Oxford scientists crack case of why ketchup splatters from near-empty bottle

Ketchup and mayonnaise are two of the most popular condiments in the US, but getting a small amount out of the bottle can cause a sudden splatter. It can ruin clothes, but can we do anything about it? At the American Physical Society meeting on fluid dynamics in Indianapolis, Indiana, the University of Oxford's Cuttle spoke about his research. Can understanding this phenomenon help us with other issues?

According to Cuttle the answer to both questions is yes. He and his Oxford colleague, Chris MacMinn, conducted a series of experiments to identify the forces at play. It was found that squeezing the bottle more slowly and doubling the diameter of the nozzle helped prevent splatter. There is a threshold where the flow of Ketchup suddenly changes from not splattering to splattering. A paper has been posted to arXiv and is being reviewed.

The properties of an ideal liquid were identified by the man. Viscous is defined as how much resistance there is to flow in a substance. A flowing liquid is a series of layers sliding past each other. The quicker one layer slides over another, the more resistance there is, the less resistance there is.

Not all liquids behave in the same way. Water will act like water regardless of other forces acting on it, such as being stirred or mixed, in the ideal fluid. The boundary between liquid and solid behavior is straddled by a non-Newtonian fluid's rhythym. The water shears to move out of the way when a cup of water is stirred. There is no change in the Viscosity. When a shearing force is applied, the viscosity of non-Newtonian fluids change.

Other examples of ketchup include blood, yogurt, gravy, mud, pudding, and pies. None of them adhere to the definition of an ideal liquid, even though they aren't all alike.

Ketchup is made from tomato puree suspended in liquid, which makes it more of a soft solid than a liquid. One must overcome the strength of the network in order to get the ketchup to flow by tapping or hitting the bottle. The faster the Ketchup flows, the more it decreases in thickness. The optimal flow rate is 0.0045 per hour, according to scientists at the company.

You need to hit it harder when you only have a small amount of the sauce left in the bottle. Cuttle said that by the time you reach the end, most of what is inside is air. When you squeeze, the air in the bottle builds up pressure that drags the sauce out. There is less and less ketchup in the bottle. There is more and more room for the air to expand inside the bottle because of the outflow of liquid.

Understanding the dynamics of why the smooth flow suddenly shifts to a splatter is the first step. Cuttle and MacMinn injected different amounts of air at different compression rates to see how the amount of air affected the flow rate. In order to better control the key variables, they repeated the experiment with a syringes filled with Silicon oil.

The result was a large amount of air injected into the syringes. Cuttle said that this tells them that you need some air in the bottle to make a splatter. Depending on factors such as the amount of air, the rate of compression, and the diameter of the nozzle, that threshold is called asauce splatter critical threshold. The driving force and liquid outflow are balanced below that threshold. The driving force goes higher than the outflow. The air gets too compressed, like a spring, and the last bit of food is thrown out.

"Squeezing too hard will cause a splatter rather than a steady stream of liquid," said Cuttle. The rate at which the air is compressed can be reduced by squeezing more slowly. Since the rubber valve at the spout can increase the risk of splatter, widening the nozzle's diameter would be more beneficial. The valves help avoid leads, but they also force you to build up a certain amount of pressure in order to make the bottle. Cuttle suggests taking the cap off the bottle when it's nearly empty to squeeze the last bits of the sauce out of the neck.

It's common sense, but now there's a rigorous mathematical framework to back it up. A gas pushing a liquid out of the way is common in other contexts. Some volcanic eruptions and re-inflating collapsed lungs are included.

ArXiv is published in the year 2022. The About DOIs can be found in 10.48550/arXiv.