**Contents**

- Introduction
- Factors in colloid stability
- Gravitational effects - Stokes law
- Brownian motion
- Factors in Brownian motion
- Sedimentation equilibrium
- Further reading
- Return to contents page

A colloid is a two phase system in which one phase, *the disperse phase*, is suspended in the form of very
fine particles in a second phase, *the continuous phase*. Colloids are distinguished from other forms of suspension
by the size of the disperse phase particles (typically in the range 1 nm - 1m m and
by their apparent stability. In fact, colloids are inherently unstable systems and, given time, the two phases
will separate. The time scale for separation may range from hours to months and even years. Colloids may take a
variety of forms with both continuous and disperse phases being solid, liquid or gas. Some more common types of
colloid important in a food context are listed in table 1 below

**Table 1. Types of colloid**

Type | Disperse phase | Continuous phase | Example |

Aerosol, Smoke | Liquid | Gas | smoke |

Fog, mist aerosol | Solid | Gas | exhaled breath |

Foam | Gas | Liquid | Whipped cream, beaten eggs. |

Emulsion | Liquid | Liquid | Milk, Mayonnaise |

Sol, Colloidal solution, gel, paste | Solid | Liquid | Cloudy beer, milk, gelatin, tomato paste |

Solid foam | Gas | Solid | Ice cream, Meringue |

Many foods are colloidal in nature and are generally complex in nature with the continuous phase being in the
form of a true solution and there being more than one disperse phase. A good example of this is milk which has
a continuous phase comprising polysaccharides, electrolytes and proteins in aqueous solution and disperse phases
comprising both liquid fats and solid protein.

**Factors in colloid stability**

There are four key factors which contribute to colloid stability;

- Gravitational effects
- Brownian motion
- Interactions between particles and between phases.

These will be considered in turn.

**Gravitational effects - Stokes Law**

Gravitational effects are a consequence of differences in density between the disperse and continuous phase.

If the disperse phase is more dense than the continuous phase, the disperse phase particles will migrate downwards
and tend to settle at the bottom. This is known as *sedimentation*. If the disperse is less dense than the
continuous phase, the disperse phase particles will migrate upwards and tend to settle at the top. This is known
as *creaming*. Both phenomena are essentially the same and are governed by stokes law. This may be illustrated
by the following diagram. (Fig 5.1)

**Fig 5.1. Stokes Law**

The buoyance force depends the density difference between the disperse and continuous phase and acts upwards on the particle.

The gravitational force depends on the mass of the particle and acts downwards on the particles.

Depending on the difference between the bouyancy force and the gravitational force, the particle will move upwards
if r _{L}>r_{P} and downwards if r _{L}>r_{P}.

The frictional force opposes the motion of the particle and depends on the particle velocity.

As a result of the factors influencing these forces, there will arise a velocity at which the upward and downward
forces are equal in magnitude. This is known as the *terminal velocity*. By assuming the suspension is a dilute
one (ie. neglecting inter-particle interactions), stokes law allows us to calculate the terminal velocity of a
particle.

For a spherical particle, the net force resulting from the buoyancy and the gravitational effects is

1.1 |

This applies where r _{L}>r_{P} and
the particle will move upwards ie. we have creaming. The motion of the particle is opposed by a frictional force
F_{F};

1.2 |

The terminal velocity, *v _{S}* is reached when F

1.3 |

**Brownian Motion**

Brownian motion is the apparently random motion of small particles when suspended in a fluid. It can be seen with the naked eye when dust particles in the air are illuminated by a shaft of sunlight shining through a window, though it more commonly needs a microscope to be observed. It is the consequence of the motion of the liquid or gas molecules of the continuous phase. The molecules strike the suspended particles and exert a small force on them as a consequence. If the particles are small enough, the force on the particles as a result of these collisions is sufficient to produce observable motion.

Brownian motion arises as a consequence of the kinetic theory. Very small particles are "buffeted"
by collisions with fast moving molecules. As a result, the particles describe a random walk continually moving
and changing direction. The colloidal particles possess kinetic energy (½ mv^{2}). As the mean kinetic
energy of the moving particles is proportional to the absolute temperature, T then the kinetic energy is given
by

2.1 |

Where k is the Boltzmann constant (= 1.381x10^{-23} J K^{-1})

An important consequence of this relation is that as the particle mass increases, its velocity decreases. This
puts an practical upper limit on the size of particles which will display Brownian motion as the velocity will
eventually become too small.

**Factors in Brownian motion**

- The motion of colloidal particles will be subject to frictional resistance. This is proportional to the mean
kinetic energy. In fact it can be shown that the mean displacement of a particle from its point of origin in time,
t is given by]
2.2

Where: *k*= Boltzmann constant = 1.381 ´ 10 ^{-23}J K^{-1}*T*= Absolute temperature *f*= Frictional coefficient - Because of the random motion of the particles, they will diffuse from regions of high concentration to ones of low concentration. This diffusion is governed by Fick’s law which states

2.3 |

Where | m/t | = rate of mass transfer |

d | = diffusivity of particles | |

A | = ´ -sectional area over which diffusion occurs | |

dc/dx | = concentration gradient. |

The – sign denotes a flow in a direction from high to low concentration ** ie** a negative gradient.

By relating the distance moved by a particle in Brownian motion to the mass transferred the diffusivity for a spherical particle is given by;

2.4 |

Thus, the distance moved by a particle in time, t as a result of Brownian motion is

2.5 |

**Sedimentation equilibrium**

If the colloid particles are sufficiently small, the colloid will be stable as a result of an equilibrium between the tendency for the particles to fall or rise due to Stokes law and the rate of diffusion as a consequence of Brownian motion.

As the particles fall (or rise) due to the effect of gravity and buoyancy, a concentration gradient will be set up. As a result of this concentration gradient, there will be diffusion in the opposite direction. As the rate of diffusion increases with increasing concentration gradient, there will a concentration gradient where there is an equilibrium between the terminal velocity of the particles and the rate of diffusion.

The total mass transferred by particles descending (or ascending) at velocity, v_{s} as a result of
gravity/buoyancy is equal to velocity ´ concentration. Thus

2.6 |

The rate of mass transfer due to diffusion will be governed by Fick’s law. At equilibrium this will be equal and opposite to the mass transferred by the effects of gravity/buoyancy.

2.7 |

We know that

and | from Stoke’s law |

Substituting in equation 2.12, rearranging and integrating gives a relationship between particle displacement and concentration difference at equilibrium.

2.8 |

Where | V_{P} |
= particle volume = 4/3 p r^{3} for spherical particles |

c_{o} |
= concentration at some point in the colloid | |

c_{x} |
= concentration at a distance, x from c_{o} |

**Note**. This is a kinetic equilibrium and not a thermodynamic equilibrium. Colloids are not in thermodynamic
equilibrium and hence are unstable or at best in a metastable state.

**Further Reading**

Dickinson E, *Introduction to Food Colloids*, Chapters 1, 2 & 4

Beckett, S T, *Physico Chemical Aspects of Food Processing*, Chapter 3.

Produced by Geoff Walker

Last Modified 29 February 2000