Describe the capillary method for measurement of surface tension

The surface tension is the ability of a liquid to stay in its fixed shape. For example, when a drop of oil falls, it tries to remain in a spherical shape; this is the case in surface tension. When we experiment with a capillary tube, we observe that when a liquid rises in a capillary tube, the weight of the column of the liquid of density ρ inside the tube is supported by the upward force of surface tension acting along the circumference of the points of contact. Here, we will learn to find the surface tension of water by the capillary rise method and derive the rise in capillary tube formula.

Capillary Rise Method

A liquid of density ρ and surface tension σ rises in a capillary of inner radius ‘r’ to a height ‘h’ is given by:

h = 2σ cosθ/ρgr

where 

Θ = The contact-angle made by the liquid meniscus with the surface of the capillary.

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Point to Note:

The liquid rises because of the three types of forces, viz: adhesion, cohesion, and surface tension. 

If adhesive force/the liquid capillary is greater than the cohesive force between two liquids, then liquid rises as we see in the case of water rise in a glass capillary. 

If in this case, the contact angle is less than 90 degrees, then the meniscus is concave. However, when the adhesive force is less than the cohesive force, then liquid depresses or reduces in height, as in the case of mercury in a glass capillary. 

Now, let’s suppose that the contact angle is greater than 90 deg, the meniscus is convex.

We can derive the capillary rise formula by balancing forces on the liquid column. The weight of the liquid is given by:

πr² hρg

This weight is balanced by the upward force due to surface tension, whose formula is 2πrσcosθ

Please note that this formula can also be derived by using a pressure balance.

Our Objective:

The surface tension of water by capillary rise method using capillary tube method.

Materials Required

• Two-three capillary tubes of different radii

• A pointed clamp in a metallic plate with a handle

• Travelling microscope

• Movable and adjustable height stand

• A flat bottom open dish

• Clinical thermometer

• Fresh water in a beaker

• A clamp and a stand

Theory

The  rise in capillary tube formula is given by the following surface tension of water formula:

T= r(r+h/3)ρg2cosθ

Steps to Follow for Arranging the Apparatus:

1. Place the movable height stand on the table and adjust its base horizontally by leveling the screws.

2. Take a speck of dirt and grease-free water in an open dish with a flat bottom and put it on the top of the height stand.

3. Now, take three capillary tubes of different radii.

4. Clean the capillary tubes with a clean cloth and dry them. 

5. Clamp these tubes to a metallic plate to increase their radius. Next, clamp a pointer after the third capillary tube.

6. Clamp/affix the horizontal handle of the metallic plate in a vertical stand in such a way that the capillary tube and the pointer become vertical.

7. Now, adjust the height of the metallic plate in a way that the capillary tubes dip in the water in an open dish.

8. Adjust the position of the pointer in such a manner that the tip touches the surface of the water.

Steps to Follow to measure the Capillary Rise:

1. Find the LC of the traveling microscope for the horizontal and the vertical scale. Record the same in the tabular form.

2. Increase the height of the microscope by keeping its axis horizontal and pointing towards the capillary tubes.

3. Now, bring the microscope in front of the first capillary tube that has a maximum rise.

4. Adjust the horizontal crosswire touching the central part of the concave meniscus observed convex through a microscope.

5. Note all the readings of the position of the microscope on the vertical scale.

6. Now bring the microscope in front of the second capillary tube.

7. Lower the height of the microscope and repeat steps 12 and 13.

8. Repeat steps 12 and 13 for the third capillary tube.

9. Lower the height stand to make the pointer tip visible.

10. Place the movable microscope horizontally in front of the pointer and lower it to make the horizontal crosswire touch the tip of the pointer. Then repeat step 13.

Observation: Height of Liquid Rise

Calculation Part:

Take the value h and r for all three capillary tubes separately and find the values of T using the following formula:

T= r(h+r/3)ρg2cosθ

Find the mean value of the obtained T values as follows:

Tavg=(T1 +T2 + T3)/3

So, Tavg = _____ dynes/cm.