The world's longest running experiment
In 1927, Professor Thomas Parnell started an experiment to demonstrate to students that some substances have both solid and liquid properties. Parnell poured a heated sample of pitch into a sealed funnel and allowed it to settle for three years. Turns out, three years was far too less to play out the entire experiment. To this day, droplets fall roughly once every 10 years. But if you were to smash it with a hammer, it would shatter like a solid. Thus this poses a puzzle - is pitch a solid or a liquid?
While pitch might sound like a special material, it is in fact not. Pitch is derived from petroleum or coal tar, and is used to make road asphalt and in commercial roofing as a waterproofing agent. In fact — Most everyday materials such as glass, plastic, even mayonnaise have a combination of elastic (solid) and viscous (liquid) properties. These everyday materials are called viscoelastic materials.
Is it possible to run on a liquid?
One of the key distinguishing features between solids and liquids is solids can support stress: you can walk on a solid whereas liquids don't. Why is this? As we discussed before, atoms in solids act as springs. When you apply a certain force on a spring, it recoils back with the same force. Think about jumping on a mattress or a trampoline - the harder you jump down, the equivalently large force that pushes you upward. Scientifically, you are applying a stress (force/area) on the solid, which results in the atoms in a solid displacing like springs coiling (strain). This results in the atomic springs in the solid pushing back just like a spring and supporting the force you apply (see Ch. 4). Turns out these atomic springs are essential for walking. When you walk on paved concrete, you are compressing the concrete atoms ever so slightly and that provides the equivalent force back to support your feet.
For liquids however, any stress you apply, leads to the atoms moving or flowing at a certain strain rate (see Ch. 4). Thus, more force you apply to the liquid, more the flow leading to an opposite effect as a solid. If you jump into the pool, you fall in deeper as compared to if you just waded in. However, most everyday materials break this traditional view of solids and liquids. One classic example is a common household thickening agent, cornstarch.
Cornstarch powder when mixed with water gives a thick, soupy solution. As the ratio of cornstarch powder relative to water increases, the solution becomes thicker and thicker. However, this solution is not simply a thicker more viscous solution. Cornstarch in water is also known as Oobleck. When you have a large container with a mixture of equal parts water and cornstarch, try to slowly push a spoon through it. You will find that it moves like spoon through honey or any other viscous liquid. However when you try to push the spoon at a faster rate, the Oobleck resists flow and at an even higher rates, it breaks up like a solid.
But why is this happening? Turns out that Oobleck has different viscosity based on the force you apply on it. Larger the force, higher the viscosity. So if you push softly through Oobleck it behaves like honey. But if you push hard, it behaves like concrete. The reason behind this is cornstarch powder is composed of microscopic grains. When you push slowly on a dense mixture of cornstarch in water, the grains of cornstarch flow past each other without much disturbance. But if you push hard, these grains suddenly bump into each other and get stuck. Because of this, when more force is applied, cornstarch becomes more viscous. This property of larger viscosity corresponding to larger applied stress is known as shear thickening .
If you thought that shear thickening pretty much explains why you can run on Oobleck; think again! Shear thickening explains why cornstarch-water mixtures get more viscous with higher applied force, which means that cornstarch gets harder to spread. However it still doesn't explain why cornstarch acts like a solid and supports the stress of a person jumping or running on it. According to a 2012 article in Nature, physicists Scott Waitukaitis and Heinrich Jaeger find the reason this is possible is because once you jump in a pool of cornstarch-water, you quickly create a solid by compacting nearby grains together. This is similar to inducing a traffic jam at a bottleneck.
Let’s pause to think about this a bit. As vehicles enter a roadway with a bottleneck such as a few lanes blocked due to an accident, they need to cooperate with each other to navigate smoothly. More often than not, some people try to swerve in at the last minute, and others are too polite. All this sudden confusion at the bottleneck leads to inefficient navigation and pile ups close to the origin of the disturbance. It’s the same idea for jumping on cornstarch. the grains next to the point of the jump can’t efficiently rearrange and cooperate in the immediate aftermath of the jump. Instead, they just get compacted, providing enough force to support the weight of the person. But once the jump is finished, the compacted grains slowly return back to their original configuration as if nothing ever happened. This is similar to a traffic bottleneck caused due to an accident that dissipates some time after the lanes are cleared.
The same underlying physics of congestion is seen both in household cornstarch as well as traffic jams; even though grains of cornstarch and human drivers are quite different. Isn’t that fascinating! The 2012 study also found this effect is stronger in shallower pools, where an immediate solid core forms that supports your stress, all the way down to the bottom of the pool. If you had a deep pool, running on it gets much harder — keep that in mind for your next cornstarch pool party!
A lab on cornstarch water mixtures is a great way to ensure student engagement and a great way for students to learn! All you need is basically household cornstarch, water, a measuring cylinder and a shallow mixing container. This way, each student can purchase these low-cost materials and do it themselves. its a great option for hands on labs even if centralized group lab activities are not feasible due to social distancing concerns.
Is ketchup solid or liquid?
When you pour ketchup out of a bottle, you need it to flow like a liquid. However, once it is on your plate, you don't want it flowing anymore. Instead, you would like it to remain stationary. So how is ketchup able to read your mind and know what phase to be in? The trick is in how you pour ketchup.
If you remember, you need to shake ketchup in order for it to flow out of the bottle. This is quite contrary to cornstarch in water. If you had cornstarch-water in a bottle, it would get clogged at the bottleneck rather than flowing when you shook it! So why does ketchup do this?
Unlike cornstarch-water, ketchup is shear thinning. As you apply more force to ketchup, its viscosity decreases, i.e. it becomes easier to flow. Ketchup not only has tomato juice, it also has Xanthan gum added to it, and its the Xanthan gum that makes it shear thinning. Its actually quite similar to quick sand. Unlike running on cornstarch-water, running is quicksand has the opposite effect in that you sink in quicker.
Spring and dashpot models
Viscoelastic materials like ketchup or cornstarch have properties of both solids and liquids. Such materials can be thought of as combinations of springs (solid part) and dashpots (liquid part) such as the Maxwell model in the image above, proposed by James Maxwell in 1867. The dashpot can be thought of as similar to a syring that takes a certain time to absorb a fluid depending on the viscosity of that fluid, and whose displacement does not go to zero once the pulling force is removed. This model captures the solid behavior at short timescales and liquid behavior at longer timescales. An example of this is silly putty which bounces as a solid when struck on the ground, but flows as a liquid when kept on a table. There are a couple of nice videos illustrating the Maxwell model.
The displacement of the entire system is a combination of spring and dashpot displacement, given by the equation below. The spring and dashpot are in series - they experience the same force, and their displacements add up.
For an ideal spring, the displacement is independent of time, and only dependent on the force applied as well as the spring constant of the spring. However for the dashpot, the displacement depends on the force applied, viscosity of the fluid, as well as how much time the force is being applied over. If time is close to 0, the displacement is mainly from the spring, and thus the material behaves more as a solid. Whereas if the timescale is long, the dashpot shows larger displacement than the springs initial displacement, and the material acts more as a liquid than a solid, since the dashpot deformation does not go back to zero once the force is removed.
Another common spring and dashpot model is the Kelvin-Voigt model. In this model, the spring and dashpot are in parallel - meaning they are constrained to the same displacement.
This type of model captures a phenomenon known as creep. Creep denotes the slow increase in strain when a viscoelastic material is subject to constant stress. An example is the movement of ice in a glacier, known as glacial creep.
The Kelvin-Voigt model does a better job at predicting how the strain of a material exhibiting creep increases in time.