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۱٫ Concepts, De nitions, and the Di usion
Equation
Environmental uid mechanics is the study of uid mechanical processes that a ect the
fate and transport of substances through the hydrosphere and atmosphere at the local or
regional scale1 (up to 100 km). In general, the substances of interest are mass, momentum
and heat. More speci cally, mass can represent any of a wide variety of passive and reactive
tracers, such as dissolved oxygen, salinity, heavy metals, nutrients, and many others. Part I
of this textbook, \Mass Transfer and Di usion,” discusses the passive process a ecting the
fate and transport of species in a homogeneous natural environment. Part II, \Strati ed
Flow and Buoyant Mixing,” incorporates the e ects of buoyancy and strati cation to deal
with active mixing problems.
This chapter introduces the concept of mass transfer (transport) and focuses on the
physics of di usion. Because the concept of di usion is fundamental to this part of the
course, we single it out here and derive its mathematical representation from rst principles
to the solution of the governing partial di erential equation. The mathematical rigor
of this section is deemed appropriate so that the student gains a fundamental and complete
understanding of di usion and the di usion equation. This foundation will make the
complicated processes discussed in the remaining chapters tractable and will start to build
the engineering intuition needed to solve problems in environmental uid mechanics.

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