One definition of diffusion is the spontaneous spreading of matter, heat, or momentum. Such definition is rather general, and does not differentiate the process based on the cause of the spreading. A key feature of all diffusion processes is the flux of mass from higher to lower concentration.

Diffusion is a spontaneous process that occurs as a result of the second law of thermodynamics, which states that the entropy or disorder of any closed system must always increase with time. The effect of diffusion can only be counteracted by expenditure of external energy. Because substances diffuse from regions of higher concentration to regions of lower concentration, transport occurs only if there is a spatial variation of the concentration. In all cases of diffusion, the net flux of the transported substance is expressed as equal to a physical property (diffusivity, D [L T~ ]) multiplied by a concentration gradient:

where the symbol (V) indicates the gradient differential operator.

In molecular diffusion, eqn [6] is written with D = Dm independent of C and is known as Fick's first law.

All diffusion processes are modeled through the diffusion equation, which, in its general form, is a nonlinear partial differential equation obtained combining [3] with [6]:

When D is constant, as in the case of molecular diffusion, eqn [7] reduces to Fick's second law (or heat equation):

The value of the molecular diffusion coefficient varies according to the combination of solute and solvent. As far as water is concerned, molecular diffusion is easier for polar molecules such as salt and sugar due to the interactions with polar water molecules. The molecular diffusion coefficient is of the order of 10-9-10- m s . Conversely, apolar molecules like oils and proteins are subject to hydrophobic effects and diffuse in water at a lesser rate. The molecular diffusion coefficient for these substances is of the order of 10-10m2s-1.

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