Spilling Juice From Cartons or ‘Tetra Paks®’

spilling juice from cartons

Introduction

This post contains instructions on how to avoid spilling juice from cartons or Tetra Paks®, with a rectangular cross-section, while opening or lifting them. It’s quite natural to grip cartons by the easiest method (the broad sides) while opening them, or lifting them when they’re still full, causing the contents to pour or squirt out inadvertently. Cartons with a square cross section are indifferent to the sides that are gripped when lifting or pouring.

Situation

You go to the refrigerator and take out a new cool carton of juice. You hold it firmly and take off the seal and juice spurts out at you and runs down the side of the carton, or you pick it up after removing the seal and juice pours out as you grip it. Before you’ve got it in a glass you’re in a mess. This is usually caused by the way you grip the carton.

Method To Avoid Spilling Juice From Cartons or Tetra Paks®

Don’t pick it up like this:

spilling juice from cartons
Method 1

Pick it up like this:

spilling juice from cartons
Method 2

What happens?

Method 1 shows the carton being squeezed on the broad sides. This action tends to reduce the internal volume of the carton because the narrow sides are too rigid and won’t bulge out to compensate. This puts pressure on the contents and the juice is ejected when the carton is full and the seal is broken.

Method 2 shows the carton being squeezed on the narrow sides. The broad sides easily bulge out, and since they are not so rigid as the narrow sides, the carton tends to retain its original volume. The volume may increase when the seal is broken sucking air into the carton. There is no extra pressure on the contents and the juice isn’t ejected.

Scientific Principle

This is based on the principle that a sphere has a surface area to volume ratio of 3:1 and is the highest ratio of any shape. A carton with a rectangular shape therefore has a lower ratio.

The carton shown here has the following dimensions:

  • Height 19 cm.
  • Width 9 cm.
  • Depth 5.5 cm.
  • Surface Area 650 cm2
  • Volume 940.5 cm3

Therefore it has a (Surface Area):(Volume) ratio = 650:940.5 = 0.7:1 which is much lower than that of a sphere.

So if the shape can be changed, by squeezing when it’s gripped, such that it becomes more like a sphere the ratio will go down. The surface area is fixed so therefore the volume will rise and air will be sucked in and the contents will not spill. This is done by squeezing the narrow sides and their edges so that the broad sides bow out.

If the broad sides are squeezed when lifting a carton they become flattened and less like a sphere. The narrow sides are comparatively rigid and don’t bulge out like the broad sides do. Common sense tells you the volume is reduced when you squeeze the broad sides. So the converse will be true, i.e. the surface area will stay the same but the surface area to volume ratio will go up. Therefore the volume will go down and juice will squirt out of the carton.

Author: Helpful Colin

I have a background in telecommunications and a fascination with all things scientific and technical - from physics to electronics, and computing to DIY.

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