UKC

So, blowing up some balloons the other other day, I noticed the following phenomena and haven't been able to understand it.

When blowing up a balloon there is an initial strong resistance, once past this resistance point however, the balloon then resists inflation less. I don't understand this. If I were to stretch an elastic band, the resistance would increase as the stretch increased. Why is inflating a balloon different?

Elastic band - one direction of motion, one direction of energy stored in stretch.

Baloon - each puff of breath is a constant volume, energy is stored in two dimensions of stretch (surface area), volume added is stored in three dimensions (volume of balloon).  Each successive, same-sized increase of volume requires less change in stretch of the balloon membrane.

The ratio of change in area to change in volume goes as 1/radius so it falls pretty steeply to start with then the change becomes much less noticeable.

That's my first thought; I’m sure the physics is way more complicated but perhaps that’s an intuitive starting point.

Next up, use a section of pipe or a hoselock F/F coupler to join an inflated balloon to an empty balloon.  What do you think will happen?  I was surprised.  But it’s the same physics at work.

No, I think you missed what he was observing. Once you get the balloon going, it's the physics you say but you have to overcome a starting resistance.

Most noticeable with a long thin balloon like making animals etc, you even see people stretching them to warm them up, the initial effort is hard but as soon as the first bit.. err... "balloons" it gets much easier. 

It's not plastic because you can return the balloon and rest it and repeat the effect

Think about the singularity at r=0; the first piece of stretch is infinitely hard for an ideal balloon - which of course it isn’t.  The physics I describe explains the first breath being much harder.  That is repeatable after deflation.  Because it’s 1/r the work needed over expelling a normal breath drops off rapidly.

Stretching them might break stiction between opposite sides?  It may also leave them larger, moving them further from the theoretical singularity.

I think initial higher resistance marks expansion within the elastic limit of the material.  If you stop blowing within this period the balloon will return to its original state and you can repeat the process.  If you continue beyond this pointer gets easier because the elastic limit has been exceeded and it will continue to get easier until breaking point.  If you stop and deflate the balloon it will be all wrinkly.

It’s a testable hypothesis anyway!

It is because the elasticity of rubber is very non-linear.  If you stretch a rubber band, it actually softens first before the resistance increases as you mention.  Rubber is made up of a whole mass of polymer chains that are linked together to make a network.  In the unstretched state each chain is a random walk; when you stretch the rubber, each chain is stretched in proportion, and this reduces their entropy - the chain is less disordered in a stretched state than at rest, and the 2nd law tells you you can only decrease the entropy by doing work.  This is where the resistance to stretching comes from.  The simplest theory based on this idea predicts that  the stress is proportional to (extension ratio - (1/extension ratio)^2).  

It's a very nice problem to show, assuming the classical theory of rubber elasticity, that the maximum resistance point when blowing up a spherical balloon occurs when the balloon is 1.38 times its original radius.  (I set it as a homework problem for my students!). It's a little bit subtle because the deformation when you blow up a balloon isn't a simple stretching, but an equal stretching in the two directions in the plane of the sheet, and a contraction of the thickness to keep the volume constant.

I have an urge for you to mark my first answer!  It’s odd but I miss the scathing negativity of peer review…

YHM.

I'm with you.

Extension is proportional to force (Hooke). Extension is pretty obviously not linear with volume in a balloon.

youtube.com/watch?v=_btWTwDVRj8&

Law of Laplace, can't quote it, too long ago, but YouTube has the answer.

I’ve noticed that when you blow up those elongated balloons for making giraffes and sausage dogs, they take a huge amount of puff to get going. Why? Or am I imaging it?  

You’re supposed to twist them into animal shapes after you’ve blown them up, not before. 

It's more materials science than physics.

It's the elastic modulus (I think, been years since I looked this up). The balloon material resists the pressure up to a certain point, (elastic modulus) then suddenly deforms (think stretching a small spring until it suddenly elongates and won't spring back).

Your first puffs need to pressurise the balloon up to the point where it suddenly weakens, at which point the balloon suddenly expands, dropping the pressure and making subsequent puffs much easier.

(I had to look at why the gloves in gloveboxes were suddenly bursting under negative pressure in the glovebox without the low pressure relief valve opening to let more air into the glovebox. The pressure dropped to just below the trip level, the gloves went past their elastic modulus before the valve opened, then the negative pressure slowly decreased as the gloves 'balooned' inside the box and then went bang. Solved by fitting vortex amplifiers to the glovebox vent).

Intuitively this seems right.  It's analogous to why bubbles can't form in a liquid without a nucleation site.

Wow, some amazing answers here. I think I understand some of what's going on in the most rudimentary fashion now. Thanks everyone!

I observe the same phenomenon with Mrs Num Num's knicker elastic. The fatter she gets, the more fatigued and slack they become.

Why are you blowing up her knickers?

Snakes are the animal I can make - my speciality. The kids seem to tire of it quickly though..

Deflate and reinflate. It's easier - so there is a non reversible expansion on the first inflation. So you've got the simple Hooke's law below with change in dimension Vs volume explaining the main part.

But there is an initial stretch that is more resistant to deformation and non-plastic. That is why the first blow is harder.

When I worked in a plastics lab (a long time ago), we regularly tested the tensile strength of uPVC and polypropylene sheet materials at room temperature. The tensile strength graph usually peaked high initially, then dropped into a relatively lengthy elastic phase, or 'cold draw' before failing suddenly and completely.

The samples formed a lighter coloured, distinctly smaller diameter, increasingly long 'neck', which was the clue that the elastic phase had been reached.

The initial strength phase (if I remember correctly) was due to the presence of relatively taut, brittle polymer chains which then snapped at the molecular level under tension, leaving the lower strength elastic polymers to hold on  - hence cold draw - before they too failed.

I'm guessing there may be a similar thing going on blowing up balloons and stretching elastic bands. They would have a lot more elastic polymer component, as they can virtually return to their initial size when deflated again (uPVC and polypropylene can't return after stretching). It's easier to re-inflate a balloon afterwards because the few brittle polymers present have already been broken.

Stress strain graphs for rubber are non linear and on relaxation contain hysteresis.... a few quick stretches warms the rubber up and being warmer reduces the elastic modulus....I still think the main cause of being initially hard to inflate is as you describe.

I agree that rubber does show some hysteresis on cyclic deformation, but I don't think this is a big contributor to this effect - rubber, unusually, has an elastic modulus that gets larger rather than smaller when it is heated.  It's stiffness is close to proportional to absolute temperature, which shows that rubber elasticity is almost entirely entropic in origin.  When you stretch rubber, the polymer strands get straighter, i.e. less disordered & lower in entropy - the second law says you can't make things less disordered without doing some work, and that's where the resistance to stretching comes from.

I think Wintertree's explanation is a good starting point - as you inflate the balloon, the work you're doing is the pressure times the change in volume, and you trade this work done for the elastic energy in the stretched balloon.  A starting assumption would be that the change in elastic energy is proportional to the change in area, then as Wintertree says trading a volume term against a surface term does indeed give you a peak in the pressure vs radius graph, hence the initial strong resistance and later easier inflation.  As GrahamD says, this is exactly analogous to the physics of nucleation of a fluid droplet from a vapour.

But this still isn't quite right, because of the effect I mentioned in my earlier post.  Because rubber is pretty close to being incompressible, as you inflate the balloon the rubber is stretched in the two directions in the plane of the sheet, but it also has to get thinner to keep the volume of rubber constant.  This has the effect of reducing the effective modulus at larger degrees of stretching, so the increase in elastic energy isn't strictly proportional to the increase in energy - as it gets stretched the balloon gets easier to inflate.  The effect of this is to make the peak in pressure sharper, with the peak pressure occurring (in simple theory) when the ratio of balloon radius to original radius is the sixth root of seven.  I think it's rather a lovely problem to derive this ... (but I may be in a minority on that).

Although what you say makes complete sense in terms of the physics, there must be other factors involved. I did experimental work on rubber in an A level project, looking at force extension data at varying temperatures (converting to stress-strain). This was mainly 0 to 100 centigrade,  but part of the fun was I got to play with liquid nitrogen: this made the rubber brittle, not more stretchy. Also balloons are easier to blow up when stretched several times (and the rubber does warm up when you do that).

Two same-sized rubber balloons were selected at random from the same packet of unknown provenance.  Both were inflated and deflated 3 times to eliminate any irreversible changes from inflation.  The portal and neck of a deflated balloon was pulled over one side of a Verve branded 1/2” hose pipe connector [1].  A second deflated balloon was manually inflated by blowing in to it.  The portal and neck of this inflated balloon was carefully pulled over the other end of the hose pipe connector.  It was observed that the deflated balloon inflated ever so slightly with little perceptible change to the inflated balloon.  The inflated balloon was squeezed in a bear hug with contact points from both arms, both knees and the belly to provide approximately uniform surface compression.  The hose joiner was carefully supported to prevent either balloon’s neck from kinking.  The large balloon only started deflating and inflating the other balloon at the point the experimenter was involuntarily closing their eyes in anticipation of a burst.  Squeezing the balloon became progressively easier as it shrank and the other balloon inflated.  This effect whereby the initial squeeze is the hardest was observed to be fully reversible across six transfers between the two balloons.  The experiment was significantly hindered by the appeal of balloons to the experimenter’s child and said child’s wilful lack of self control, good listening ears and an appreciation of the importance of either surface/volume ratios or materials physics.
 

[1] - https://www.diy.com/departments/verve-hose-pipe-connector/5059340251134_BQ....

Cool.

Just because I can't help myself, here's a pic from some Scottish research into the application of balloons and static electricity for political protest.  (It's more subtle than the better known 'protest balloon'.)

Given that air and rubber are pretty good insulators, I would be inclined to say it is adiabatic.

Although Richard is indeed a Professor of Rubber Balloon Science (or some similar title, I forget) it is nice to see someone doing some serious experimental work to confirm his theoretical predictions.

Yes, there's great primitive satisfaction to be had in dipping rubber tubes into liquid nitrogen and then hitting them with a hammer, to see them shatter.  What's going on there is that below a certain temperature the chains lose all ability to move relative to each other, and you get a glass, which has a much higher modulus than rubber, but which is very brittle.  The physics of the transition from a glassy state to a rubbery one is entirely different story...

A very enlightening experiment you can do is take a rubber band, or (better) a balloon folded into a strip, stretch it suddenly, and then put it to your lip.  It will be noticeably warm.  But this is (mostly) reversible, so it's not simple dissipation.  If you then release the stretching, you'll find it has returned to its starting temperature.  If you do the same thing, but after the initial stretch, hold it in the extended state for a while, so the temperature returns to room temperature, and then release it and put it to your lips, it will be noticeably cold.  You can understand this all in terms of the decrease in entropy when the rubber is stretched.  It's easy to imagine that you could use this principle to make a rubber band powered refrigerator - this video shows someone doing just that, with some nice explanations

youtube.com/watch?v=lfmrvxB154w&

Much better than my actual job title, I should put that on my business cards...

Brilliant stuff

I think with this latest addition, i.e. the rubber band powered refrigerator, this thread now has enough sensible discussion mixed in with surreal weirdness to achieve UKC classic thread status 😁

Squash balls bounce more when warm. Is this due to the rubber's elasticity or an increase in internal pressure (or both or something else)?

And a CNC router attachment as well, I want one.

I think that is due to the hysteresis effect that Offwidth mentioned - when you cyclically deform & undeform rubber - as happens when the squash ball hits the wall, is compressed, and then springs back - you lose some energy in each cycle.  For rubber it turns out that the amount of loss you get is quite a strongly peaked function of temperature.  For normal rubber that peak temperature is probably a bit below zero, so when your squash ball warms up it gets bouncier.

It's the same loss peak that makes climbing shoes feel stickier on cold days - but that's a discussion for another time.

Please, please, start a thread on climbing shoe rubber one day not too far into the future.

Rubber also contracts when heated - IIRC, We did an experiment in physics where we suspended weights from rubber bands then heated the bands with a hairdryer and the weights were lifted up.

The point at which elastic behaviour (material returns to original shape & size once stress is removed) becomes plastic behaviour (permanent deformation occurs) is called the 'yield stress'.  The 'stress/strain' curve of a material often changes slope drastically at this point.

I had a very satisfying moment when I was preparing some slides on dielectric capacitors and realised there must be a decrease in entropy and rejection of heat from the loss of a degree of freedom when they’re charged, and a corresponding cooling down when they’re discharged.  The analogous effect is used with magnets to make milli kelvin refrigerators within liquid helium cooled systems. 

I’d not thought about it occurring with stretchy stuff.  In all cases it must presumably mean that some of the energy stored when stretching/charging/magnetising is stored thermally; cool the systems enough and they can’t randomise/thermalise, leaving them in their charged state.  An almost imperceptible change in temperature if they’re in good conductive contact with the environment but an absolutely critical source of heat for reversibility.  Tenuously like pulling a beach ball under the ocean - a violent release of energy stored as an imperceptible rise in sea level.

As perhaps you remember, we did one of those 2 decades ago...

https://www.ukclimbing.com/forums/rock_talk/why_does_colder_weather_result_...

And, giving that epic thread another look makes me reluctant to repeat it!

Yes, exactly, thats another aspect of the same phenomenon. The modulus is stress/strain, when you heat it it gets stiffer, so for a constant stress (i.e. with a weight hanging on it) the strain must decrease as the modulus increases - the weighted band contracts. You can make a heat engine on thus principle.

I vaguely remember it but had not linked you to it. Rereading it I think you came out well.

I tried to get some sports science and physics projects going back then, through pals, on climbing shoe friction and hand friction (that paper that said chalk didn't work really annoyed the experimentalist in me) but I failed.