tion at the end of previous day, [TAN]k−1, and the ammonia generated on the kth day (TMTAN,k, grams) divided by the volume (V, cubic meters) of the liquid manure in storage, as shown below:

[TAN] k = [TAN]k−1 + TMTAN,k /V.

The mass-transfer coefficient KL is a function of manure temperature, air temperature, wind velocity, and relative humidity. Various equations for KL are available in the literature. However, most of them were developed using controlled experiments by means of convective mass-transfer chambers, and have not been well validated using field-scale experiments. More research is needed to calibrate and validate them. An example is given below is based on the two-film theory.


The mass-transfer coefficient for ammonia as derived from the two-film theory (Whitman, 1923) is given as follows:

where KL is the overall mass-transfer coefficient in meters per second, KH is Henry’s law constant (dimensionless) calculated as a function of water temperature (Taq, kelvin),

and and are mass-transfer coefficients (meters per second) through gaseous and liquid films, respectively, at the interface of water and air, and are related to the diffusivities (square meters per second) of ammonia and water in air ( and ), and of ammonia and oxygen in water ( and ):

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