Chemistry Applied to Drops, Blobs and Bubbles.

 

A few days back in the early morning, I was out for a stroll when I noticed something very usual which triggered certain levels of reflection.

It was about the morning dews on leaves.  

Why is it that when you pick up a leaf containing several drops of water(dew) and toy around with it the larger drop absorbs the smaller drops (or why do the smaller drops pop in contact with other larger or similar size drops to form an even larger drop?)Why does it not happen that the drops stay intact??

One can even extend this phenomenon to a similar situation consisting of large blobs of oil in suspension in water: A similar observation is obtained in oil droplets suspended in water: a quick shake causes large blobs to break into smaller ones, only to eventually, reform larger ones.

Why is this the case??

Another similar scenario is about the soap bubbles a lot of us used to play with when we were kids.

Have you ever noticed that when two moderate-sized bubbles come in contact, usually one of them pops and the other one grow in volume?

To be honest, these questions kept bothering me. I tried various scientific reasonings and lot of them failed and were invalid.

After some literature search and some critical thinking, I finally understood the principle of these proposed phenomena with two different school of thoughts (but both related to the application of Thermodynamic principles.)

For some of us (including myself), thermodynamics is a real pain... But don't worry, I tried to shape the explanations as simple as possible.
 Hang on!!
“Nothing in life is to be feared, it is only to be understood. Now is the time to understand more, so that we may fear less.”― Marie Curie

Coming back to our questions, why do the smaller sized blobs, bubbles... merge to form larger ones? Why don't they co-exist in equilibrium?

The simplest explanation:

Usually, when we describe the thermodynamic properties of a bulk quantity of substance, the surface/interface is ignored. But for very small amounts of substances, the effects of the surface become preponderant since the number of atoms on the surface/interface is comparable to the number of atoms in the bulk. The effect of the surface is termed as the surface energy and is closely related to surface tension. (Also the greater the surface area, the greater is the surface energy.)

For those of us who have studied Thermodynamics and have a good understanding, we know that any thermodynamic system attempts to achieve greater stability by lowering its energy.

This applies the same for the proposed question. When the oil blob is shattered into large amounts of small blobs, the total surface energy increases as the total surface area of the oil blobs (in contact water) has increased. As such the small particles will pop and form a larger one, thereby reducing the total surface area and hence achieve greater stability.

So far, this explanation seems to hold good and kind of explains the phenomena. But for those who like mathematical implications and proofs, this explanation will not soothe their curiosity.

The long explanation

This explanation is relatively simple but it requires certain background knowledge and some levels of understanding.

For a better understanding, one should be familiar with the term chemical potential.

- Chemical potential(μ) is basically a thermodynamic parameter which tells us the directionality of flow of matter. Matter flows from a region of high chemical potential to a region of low chemical potential. (I have also added the proof to this notion for those who are really interested in equations and some other equations that might be useful shortly, but the proof is not that important here and one may just jump over it and continue the read.)

Now that this is explained, let us consider a half-sphere(soap bubble or dewdrop) as follows:

r is the radius of the half-sphere

circumference = 2ㄫr

δP is the internal pressure relative to the outside pressure on the drop

γ is the surface energy

One should know that the surface tension is parallel to the drop and is distributed around the perimeter of the cross-section.

Therefore surface tension= γ2ㄫr

Internal pressure acts on the surface area of the cross-section and is calculated as δPㄫr^2.

For the bubble to remain intact, the two forces explained above must be equal (equilibrium). By equating both equations, we obtain:

δP= (2γ)/r

As such, as the radius of the bubble decreases, the internal pressure shoots up and vice versa (internal pressure is inversely proportional to the radius) and hence, the stability decreases.

(One can stop here and say that okay, small particles(smaller radius) have a larger internal pressure and hence will combine to form larger particles(smaller internal pressure) to achieve better stability)

But let us drive things mathematically further😈.

The following set of equations is only for the derivation of the final equation with a star.

Even though you do not understand the derivation, no worries, only the final equation is important in our case.

From the final equation,

μ represents the chemical potential and the equation basically tells us that as pressure increases, the chemical potential of the system will increase.

Important things we have seen till now:

• Matter flows from a region of high chemical potential to a region of low chemical potential.
• As the radius of the particle (blob, dewdrop...) decreases (size decreases), the internal pressure increases.
• And finally, from the last derived equation about chemical potential, we know that as pressure increases, chemical potential increases.

Now if we merge all this; smaller particles have a larger chemical potential because of a larger internal pressure, which is because of their small radius.

Then, the small particles(blobs, dews, bubbles) will then combine (matter will flow from a region of high chemical potential to a region of low chemical potential) to basically form larger particles which are more stable.

Whatever is explained in this blog article is one way of viewing things and of course, anyone of you can come up with another explanation.

One cannot restrain to only a single explanation/concept to explain a proposed phenomenon. There are otherwise very plausible explanations driven from curious minds and I believe that this is what makes science thrilling.

If Albert Einstein was not curious, perhaps today we would have still thought that time and space are absolute.