The actual diffusion of nutrients is the movement of the molecules along a gradient or concentration difference at the water and sediment interface during a given period of time.
To obtain the surface rate of actual diffusion, the concentration of the interstitial water (ciw) in the top layer of the sediment of hs thickness and the concentration (cw) of the water right above the sediment of hw thickness, should be measured. At the same time the water content (W%) should be determined by drying until constant weight at 105°C. With linear form of Fick's first law, the surface rate (v) of the actual diffusion in a given compartment as related to a unit surface of the sediment at the water sediment interface can be calculated. Fick's first law is:
or in its linearized form
The surface rate of diffusion (v) is the rate of diffusion as related to a unit surface of the sediment, that is:
The qD/F ratio can also be given as porosity (p) as:
The porosity expresses the ratio of the free, water-filled volume (Vw) and the whole sediment volume (Vs) in a given sediment layer
Knowing the water content (W%) of the sediment layer investigated, the density of the interstitial water (qiw), and that of the solid phase (qs), the porosity can be expressed:
from which, if the density of interstitial water is 1.00 g cm-3 and that of the solid phase is 2.65 g cm-3, the porosity can be estimated (K):
Equipment and chemicals required to obtain interstitial water and determining the concentration of nutrients.
The surface rate of the actual diffusion as related to a unit region of sediment surface is:
| where: | DK | = | the diffusion constants of the nutrient investigated (cm-2h-1) |
| K | = | the estimated porosity of the sediment layer in question | |
| ciw | = | the concentration of the investigated nutrient in the interstitial water of the sediment layer of fixed thickness (nmol cm-3) | |
| cw | = | concentration of the investigated nutrient in the water above the sediment (nmol cm-3) | |
| hs | = | thickness of the sediment layer (cm) | |
| hw | = | thickness of water-layer above the sediment (cm) |
The direction of diffusion is towards the sediment if ‘v’ is a negative value and from the sediment to the lake if ‘v’ is positive.
The surface rate of the actual diffusion (vD) as related to an extended region and to a longer period of time, can be obtained by calculating the average of actual diffusion values characteristic of different periods of time and space.
| where: | tik | = | duration of different periods of time |
| n | = | number of different periods of time | |
| Fik | = | area of different regions | |
| m | = | number of different regions | |
| K | = | constants depending on the units of measurements chosen |
