How to use particle agitation to reduce pollution

I would like to talk to you about many things, about the Roman remains near Coimbra, about how the world would be different if Putin listened to the music of Glinka (who studied in Milan as a young man), about how astrophysics is changing the position of man in the universe. I hope there will be time for all of this and more. But now, for continuity, I would like to continue the reasoning on the physics of the aerosol and how it enters our lives, in individual and collective choices. A mini-course in everyday physics, to reduce air pollution and, in the end, live better.

For those who have not followed me in the previous “episodes” I repeat that that of particles suspended in a gas is a world of combination and synthesis of the two spheres. We frame it by choosing two essential parameters: the average distance traveled by the molecules between two successive collisions, on the one hand, and a typical size of the particles on the other. The ratio between these two parameters (which are both lengths) is a number, the Knudsen number, Nkn. Let us now consider the “molecular” regime: the particles are so small that they could almost be considered themselves as huge molecules, however large enough to be observable, certainly not with the naked eye but always with the help of an optical and even electronic microscope . And here we must speak of an English botanist, Robert Brown which forcefully enters the history of physics by discovering a phenomenon, in 1827, just after the first achromatic objectives came into use. Brown observed under the microscope that small particles in water (we will see that it will be easier to observe them in water than in air) instead of falling by gravity were animated by very lively and very disorderly movements: an incessant motion that never found rest. He observed these motions in all fluids, but the more active were the motions the less viscous were the fluids. Buffon and our Spallanzani, long before Brown, were aware of the phenomenon, but they hadn’t been able to understand its nature and thought it was about sub-microscopic animals. Returning to Brown, he observed that, given a fluid, the size of the particles mattered a lot: the agitation was all the greater the smaller the particles were. In the decades following his discovery, observations multiplied. It has been seen that the chemical nature or composition of the particles does not matter; they shake equally as long as they are the same size. The motion never stops, it is observed for months or years, eternal and spontaneous, as long as even a single suspended particle remains. But with what we know of the “molecular” regime (Nkn greater than one) we have an immediate explanation of the phenomenon. Each particle, continuously jostled by neighboring molecules, receives impulses which, however, do not balance each other and the particle is continually tossed about by this non-equilibrium. The collisions are many in the unit of time, but not so many as to balance and keep the particle still. There is no external cause to explain this agitation, and one has to resort to this “mental conjecture” about molecules and their collisions both with the particle and with each other.

An acute critic, and already introduced to physics, one might ask: but isn’t this continuous agitation in contradiction with the principle of conservation of energy? No, because every increase in the speed of the particle is accompanied by a “cooling” of the gas in its vicinity, and every slowing down of it is accompanied by a “heating” of the gas that surrounds it. Many things can be said about this, and Einstein himself in 1905 managed to give the phenomenon a quantitative theory as well. A hypothesis (mental conjecture) has been made that puts molecular agitation at the origin of Brownian motion. But then abundant experimental tests followed to confirm the theory and from this a great contribution will come to the practical problem that interests us, ie reducing pollution: how to separate the particle from the gas that hosts it.

We have said that Brownian motion is eternal, but its consequences are relevant and depend on time. This singular characteristic is not marginal, but fundamental, precisely for the purpose of separating the particle from the gas. What aspects of this eternal phenomenon are dependent on time? They are two. We recall that when a particle touches a foreign surface it remains adherent to it for the adhesion forces already described (of Van der Waals). So in the incessant motion a particle can meet the wall of the vessel or another particle. In the first case the internal aerosol loses a member, and the incessant motion of the remaining particles continues. In the second case two particles touching each other form one particle and the sum particle of the two will continue to move with the sum mass of the two. This second process is called coagulation.

Let us therefore focus the microscope on the small glass cell which contains the suspension of the particles. For example, let’s follow a particle of half a thousandth of a millimeter: by marking its position every 30 seconds we would find a graph like this.

And if we observed the positions at closer time intervals (for example every second) we would find an even more jagged polygonal path.

The complete theory is more complicated but I would now like to point out that through the movements of the particles that are seen we get to know properties of the molecules that are not seen. Thus we have come to know the value of Avogadro’s number. Before, it was only known that it existed. Observing the Brownian motion, it was possible to find the value of this number: 6.06 times 10 to the twenty-third power.

When instead we focus on the inner wall, the particles that touch the wall will remain adherent and we will see them still; over time the stationary particles will grow in number. If we took successive photographs we would show that the particles spread (we call it Browninan diffusion) towards the wall and the number of particles that stick together increases over time. Also the reciprocal capture of the particles which we have called coagulation obviously depends on time and contributes to the reduction of pollution, but only to the decrease of their concentration and the shift of their dimensions towards the larger classes.

We stop here for now, summarizing that we have a decrease in the number of particles by capture on external surfaces or by mutual capture. Using our metaphor, the same size gap between suspended particles as between an ant and a hot air balloon, we have been on the side of the ant (molecular regime). One by one we will see the other mechanisms, in the viscous regime (on the side of the balloon) and in the intermediate regime, with the dimensions between the two. Until next time.