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I was thinking on a experimental question, but I couldn't get the answer:

How can we measure how the Mullins effect influences in the pressure inside a balloon? (I mean that, if there is a formula, tell me!)

ACuriousMind
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Michaele
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1 Answers1

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A good way to measure pressure inside a balloon is to create a setup with a balloon, a manometer (long thin liquid filled U shaped tube), and a three way valve. You increase the pressure in the balloon by pumping it up, then measure the pressure with the manometer. Keep increasing the pressure and measure the diameter of the balloon as you go. Let the pressure out, and repeat. You will find that the pressure-diameter curve keeps shifting, just as it does in the curves in the article you linked.

Key to doing this experiment properly is having a good technique for measuring the volume. I would recommend placing the balloon in a darkened room with a small bright source of light, casting a shadow onto a piece of graph paper. Or cast the shadow onto a piece of tracing paper and take a digital picture of the shadow. Or just take a picture of the balloon against a differently-colored background. The volume will scale approximately with the area to the power $\frac32$, but if you plot area itself as a measure of "strain", it would show the effect. In fact, since the area of the balloon surface scales with the area of the projected volume (for an object with reasonable symmetry), just measuring the projected area and not converting to volume will actually be better...

There is one other thing to keep in mind - and that is the analysis given in this earlier answer to this question which relates to the fact that a balloon becomes thinner during inflation, and that this will affect the pressure as a function of diameter. But by repeated cycling and seeing that the curves shift you should be able to differentiate between Mullins effect and this other phenomenon.

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Floris
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  • Mullins as well as that other effect is seen in "filled" rubber. The rubber for baloons isn't. – Georg Jan 26 '15 at 18:03
  • @Georg - fair point, but the question was "how can we measure". If the rubber of the balloon under test does not exhibit Mullins, the experiment will show it (meaning: will show no effect). I don't want to presume that I know what balloons OP wants to use in the experiment. – Floris Jan 26 '15 at 18:06
  • So , How can I measure ? (means that Is there a formula that I can measure Mullins effect with it?) – Michaele Jan 26 '15 at 20:17
  • No, I don't think there is a "formula". The experiment as described allows you to draw a graph of the relationship between volume and pressure; if the Mullins effect is significant, cycling pressure and volume will give you a different value after you take the balloon up to a new max pressure (just as in the diagram in your link). – Floris Jan 26 '15 at 21:04
  • So , you just told me the way of measuring Mullins effect but is it true ? I mean that is it true to solve this question with some experiments??? – Michaele Jan 28 '15 at 16:02
  • Whether the effect occurs in a balloon depends on the balloon. I gave an outline of an experiment that might be able to show the effect, but it's hard to say "it is true" without going through the experiment, thinking about your observations, adjusting the experiment, etc. I have not done the experiment so I can't tell you what the result will be - especially since I don't know what balloon you will be using (and as others commented, the latex in most balloons does not exhibit the effect). I am puzzled at the way you phrase your question... – Floris Jan 28 '15 at 16:07