Down-gradient mixing

In contrast, convection currents are not possible in the stratosphere, because of the positive temperature gradient. Mixing there is caused by differential solar heating of the stratospheric gas across the latitudes and is known as advection. Air heated at the equator expands and moves towards the poles. Displaced air tends to rise at the poles and comes back down to replace the sinking heated air at the equator. An important point is that air on either side of the tropopause, moves horizontally and parallel, which makes mixing across the boundary difficult. The stratospheric air mass is therefore, partially isolated from that of the troposphere. Thus, whereas effective mixing within the troposphere may take only a few days or weeks, effective mixing across the boundary may take many months. 

Fauna also influence soil carbon cycling. Bioturbation mixes and aerates soil, physically breaks down litter, creates flow paths for water in soil, and can reduce surface litter stocks and enhance erosion (Bohlen et al., 2004). For example, along a gradient of European earthworm (Lumbricus terrestris) colonization in a deciduous forest of northern Michigan, earthworms are associated with a decrease in litter-layer thickness, apparently mixing some forest floor organic matter into the mineral soil. Thus, fauna can create spatial patterns in SOM stocks. 

They also studied the terminal mixing time 0m, required for reducing concentration gradients down to a specified level by multiple recirculations. They found 0m/tc = A + B( s/tc), s/tQ > 0.8,so that 0m H11(Nd ) when A is small. The power input is thus P % (Nd)2(V/tc). 

Fry, B. (2002) Conservative mixing of stable isotopes across estuarine salinity gradients a conceptual framework for monitoring watershed influences on down stream fisheries production. Estuaries 25, 264—271. 

Similar considerations apply to distillation columns. Entropy is generated on the trays due to mixing and heat transfer between dissimilar streams. We can reduce the entropy production by adding more trays to the column. With more trays there is less of a gradient across each tray and the entropy production goes down. A column with many trays requires less reflux and therefore less heat to the reboiler. The energy consumption is reduced only at the expense of added capital investment for the taller column. 

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