and the height h up to which water rises change. these changes are:

1) θ increases and h also increases
2) θ decreases and h also decreases
3) θ increases and h decreases
4) θ decreases and h increases

Solution:

when θ<90∘ (i.e. concave meniscus) then, In this case, Liquid wets the solid surface

and when θ>90∘ (i.e. Convex meniscus) then, In this case, Liquid does not wet the solid surface.

As given in the question

When Wax is coated on the inner wall of a capillary tube then water loses its ability to wet the sides of the tube.

So θ will increase
h=2Tcos⁡Θρgr
and as
i.e hαcos⁡θ so h will decrease

Hence, the answer is option (3).

Example 5: When liquid is subjected to horizontal acceleration-

1) tan⁡θ=g/a

2) tan⁡θ=ag

3) tan⁡θ=ag

4) tan⁡θ=2ag

Solution:

tan⁡θ= linear duet gravity. tan⁡θ=ag

Hence, the answer is option (2).

Summary
The contact angle is the angle at the triple junction formed by a liquid interface with a solid surface. It is one of the important measures of wettability, specifying the interaction between a liquid and a solid. A low contact angle, less than 90 degrees, denotes that the liquid is spreading or wetting the surface well. In return, a high contact angle of above 90 degrees means formation into droplets and[edge ] spreading. The contact angle at a point depends on the nature of the liquid and the surface. It is important in very many applications, from the manufacture of waterproof materials to the improvement of paint adhesion and the development of medical devices that interact with human biofluids. Contact angles can be measured to enable scientists and engineers to adapt a surface for a particular function.