Search

# Diffusion

Diffusion is the spontaneous spreading of something such as particles, heat, or momentum. The phenomenon is readily observed when a drop of colored water is added to clear water, or when smoke from a chimney dissipates into the air. In these cases, diffusion is the result of turbulent fluid motion rather than chemical reactions or the application of external force. In cell biology, diffusion is described as a form of "passive transport", by which substances cross membranes.

 Contents

## Background

Diffusion is one kind of transport phenomenon: compare it, for example, to radiation. All diffusion can be modelled quantitatively using the diffusion equation, the solutions of which go by different names depending on the physical situation. Steady state bi-molecular diffusion is governed by Fick's first law. Steady-state thermal diffusion is governed by Fourier's Law. Diffusion of electrons in an electrical field is essentially Ohm's law. In each, a flux (of atoms or energy or electrons) is equal to a physical property (diffusivity or thermal conductivity or electrical conductivity) multiplied by a gradient (concentration gradient or thermal gradient or electric field). The generic diffusion equation is time dependent (i.e. also applies to non-steady-state situations).

In each case, there is only a noticeable diffusion if there is a gradient: for example in thermal diffusion, if the temperature is constant, heat will move as quickly in one direction as in the other, producing no change.

## Types of diffusion

### Diffusion in cell biology

#### Diffusion in the respiratory system

In mammalian lungs, a process of diffusion takes place in the aveoli: due to differences in partial pressures across the alveolar-capillary membrane, oxygen diffuses into the blood and carbon dioxide diffuses out.

#### Facilitated diffusion

The passive transport of ions or molecules by a specific carrier protein in a membrane. As in simple diffusion, net transport is down a concentration gradient, and no additional energy has to be supplied. Compare with diffusion and active transport.

#### Net flux

Net flux is used to measure diffusion.

#### Polarity

Nonpolar molecules diffuse faster through the lipid portion of the membranes.

#### Ions

Diffusion of ions depends on the concentration gradient, and the membrane potential. The net flux of ions can be altered by opening or closing ion channels.

### Diffusion in chemical engineering

Diffusion is the movement of matter due to the movement of the individual molecules (or atoms). Diffusion occurs in solids, in liquids, in gases and in supercritical fluids. Diffusion is caused by the thermal movement of individual molecules. Some examples of diffusion are:

• A balloon filled with helium will deflate a little bit every day because helium atoms diffuse out of the balloon through its wall.
• When spaghetti is cooked, water molecules diffuse into the spaghetti strings, making them thicker and more flexible.
• Carbon dioxide bubbles in soft drinks start as small nuclei and grow because of the diffusion of carbon dioxide molecules towards them.
• A smelly gas distributes itself over a room by diffusion.
• A sugar cube in a glass of water that is not stirred will dissolve slowly and the sugar molecules will distribute over the water by diffusion.

### Atomic diffusion

This is the process whereby the random thermally activated hopping of atoms in a solid results in the net transport of atoms. For example, helium atoms inside a balloon can diffuse through the wall of the balloon and escape, resulting in the balloon slowly deflating. Other air molecules (e.g. oxygen, nitrogen) have lower mobilities and thus diffuse more slowly through the balloon wall. There is a concentration gradient in the balloon wall because the balloon was filled up with helium, and thus there is plenty of helium on the inside, but there is relatively little helium on the outside, because helium is not a major component of air. The rate of transport is governed by the diffusivity and the concentration gradient.

### Brownian motion

Brownian motion occurs when discrete particles diffuse in a liquid medium. Since the energy is thermal, the mass of the particles must be very small in order that the motion be observable ($v\sim\sqrt{k_BT/m}$). The direction of the motion is random and thus constantly changing. In principle, Brownian motion also occurs in gases, but usually the motion of particulates in gases, e.g. smoke, is dominated by turbulence.

### Electron diffusion

Electric current flows by diffusion in most conductors. Charge carriers (usually electrons) move randomly in the absence of an electric field. When an electric field is applied, carriers drift preferentially in the field, causing a net current. The rate of transport is governed by the electrical conductivity of the conductor and the electric field.

### Momentum diffusion

In the case of laminar flow of a liquid flowing past a solid surface, momentum diffuses across the boundary layer near the surface. The gradient in this case is between the liquid in contact with the surface (which isn't moving at all and has zero momentum) and the liquid far away from the wall, which has momentum proportional to the speed at which it is flowing. The rate of transport is governed by the viscosity of the fluid and the momentum gradient.

### Osmosis

Osmosis is the diffusion of a solute across a selectively permeable membrane.

### Photon diffusion

When photons travel through a material with a high optical depth and a very short mean free path, their behavior is dominated by scattering and the path of any given photon's path is effectively a random walk. The behavior of a large ensemble of photons in this situation can be described with a diffusion equation.

### Reverse diffusion

In general, diffusion results in transport down the gradient -- i.e. things move from regions of high concentration to low concentration. However, this is not always the case: during a phase separation, material can diffuse towards regions of higher concentration. This is referred to as reverse diffusion.

### Thermal diffusion

When heat travels through a material with a thermal gradient (for example, heat traveling through the wall of a coffee mug), the rate of transport is governed by the thermal conductivity and the temperature gradient.