18.27 Diffusion through membranes, osmosis and dialysis

Before you read this, I suggest you read post 18.26.

fig 1

Molecules in solution can diffuse through the pores in a membrane, if the pores are big enough. The membrane is coloured green in the picture above. On the left-hand side of the picture , bigger molecules (red) are dissolved in water molecules (blue); on the right-hand-side there are only water molecules (blue). In this example, the pores in the membrane are big enough for both red and blue molecules to pass through. They move through the pores because, in any liquid, the molecules are moving freely (post 16.37); dissolved molecules are part of the liquid (this is the meaning of the word “dissolved”). It is highly improbable that the red molecules will all remain on the same side of the membrane and so they will spontaneously mix. This spontaneous mixing is called diffusion and is explained, in more detail, in post 18.26. If you want to read more about molecules, see post 16.30.

Diffusion through membranes is an important mechanism for molecules to move around in our bodies. When we eat simple sugars, they dissolve in water and pass through the alimentary canal; when they reach the small intestine, they diffuse through its wall into the rest of the body. Bigger molecules are broken down into smaller molecules so that they can diffuse through the wall of the small intestine. This process of breaking down big molecules is called digestion; for example, protein molecules are broken down into the much smaller amino acid molecules in the stomach, before they reach the small intestine.

Because of the importance of diffusion through membranes in our bodies, some biologists believe that diffusion is specifically about transport through membranes. But, as we have seen in post 18.26, this isn’t true – diffusion is simply spontaneous mixing that occurs in very much different situations and is a consequence of the second law of thermodynamics (see also, post 16.38).

fig 2

The picture above is very similar to the first picture in this post – the only difference is that the pores in the membrane are now too small for the red molecules to pass through them. However, according to the second law of thermodynamics, the entropy of the system will still tend to increase spontaneously; this is another way of saying that the system tends to minimise the difference between the liquids on the two sides of the membrane (post 16.38).

Since water molecules are small enough to pass through the pores, the increase in entropy is achieved by water molecules passing from the right-hand to the left-hand side of the membrane. This process is called osmosis. (Unfortunately, the word “osmosis” is frequently misused, to mean learning something subconsciously, by people who want to appear clever – especially in English newspapers like the Sunday Times and the Guardian; “diffusion” would be a better metaphor.)

Text-books often call a membrane that allows osmosis, but not diffusion of big molecules, to take place, a semi-permeable membrane. The implication is that there is a difference in kind between membranes that allow diffusion (permeable) and those that allow only osmosis (semi-permeable). I prefer to think of all membranes as being like sieves that let molecules which are smaller than the holes in the sieve pass through but hold back the bigger molecules.

fig 3

Now let’s look at the two pictures above. Picture A shows a solution on one side of a membrane and water on the other side; the pores in the membrane are too small for molecules of the dissolved stuff to diffuse through. So, water molecules will pass through the membrane, by osmosis, to try to equalise the concentrations of dissolved stuff on both sides. As a result, the level on one side (that contains solution) increases, as shown in picture B; the level on the other side (that contains water) decreases. The resulting hydrostatic pressure (post 17.5) tends to push the water in the opposite direction to the flow induced by osmosis. The system reaches equilibrium when this hydrostatic pressure prevents further osmosis. The equilibrium pressure is called the osmotic pressure of the solution; in this example, it is the osmotic pressure of the diluted solution (pink in B) that is in equilirium with water (blue).

If ρ is the equilibrium density in the solution of height h above the water level (see picture B above), then the osmotic pressure, π, is given by

π = hρg

where g is the magnitude of the gravitational field (acceleration due to gravity, post), as explained in post 17.5. Some people believe that osmotic pressure and hydrostatic pressure are different but when you see where the idea of osmotic pressure comes from – you can see that they are the same.

In dialysis the pores in the membrane are sufficiently large to allow water and some larger molecules to diffuse through but are too small to allow much larger molecules to pass through. In our bodies, dialysis is performed by the kidneys. It enables us to get rid of waste products, like urea, from the blood and to control the concentrations of, for example, sodium and potassium ions (post 16.39). However, protein molecules and blood cells remain in the blood. If our kidneys fail, dialysis is performed artificially, either using a machine with an artificial membrane or using the membrane (the peritoneal membrane) that surrounds the abdominal cavity (peritoneal dialysis).

The next two paragraphs are much more abstract – you might want to skip them!

Let’s go back to the third picture in this post (part B) – the one that explains the idea of osmotic pressure. Osmosis occurs spontaneously to increase the entropy of the system. But, at the same time, its energy increases because the column of solution, height h, has potential energy (post 16.21). In earlier examples of systems with potential energy, in this blog, the potential energy is available to do work – examples are an unsupported object at some height above ground level (post 16.21) and a stretched spring (post 16.49). If we had a column of water, like the one in the picture, and made a hole at the bottom, the water would flow out to minimise the potential energy. This flowing water could be used to do work (post 16.48), for example, by turning a turbine. In the picture the water could minimise its potential energy by flowing through the pores in the membrane to equalise the level on both sides (as in part A before osmosis occurs). But it doesn’t. Why not? Because there are two competing processes: (1) the tendency to increase entropy and (2) the tendency to use potential energy to do work. The entropic effect prevents our system from doing work.

This competition between the tendency of a system to use energy to do work while, at the same time, tending to increase its entropy leads to the idea of free energy. The free energy of a system is that part of its internal energy that is free to do work. So, for example, the efficiency of a car engine is limited because, at the same time as it is doing useful work, it also tends to increase entropy during the combustion of fuel. In a system that works at constant volume (like inside a car engine), we can calculate the free energy using the Helmholtz function – the internal energy change minus the entropy change multiplied by the temperature measured on the Kelvin scale (post 16.34). In a system that works at constant pressure (like a chemical reactor at air pressure), this pressure means that there is always an external force acting on the system (post 17.5) that can do work on it. Any work don on the system will increase its internal energy. Then we need to use the Gibbs function (the Helmholtz function plus the work done on the system) to calculate the free energy.

There are a lot of ideas in this post. However, the main one is that anything can diffuse through a membrane if the pores are big enough. If the molecules of something dissolved in a solvent (like water) are too big to diffuse through, a concentrated solution can be spontaneously diluted by flow of solvent molecules – this process is called osmosis.

 

Related posts

18.26 Diffusion
18.25 An ideal gas
17.15 Fluid flow
17.5 Stationary fluids
16.48 How does soap work?
16.38 Entropy and disorder
16.37 Solids, liquids and gases
16.35 Heat
16.34 Temperature

 

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