Introduction Advection and Diffusion

In natural systems there are two types of transport phenomena (1) transport by random motion, and (2) transport by directed motion. Both types occur at a wide range of scales from molecular to global distances, from microseconds to geological times. Well-known examples of these types are molecular diffusion (random transport) and advection in water currents (directed transport). There are many other manifestations such as dispersion as a random process (see Chapters 24 and 25) or settling of suspended particles due to gravitation as a directed transport. For simplicity we will subdivide such transport processes into those we will call diffusive for ones caused by random motions and those called advective for ones resulting from directed motions. 

This chapter deals with the mathematical description of diffusion. Since it is easier to understand the nature of random transport by comparing it with directed transport, we briefly discuss advection as well. A more complete discussion of advective transport follows in Chapter 22. 

Next you ask the question How does the situation change when you lift the cup to your mouth Obviously, this is a movement relative to the dining car most objects in the car don t experience this movement of your arm. But the movement as such is still directed and shared by all the fluid elements in the cup and by the cup itself. Thus, this is still an advective motion, although on a smaller scale compared to the motion of the dining car. The combined effect on the milk molecules from the motions of car and cup can be expressed as the sum of two vectors vtot = vcar + vcup. 

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