Mass transport
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Mass transport

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Mass transport Mass transport Presentation Transcript

  •  In this chapter we start by giving Fick's law of diffusion, which describes the movement of one chemical species A through a binary mixture of A and B because of a concentration gradient of A.
  •  The movement of a chemical species from a region of high concentration to a region of low concentration can be observed by dropping a small crystal of potassium permanganate into a beaker of water.  The KMnO, begins to dissolve in the water, and very near the crystal there is a dark purple, concentrated solution of KMnO,. Because of the concentration gradient that is established, the KMnO, diffuses away from the crystal. The progress of the diffusion can then be followed by observing the growth of the dark purple region.
  •  Consider a thin, horizontal, fused-silica plate of area A and thickness Y. Suppose that initially (for time t < 0) both horizontal surfaces of the plate are in contact with air, which we regard as completely insoluble in silica. View slide
  •  In this system, we will call helium “species A” and silica “species B”. The concentrations will be given by the "mass fractions" wA and wB.  The mass fraction wA is the mass of helium divided by the mass of helium plus silica in a given microscopic volume element. The mass fraction wB is defined analogously. View slide
  • The mass fraction of helium, wA is everywhere equal to zero The air below the plate is suddenly replaced by pure helium. At the lower surface, y = 0, the mass fraction of helium is equal to wA0. Helium slowly penetrates into the plate by virtue of its molecular motion - DIFFUSION As time proceeds the mass fraction profile develops, with wA = wA0 at the bottom surface of the plate and wA = 0 at the top surface of the plate. The profile tends toward a straight line with increasing t
  •  At time t = 0, the air below the plate is suddenly replaced by pure helium, which is appreciably soluble in silica. The helium slowly penetrates into the plate by virtue of its molecular motion and ultimately appears in the gas above.  This molecular transport of one substance relative to another is known as diffusion.  The air above the plate is being replaced rapidly, so that there is no significant buildup of helium there.
  •  In this section we discuss the prediction of the diffusivity DAB for binary systems by corresponding-states methods.
  •  binary diffusion