Brownian Motion Experiment

[Klacee Sawatzky]

DerekThat doesn't sound enthusiastic enough for the Naked Scientists, so we are going to try and turn you onto science. We have a very simple experiment for you to do and if you want to do it at home these are the things that you will need: two bowls which are able to hold, say, a litre each; a boiled kettle; and some food colouring. Now Sheena is going to tell us what we do with all these things

Sheena - First fill one bowl with cold water, and another with our boiled hot water. Then we just need to let them settle, so put a cover on the hot one to retain the heat and leave them to settle for 5-10 minutes.

Sheena - Then we add just a little food colouring in each bowl in a nice controlled way. So I would suggest dipping maybe a handle of a teaspoon into the food colouring and then just touch the surface of each bowl of water with it.

Derek - Hello there and welcome back to Downham Market High School. We've been waiting here to do this experiment with hot and cold bowls of water. Tom is here from Downham Market High School and Sheena set up the experiment too. So Sheena, would you care to instruct Tom over what to do right now.

Derek - Yeah and I suppose we've got a really definite shape in the cold water one. We've got this weird structure of food dye that's suspended in the water and it doesn't appear to be movign anywhere does it?

Tom - That sounds like a perfectly good explanation. I think there are actually two things that might be happening here. First of all, in the hot water the molecules will be moving much faster and have much more kinetic energy. When we talk of heat, what we're actually talking about is kinetic energy and all these molecules are moving very fast. That's what we perceive as being hot.

Sheena - Yeah, they'd be moving around like crazy in there. So that's what I originally thought would be causing the food dye to be bashed around. It's Brownian motion: they're all being hit by the hot molecules around them. In the cold water you still have these molecules moving but they won't be moving as fast. However I think there might be another explanation that's actually the one we're seeing so quickly here. I think that's convection currents. The hot water at the top of the surface where it's next to the cold air will evaporate and cool down and it will no longer be the hottest water in the bowl. Hot water from below will then rise and take its place because hot liquids rise. You then set up these currents where hot water from below keeps rising and the cold water gets pushed down. All these currents cause the mixture to mix up very quickly.

First fill one bowl with cold water, and another with our boiled hot water. Then we just need to let them settle, so put a cover on the hot one to retain the heat and leave them to settle for 5-10 minutes.

Then we add just a little food colouring in each bowl in a nice controlled way. Perhaps by dipping a handle of a teaspoon into the food colouring and then just touch the surface of each bowl of water with it.

If you looked at all the molecules in the water with a really powerful microscope they would appear to be jiggling around. The hotter they are the more they jiggle around, they will tend to push around any other particles in there too, such as the food colouring. So the hot water should spread the colour out faster than the cold. This process is called diffusion.

Because the hot molecules are jiggling about more they will tend to push each other apart, so you will get fewer molecules in a litre, so hot liquid will be less dense and float on the colder liquid. The liquid on the surface is least well insulated so it will tend to cool down quickest, so the hotter liquid underneath will float up over it. This is called a convection current, and will tend to mix up the food colouring with the water.

This motion pattern typically consists of random fluctuations in a particle's position inside a fluid sub-domain, followed by a relocation to another sub-domain. Each relocation is followed by more fluctuations within the new closed volume. This pattern describes a fluid at thermal equilibrium, defined by a given temperature. Within such a fluid, there exists no preferential direction of flow (as in transport phenomena). More specifically, the fluid's overall linear and angular momenta remain null over time. The kinetic energies of the molecular Brownian motions, together with those of molecular rotations and vibrations, sum up to the caloric component of a fluid's internal energy (the equipartition theorem).[citation needed]

This motion is named after the botanist Robert Brown, who first described the phenomenon in 1827, while looking through a microscope at pollen of the plant Clarkia pulchella immersed in water. In 1900, the French mathematician Louis Bachelier modeled the stochastic process now called Brownian motion in his doctoral thesis, The Theory of Speculation (Thorie de la spculation), prepared under the supervision of Henri Poincar. Then, in 1905, theoretical physicist Albert Einstein published a paper where he modeled the motion of the pollen particles as being moved by individual water molecules, making one of his first major scientific contributions.[3]

The direction of the force of atomic bombardment is constantly changing, and at different times the particle is hit more on one side than another, leading to the seemingly random nature of the motion. This explanation of Brownian motion served as convincing evidence that atoms and molecules exist and was further verified experimentally by Jean Perrin in 1908. Perrin was awarded the Nobel Prize in Physics in 1926 "for his work on the discontinuous structure of matter".[4]

The many-body interactions that yield the Brownian pattern cannot be solved by a model accounting for every involved molecule. Consequently, only probabilistic models applied to molecular populations can be employed to describe it.[5] Two such models of the statistical mechanics, due to Einstein and Smoluchowski, are presented below. Another, pure probabilistic class of models is the class of the stochastic process models. There exist sequences of both simpler and more complicated stochastic processes which converge (in the limit) to Brownian motion (see random walk and Donsker's theorem).[6][7]

Observe what happens when sunbeams are admitted into a building and shed light on its shadowy places. You will see a multitude of tiny particles mingling in a multitude of ways... their dancing is an actual indication of underlying movements of matter that are hidden from our sight... It originates with the atoms which move of themselves [i.e., spontaneously]. Then those small compound bodies that are least removed from the impetus of the atoms are set in motion by the impact of their invisible blows and in turn cannon against slightly larger bodies. So the movement mounts up from the atoms and gradually emerges to the level of our senses so that those bodies are in motion that we see in sunbeams, moved by blows that remain invisible.

Although the mingling, tumbling motion of dust particles is caused largely by air currents, the glittering, jiggling motion of small dust particles is caused chiefly by true Brownian dynamics; Lucretius "perfectly describes and explains the Brownian movement by a wrong example".[9]

While Jan Ingenhousz described the irregular motion of coal dust particles on the surface of alcohol in 1785, the discovery of this phenomenon is often credited to the botanist Robert Brown in 1827. Brown was studying pollen grains of the plant Clarkia pulchella suspended in water under a microscope when he observed minute particles, ejected by the pollen grains, executing a jittery motion. By repeating the experiment with particles of inorganic matter he was able to rule out that the motion was life-related, although its origin was yet to be explained.

The first person to describe the mathematics behind Brownian motion was Thorvald N. Thiele in a paper on the method of least squares published in 1880. This was followed independently by Louis Bachelier in 1900 in his PhD thesis "The theory of speculation", in which he presented a stochastic analysis of the stock and option markets. The Brownian motion model of the stock market is often cited, but Benoit Mandelbrot rejected its applicability to stock price movements in part because these are discontinuous.[10]

Albert Einstein (in one of his 1905 papers) and Marian Smoluchowski (1906) brought the solution of the problem to the attention of physicists, and presented it as a way to indirectly confirm the existence of atoms and molecules. Their equations describing Brownian motion were subsequently verified by the experimental work of Jean Baptiste Perrin in 1908.

There are two parts to Einstein's theory: the first part consists in the formulation of a diffusion equation for Brownian particles, in which the diffusion coefficient is related to the mean squared displacement of a Brownian particle, while the second part consists in relating the diffusion coefficient to measurable physical quantities.[11] In this way Einstein was able to determine the size of atoms, and how many atoms there are in a mole, or the molecular weight in grams, of a gas.[12] In accordance to Avogadro's law, this volume is the same for all ideal gases, which is 22.414 liters at standard temperature and pressure. The number of atoms contained in this volume is referred to as the Avogadro number, and the determination of this number is tantamount to the knowledge of the mass of an atom, since the latter is obtained by dividing the molar mass of the gas by the Avogadro constant.

The first part of Einstein's argument was to determine how far a Brownian particle travels in a given time interval.[3] Classical mechanics is unable to determine this distance because of the enormous number of bombardments a Brownian particle will undergo, roughly of the order of 1014 collisions per second.[2]

The second part of Einstein's theory relates the diffusion constant to physically measurable quantities, such as the mean squared displacement of a particle in a given time interval. This result enables the experimental determination of the Avogadro number and therefore the size of molecules. Einstein analyzed a dynamic equilibrium being established between opposing forces. The beauty of his argument is that the final result does not depend upon which forces are involved in setting up the dynamic equilibrium.

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