Combined Advection Diffusion Processes

Whenever the fluid is in motion, advective transport and diffusive transport act simultaneously. The complexity arising for the combined effects can be treated mathematically by simply adding the advective and diffusive fluxes indicated in eqns [4] and [7] :

Figure 2 The combined effect of one-dimensional advection and diffusion on a cloud. The center of mass travels according to the advective process, while the cloud spreads around the center of mass at a rate dictated by diffusion.

Figure 2 The combined effect of one-dimensional advection and diffusion on a cloud. The center of mass travels according to the advective process, while the cloud spreads around the center of mass at a rate dictated by diffusion.

For incompressible fluids, eqn [9] becomes

Finally, if diffusion is only of the molecular type, eqn [10] reduces to

SC SC SC SC

St Sx Sy Sz

S2C S2C S2C Sx2 Sy2 Sz2

The overall effect of the superposition of advection and diffusion can be visualized as the translation of the center of mass of the substance according to the advective part, while mass diffuses around the center of mass at a rate dictated by the diffusive term, as shown in Figure 2.

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