Chapter 2

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Chapter The Diffusion EquationFormulationAs we saw in the previous Chapter , the flux of a substance consists of anadvective component, due to the mean motion of the carrying fluid, and of aso-called diffusive component, caused by the unresolved random motions of thefluid (molecular agitation and/or turbulence). In this Chapter , we explore someconsequences of the existence of a diffusive flux by concentrating on cases inwhich there is no mean flow in the system and thus investigating the effectscaused by concentration variations across the mass balance on an infinitesimal stretch of a one-dimensional system(Figure 2-1 a river, for example) yields:Vdcdt= Import Export =q(x, t)A q(x+ x, t)A,where the volume of the element isV=A x, and the Import and Export aresimply the flux times the cross-sectional area. The preceding equation can berewritten as:Figure control volume in one 2.

Chapter 2 DIFFUSION 2.1 The Diffusion Equation Formulation As we saw in the previous chapter, the flux of a substance consists of an advective component, due to the mean motion of the carrying fluid, and of a

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