# Lesson: Capillarity—Measuring Surface Tension

### Summary

Students are presented with a short lesson on the difference between cohesive forces (the forces that hold water molecules together and create surface tension) and adhesive forces (the forces that causes water to "stick" to solid surfaces. The interaction between cohesive forces and adhesive forces causes the well-known capillary action. Students are also introduced to examples of capillary action found in nature and in our day-to-day lives.

### Engineering Connection

Many industrial processes depend on the accurate measurement of surface tension. When an object is painted or coated, the coating surface tension must be carefully maintained to produce the desired thickness without creating uneven patches. The strength and effectiveness of detergents are also partially determined by surface tension. One accurate method of measuring surface tension is through capillary action. The height water rises in a thin tube is related to the surface tension of the climbing liquid. Besides providing a method for measuring surface tension, capillary action itself has many different applications. Capillary action in part determines the behavior of ground water in the soil, which makes it important to civil and environmental engineers in understanding the stability of buildings and roads as well as the environmental impact of human development. Petroleum engineers use their understanding of capillary action in the extraction of crude oil from its rock reservoirs. And, understanding capillary action in the transport of fluids in animals is important in biomedical engineering.

### Pre-Req Knowledge

A basic understanding of cohesive forces (attraction of liquid molecules to each other) and surface tension.

### Learning Objectives

After this lesson, students should be able to:
• Describe the differences between cohesive and adhesive forces.
• Explain how a meniscus is formed.
• Describe how the combination of adhesive and cohesive forces causes water to rise in a thin tube or other small space (capillary action).
• Explain how capillary action is used.

### Introduction/Motivation

(In advance, have handy a glass of water, food dye/coloring, and white paper towels, to use as described below.)
(Hold up a beaker or glass of water colored with food dye.) Imagine you've been outside during a hot July day. You come inside and pour a big glass of water. (Place glass on counter top.) Now let's say you start talking to your parents or a brother or sister and... (knock the glass over to spill some of the water with food dye.) What are you going to do now? (Expect someone to suggest using a paper towel to clean it up.)
(Place one edge of a white paper towel into the colored water spill. Let the water climb into the paper towel while you talk.) Will someone in front who can see what is happening to the towel describe it for those in the back? (Expect a student to describe how the color is creeping up the towel.) Why is this happening? (Give students some time to answer. Expect a student to mention the spaces or holes in the towel.) Good. What else can you think of that has holes and absorbs water? (Various answers are possible. One example is a sponge).
(Lift the paper towel out of the liquid and show the class how the liquid has climbed.) What if I tried to do this with a plastic bag, would that absorb the water? Why not? Let's list some materials that can absorb and some that cannot. We'll see what each group have in common. (With students' help, create two lists and look for the similarities within each group and the differences between them.)
One very accurate method of measuring surface tension is through capillary action, since the height water rises in a thin tube is related to the surface tension of the climbing liquid. For many industrial processes, an accurate measurement of surface tension important — such as when painting or coating an object (coating a pan with oil from a spray can, applying solder to form electrical connections on a circuit board, applying ink using inkjet printing, aircraft painting, etc.), so the surface tension of the coating is carefully maintained to produce the desired thickness without creating any uneven patches. The strength and effectiveness of detergents are also partially determined by surface tension.
Besides providing a method for measuring surface tension, capillary action itself has many different applications. Can you think of any examples of capillary action in the real-world? (Take suggestions from students.) What about: cleaning with a sponge, how the soil in your yard absorbs rain water, wax rising up a wick, or how your T-shirt gets wet when you sweat? What about some applications that engineers might be involved with? Well, capillary action in part determines the behavior of ground water in the soil, which makes it important to civil and environmental engineers in understanding the stability of buildings and roads as well as the environmental impact of human development. Petroleum engineers use their understanding of capillary action in the extraction of crude oil from its rock reservoirs. And, understanding capillary action in the transport of fluids in animals is important in biomedical engineering.
We've already learned about surface tension and the forces that hold water drops together. Today we are going to discuss why water sticks to other things and even climbs up some objects. We will see that these phenomena provide us with a method of accurately measuring surface tension.

### Lesson Background and Concepts for Teachers

In any liquid, intermolecular forces cause the liquid molecules to be attracted to each other. These forces that pull liquid molecules towards each other are known as "cohesive" forces. In the body of a liquid, a molecule is surrounded by other molecules in all directions, so the attractive forces cancel and the molecule feels no overall force (see Figure 1). On the surface of the liquid/air interface, however, a molecule of the liquid feels the attractive forces of the other molecules from within the liquid, but none from the outside. This causes the outer layer of the liquid to act like a stretched membrane and minimize the surface area. We call this elastic membrane-like behavior surface tension.
Besides cohesive forces, "adhesive" forces also exist; they cause water molecules to try to "stick," or "adhere," to solid surfaces. The most common example of the effect of adhesive forces is the meniscus that is commonly seen when using graduated cylinders. The water molecules respond to an attractive "adhesive" force pulling them towards the glass walls. Near the walls of the cylinder, the adhesive force pulling the water towards the glass walls is stronger than the cohesive force pulling the water molecules together. This attractive force pulls the water up the sides of the glass tube against the downwards pull of gravity (see Figure 2).
Conversely, liquid mercury is repelled rather than attracted to glass. The mercury tries to minimize its contact with the glass walls. This causes an upward bowing of the mercury liquid against the downwards pull of gravity as it tries to maximize the contact between mercury atoms and minimize the contact with the glass wall (see Figure 3).
Capillarity is the combined effect of cohesive and adhesive forces that causes water and other liquids to rise in thin tubes or other constricted spaces. Inside a thin glass tube, the adhesive force, the attraction between the water and the glass wall, draws water up the sides of the glass tube to form a meniscus. The cohesive force, the attraction of the water molecules to each other, then tries to minimize the distance between the water molecules by pulling the bottom of the meniscus up against the force of gravity.
In large-diameter tubes, this rise in the water level is unnoticeable. However, in very small-diameter tubes, the cohesive forces can draw the water upwards appreciable distances (see Figure 4). The water continues to climb up the tube until the downward force of gravity on the water equals the upwards force caused by the surface tension.
A simple relationship determines how far the water is pulled up the tube (see Figure 5). The force upwards due to the surface tension is given by the following relationship:
In this relationship, γ is the liquid-air surface tension at 20o C, 2πa is the circumference of the tube, and θ is the contact angle of water on glass, a measure of the attraction of the liquid to the walls. The opposing force down is given by the force of gravity on the water that is pulled above the reservoir level.
Here, ρ = 1000 kg/m3 is the density of water, g = 9.8 m/s2 is the acceleration due to gravity, and (hπa2) is the volume of the water in the column above the reservoir.

Measuring Surface Tension

One method to measure the surface tension of a liquid is to measure the height the liquid rises in a capillary tube. By setting the two forces above equal, we find the surface tension to be:
For pure water and clean glass, the contact angle is nearly zero. In a typical high school lab, this may not be the case, but θ is small and we assume that cos θ is close to 1.
Note that students must convert ρ, g, a and h into SI units before entering them into the equation. The SI unit for surface tension is J/m2 (or N/m).
The accepted value of the surface tension of water in air at 20o C is γ = 0.073 J/m2. However, you must use pure water and extremely clean glass to get this result. Usually, the measured surface tension is at least half of this number.

### Vocabulary/Definitions

 The convex or concave upper surface of a column of liquid, the curvature of which is caused by surface tension. (plural: menisci) Source: Dictionary.com. The property of the surface of a liquid that allows it to resist an external force. This property is caused by cohesion of like molecules and explains many of the behaviors of liquids. Source: Wikipedia, May 2011.

### Associated Activities

• Exploring Capillary Action - Students observe glass-water menisci and explain the shape in terms of adhesive forces. Using capillary tubes, they see water climbing due to capillary action. Then, teams design and test "capillary siphons" that can be used to filter water.
• Measuring Surface Tension - Students use capillary action to measure surface tension. They find the average surface tension and calculate the statistical error.

### Assessment

Pre-Lesson Assessment

Discussion Questions: Ask the students and discuss as a class:
• Who can remind the class what we have already learned about surface tension?
• When you water a plant, no matter where in the pot you pour in the water, the water reaches all of the roots. How does it do this?
• Why does a paper towel absorb water, while a piece of plastic does not?

Post-Introduction Assessment

Problems to Check for Understanding: Ask students to work individually (or in pairs or small groups) to answer the following two problems. Review and discuss answers as a class (or have students compare answers) in order to gauge their level of understanding before moving on to conduct the associated lab activity.
1. Estimate, in cm, how high water will reach by capillary action if the tube is the diameter of a human hair, 150μm (1.5 x 10-4 m), if we assume the surface tension of water in air is 0.073 J/m2. (Answer: 84.3 cm)
2. Explain in 3-4 short sentences why water is able to move up a thin tube.

Lesson Summary Assessment / Homework

Expand on What You Have Learned: Either in class or at home, assign students to investigate a real-life example of capillarity in action. Use the examples mentioned in the Introduction/Motivation section or others provided by the teacher. Require that each student prepare a poster and/or three-minute class presentation that includes at least four pictures to illustrate the example, and answers to the following questions:
1. How would you describe your capillarity example?
2. Why is your topic an example of capillarity?
3. What are the practical uses or effects of your example?

### References

Adamson, Arthur W., et al. Physical Chemistry of Surfaces. New York, NY: Wiley, 1997, p. 16-19.

Brown, Theodore, et al. Chemistry: The Central Science. 9th edition. Upper Saddle River, NJ: Pearson Education, Inc., 2003. (General information on surface tension and capillary action.)

JRank Science & Philosophy Science Encyclopedia. "Capillary Action." Science.jrank.org. Accessed June 2010. http://science.jrank.org/pages/1182/Capillary-Action.html

Mike. "Tree Physics 1: Capillary Action, the Height of Trees, and the Optimal Placement of Branches." Posted July 2009. Npand.wordpress.com. Accessed August 2009. (Derivation of water height in capillary tubes). http://npand.wordpress.com/2008/08/05/tree-physics-1/

Robinson, Clay. "Capillary Action." Last updated January 27, 2009. Accessed August 2009. (Includes discussion of capillary action in soil). http://www.wtamu.edu/~crobinson/SoilWater/capillar.html

Smith, S. E. "What is Capillary Action?" Accessed June 2010. http://www.wisegeek.com/what-is-capillary-action.htm

Stein, Becky. "Capillary Action." Last updated August 8, 2009. Chemwiki.ucdavis.edu. Accessed July 2010. http://chemwiki.ucdavis.edu/Physical_Chemistry/Physical_Properties_of_Matter/Intermolecular_Forces/Cohesive_And_Adhesive_Forces/Capillary_Action

### Contributors

Jean Stave, Durham Public Schools, NC, Chuan-Hua Chen, Mechanical Engineering and Material Science, Pratt School of Engineering, Duke University