The study teaches how to compress a tube without splattering

Who has never had an accident with a ketchup tube – especially when it’s on the very end. Getting those last leaks can cost you unwanted high-velocity splatter.

But science can help you avoid dirt in the home and stains on clothes.

“It’s annoying, potentially embarrassing and can ruin clothes, but can we do anything about it?” Calum Cattell of the University of Oxford said at a meeting of the American Physical Society on fluid dynamics. “More importantly, can understanding this phenomenon help us solve any other problems in life?”

The answer to both questions, according to the researcher, is a resounding yes. Together with his Oxford colleague Chris McMinn, he conducted a series of experiments to determine the forces acting upon squeezing ketchup and to develop a theoretical model for spraying.

Among the most interesting practical discoveries are the following:

• Slower pressure on the tube and increased nozzle diameter helps to avoid splashing.
• There is a critical threshold at which the flow of ketchup changes abruptly from no spatter to spatter

Pre-print article published in the arXiv repository It is currently undergoing peer review.

Why is it splashing?

Isaac Newton identified the properties of what he considered an “ideal fluid”. One is a well-defined viscosity (basically, how much friction/resistance it exerts when flowing), regardless of the forces applied to it.

But not all liquids behave as “ideal”. In non-Newtonian liquids—such as ketchup, mustard, mayonnaise, candy, yogurt, blood, and slurry—viscosity is not well defined, and varies according to the degree of pressure applied.

Physicists often call this a “shear force”: moving a glass of water creates a shearing force, and the water deforms to get out of the way, but its viscosity remains unchanged.

But ketchup consists of tomato solids suspended in a liquid, making them more of a “soft solid” than a liquid, according to Anthony Strickland of the University of Melbourne, Australia. The solids connect to form a continuous web, and you have to overcome the strength of that web to get the ketchup to flow—usually, hitting the “back of the bottle.”

When we do this, the viscosity decreases – the lower it is, the faster the ketchup will flow. Heinz scientists calculated the ideal ketchup flow rate to be 0.0045 per hour.

But when only a few are left ketchup In the packaging you have to tap harder, which increases the risk of splashing.

“By the time you get to the end, a lot of what’s inside is air,” he said. squid🇧🇷 “So when you squeeze, what you’re doing is squeezing the air inside the bottle, which increases the pressure that pulls the ketchup out.”

The nozzle plays the role of providing a drag force that counteracts the viscous flow of the ketchup, and the balance between them determines the flow rate. When you empty the bottle, the viscosity decreases because there is less and less of it ketchup To push – and more and more space for the air to expand inside, which reduces the driving force over time.

Experience

Understanding the complex dynamics of why a smooth stream suddenly changes to splatter begins by simplifying the problem.

Cuttle and MacMinn did a similar experiment with a ketchup bottle in the lab, filling syringes with ketchup and injecting different amounts of air (from 0 to 4 milliliters) at constant pressure rates to see how the change affected the rate of flow—and spatter.

They repeated the procedure with syringes filled with silicone oil, to better measure viscosity and other variables, and designed a mathematical model of how the packaging should compress.

Result: Syringes containing 1 milliliter or more of injected air produce spatter. “This tells us that it takes quite a bit of air in the syringe (or packaging) to generate an atomizer and create that intermittent flow of flow,” Cattell said.

There is a critical threshold for “pour ketchup,” when ketchup changes from a smooth flow to a splatter, depending on factors such as the amount of air, pressure ratio, and nozzle diameter.

Under this limit, the driving force and the fluid flow are balanced, so the flow is smooth. Above that, the driving force decreases faster than the outflow. The air becomes extremely compressed, like a pent-up spring, and the ketchup residue is forced out in a sudden blast.

What do you do in the end?

“The splatter of the ketchup bottle can be minimized: squeezing a little too hard will produce a splatter rather than a steady stream of liquid,” says Cattell.

A helpful tip is to compress more slowly, thus reducing the rate of air pressure.

Widening the diameter of the nozzle further will help as the rubber valve can increase the risk of splashing. Yes, the valves help prevent leakage, but they also force the person to apply more pressure to get the ketchup to start flowing out of the container.

As a practical trick, Cuttle recommends removing the cap only when the bottle is nearly empty, using the rest of the ketchup with a wider neck.

“It makes sense, but now there is a rigorous mathematical framework to support it,” Cattell said. “And gas pushing liquid out of the way is something that happens in many other contexts.”

The mathematical model and results from the study can be applied to other situations, such as aquifers storing captured carbon dioxide, certain types of volcanic eruptions, and collapsed lungs that need to be reinflated.

*With information from Ars Technica