Surface Tension

The forces acting on a liquid that cause surface tension

Surface tension is a phenomenon in which the surface of a liquid, where the liquid is in contact with gas, acts like a thin elastic sheet. This term is typically used only when the liquid surface is in contact with gas (such as the air). If the surface is between two liquids (such as water and oil), it is called "interface tension."

Causes of Surface Tension

Various intermolecular forces, such as Van der Waals forces, draw the liquid particles together. Along the surface, the particles are pulled toward the rest of the liquid, as shown in the picture to the right.

Surface tension (denoted with the Greek variable gamma) is defined as the ratio of the surface force F to the length d along which the force acts:

gamma = F / d

Units of Surface Tension

Surface tension is measured in SI units of N/m (newton per meter), although the more common unit is the cgs unit dyn/cm (dyne per centimeter).

In order to consider the thermodynamics of the situation, it is sometimes useful to consider it in terms of work per unit area. The SI unit in that case is the J/m² (joules per meter squared). The cgs unit is erg/cm².

These forces bind the surface particles together. Though this binding is weak - it's pretty easy to break the surface of a liquid after all - it does manifest in many ways.

Examples of Surface Tension

Drops of water. When using a water dropper, the water does not flow in a continuous stream, but rather in a series of drops. The shape of the drops is caused by the surface tension of the water. The only reason the drop of water isn't completely spherical is because of the force of gravity pulling down on it. In the absence of gravity, the drop would minimize the surface area in order to minimize tension, which would result in a perfectly spherical shape.

Insects walking on water. Several insects are able to walk on water, such as the water strider. Their legs are formed to distribute their weight, causing the surface of the liquid to become depressed, minimizing the potential energy to create a balance of forces so that the strider can move across the surface of the water without breaking through the surface. This is similar in concept to wearing snow shoes to walk across deep snowdrifts without your feet sinking.

Needle (or paper clip) floating on water. Even though the density of these objects are greater than water, the surface tension along the depression is enough to counteract the force of gravity pulling down on the metal object. Click on the picture to the right, then click "Next," to view a force diagram of this situation or try out the Floating Needle trick for yourself.

Anatomy of a Soap Bubble

When you blow a soap bubble, you are creating a pressurized bubble of air which is contained within a thin, elastic surface of liquid. Most liquids cannot maintain a stable surface tension to create a bubble, which is why soap is generally used in the process ... it stabilizes the surface tension through something called the Marangoni effect.

When the bubble is blown, the surface film tends to contract. This causes the pressure inside the bubble to increase. The size of the bubble stabilizes at a size where the gas inside the bubble won't contract any further, at least without popping the bubble.

In fact, there are two liquid-gas interfaces on a soap bubble - the one on the inside of the bubble and the one on the outside of the bubble. In between the two surfaces is a thin film of liquid.

The spherical shape of a soap bubble is caused by the minimization of the surface area - for a given volume, a sphere is always the form which has the least surface area.

Pressure Inside a Soap Bubble

To consider the pressure inside the soap bubble, we consider the radius R of the bubble and also the surface tension, gamma, of the liquid (soap in this case - about 25 dyn/cm).

We begin by assuming no external pressure (which is, of course, not true, but we'll take care of that in a bit). You then consider a cross-section through the center of the bubble.

Along this cross section, ignoring the very slight difference in inner and outer radius, we know the circumference will be 2pi R. Each inner and outer surface will have a pressure of gamma along the entire length, so the total. The total force from the surface tension (from both the inner and outer film) is, therefore, 2gamma (2pi R).

Inside the bubble, however, we have a pressure p which is acting over the entire cross-section pi R², resulting in a total force of p(pi R²).

Since the bubble is stable, the sum of these forces must be zero so we get:

2gamma (2pi R) = p(pi R²)

or

p = 4 gamma / R

Obviously, this was a simplified analysis where the pressure outside the bubble was 0, but this is easily expanded to obtain the difference between the interior pressure p and the exterior pressure p_e:

p - p_e = 4 gamma / R

Pressure in a Liquid Drop

Analyzing a drop of liquid, as opposed to a soap bubble, is simpler. Instead of two surfaces, there is only the exterior surface to consider, so a factor of 2 drops out of the earlier equation (remember where we doubled the surface tension to account for two surfaces?) to yield:

p - p_e = 2 gamma / R

Contact Angle

Surface tension occurs during a gas-liquid interface, but if that interface comes in contact with a solid surface - such as the walls of a container - the interface usually curves up or down near that surface. Such a concave or convex surface
Determining the contact angle, theta, of liquid in a vertical tube

The contact angle, theta, is determined as shown in the picture to the right.

The contact angle can be used to determine a relationship between the liquid-solid surface tension and the liquid-gas surface tension, as follows:

gamma_ls = - gamma_lg cos theta

where

• gamma_ls is the liquid-solid surface tension
• gamma_lg is the liquid-gas surface tension
• theta is the contact angle

One thing to consider in this equation is that in cases where the meniscus is convex (i.e. the contact angle is greater than 90 degrees), the cosine component of this equation will be negative which means that the liquid-solid surface tension will be positive.

If, on the other hand, the meniscus is concave (i.e. dips down, so the contact angle is less than 90 degrees), then the cos theta term is positive, in which case the relationship would result in a negative liquid-solid surface tension!

What this means, essentially, is that the liquid is adhering to the walls of the container and is working to maximize the area in contact with solid surface, so as to minimize the overall potential energy.

Capillarity

Another effect related to water in vertical tubes is the property of capillarity, in which the surface of liquid becomes elevated or depressed within the tube in relation to the surrounding liquid. This, too, is related to the contact angle observed.

If you have a liquid in a container, and place a narrow tube (or capillary) of radius r into the container, the vertical displacement y that will take place within the capillary is given by the following equation:

y = (2 gamma_lg cos theta) / (dgr)

where

• y is the vertical displacement (up if positive, down if negative)
• gamma_lg is the liquid-gas surface tension
• theta is the contact angle
• d is the density of the liquid
• g is the acceleration of gravity
• r is the radius of the capillary

NOTE: Once again, if theta is greater than 90 degrees (a convex meniscus), resulting in a negative liquid-solid surface tension, the liquid level will go down compared to the surrounding level, as opposed to rising in relation to it.

Capillarity manifests in many ways in the everyday world. Paper towels absorb through capillarity. When burning a candle, the melted wax rises up the wick due to capillarity. In biology, though blood is pumped throughout the body, it is this process which distributes blood in the smallest blood vessels which are called, appropriately, capillaries.

Quarters in a Full Glass of Water

This is a neat trick! Ask friends how many quarters can go in a completely full glass of water before it overflows. The answer will generally be one or two. Then follow the steps below to prove them wrong.

Needed materials:

• 10 to 12 Quarters
• glass full of water

The glass should be filled to the very rim, with a slightly convex shape to the surface of the liquid.

Slowly, and with a steady hand, bring the quarters one at a time to the center of the glass. Place the narrow edge of the quarter in the water and let go. (This minimizes disruption to the surface, and avoids forming unnecessary waves that can cause overflow.)

As you continue with more quarters, you will be astonished how convex the water becomes on top of the glass without overflowing!

Possible Variant: Perform this experiment with identical glasses, but use different types of coins in each glass. Use the results of how many can go in to determine a ratio of the volumes of different coins.

Floating Needle

Another nice surface tension trick, this one makes it so that a needle will float on the surface of a glass of water. There are two variants of this trick, both impressive in their own right.

Needed materials:

• fork (variant 1)
• piece of tissue paper (variant 2)
• sewing needle
• glass full of water

Variant 1 Trick

Place the needle on the fork, gently lowering it into the glass of water. Carefully pull the fork out, and it is possible to leave the needle floating on the surface of the water.

This trick requires a real steady hand and some practice, because you must remove the fork in such a way that portions of the needle do not get wet ... or the needle will sink. You can rub the needle between your fingers beforehand to "oil" it increase your success chances.

Variant 2 Trick

Place the sewing needle on a small piece of tissue paper (large enough to hold the needle). The needle is placed on the tissue paper. The tissue paper will become soaked with water and sink to the bottom of the glass, leaving the needle floating on the surface.

Put Out Candle with a Soap Bubble

This trick demonstrates how much force is caused by the surface tension in a soap bubble.

Needed materials:

• lit candle (NOTE: Do not play with matches without parental approval and supervision!)
• funnel
• detergent or soap-bubble solution

Coat the funnel mouth (the large end) with the detergent or bubble solution, then blow a bubble using the small end of the funnel. With practice, you should be able to get a nice big bubble, about 12 inches in diameter.

Place your thumb over the small end of the funnel. Carefully bring it toward the candle. Remove your thumb, and the surface tension of the soap bubble will cause it to contract, forcing air out through the funnel. The air forced out by the bubble should be enough to put out the candle.

For a somewhat related experiment, see the Rocket Balloon.

Motorized Paper Fish

This experiment from the 1800's was quite popular, as it shows what seems to be sudden movement caused by no actual observable forces.

Needed materials:

• piece of paper
• scissors
• vegetable oil or liquid dishwasher detergent
• a large bowl or loaf cake pan full of water

In addition, you will need a pattern for the Paper Fish. To spare you my attempt at artistry, check out this example of how the fish should look. Print it out - the key feature is the hole in the center and the narrow opening from the hole to the back of the fish.

Once you have your Paper Fish pattern cut out, place it on the water container so it floats on the surface. Put a drop of the oil or detergent in the hole in the middle of the fish.

The detergent or oil will cause the surface tension in that hole to drop. This will cause the fish to propel forward, leaving a trail of the oil as it moves across the water, not stopping until the oil has lowered the surface tension of the entire bowl.