Page 334 - Academic Press Encyclopedia of Physical Science and Technology 3rd Chemical Engineering

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Encyclopedia of Physical Science and Technology EN009H-407 July 18, 2001 23:34

Mass Transfer and Diffusion

E. L. Cussler
University of Minnesota

I. Diffusion
II. Dispersion
III. Mass Transfer
IV. Conclusions

GLOSSARY to complete mixing. It is often a slow process. In many
cases diffusion occurs sequentially with other phenom-
Convection bulk fllow, usually the result of forces on the ena. When it is the slowest step in the sequence, it limits
system, but occasionally caused by diffusion. the overall rate of the process.
Diffusion spontaneous differential mixing caused by In gases and liquids, the rates of these diffusion pro-
Brownian motion. cesses can often be accelerated by convective flow. For
Diffusion coefficient the flux divided by the concentra- example, the copper sulfate in the tall bottle can be com-
tion gradient. pletely mixed in a few minutes if the solution is stirred.
Dispersion spontaneous mixing effected by flow and— This accelerated mixing is not due to diffusion alone, but
only sometimes—by diffusion. to a combination of diffusion and convection. Diffusion
Flux the moles or mass transported per area per time. still depends on the random molecular motions that take
Mass transfer spontaneous mixing from a system’s place over small molecular distances. The convective stir-
boundary into its bulk. ring is not a molecular process, but a macroscopic process
Mass transfer coefficient the flux divided by the concen- which moves portions of the fluid over longer distances.
tration difference between an interface and the bulk. After this macroscopic motion, diffusion mixes the newly
adjacent portions of the fluids.
The description of diffusion involves three complimen-
IF A FEW CRYSTALS of blue copper sulfate are placed tary mathematical models, often dignified as “laws.” The
in the bottom of a tall bottle filled with water, the color will most fundamental, Fick’s law of diffusion, uses a “dif-
slowly spread through the bottle. At first, the color will be fusion coefficient.” In other cases, where convection is
concentrated in the bottom. After a day, it will penetrate strong, the mixing will occur following the same math-
upward a centimeter or so. After several years the solution ematics as Fick’s law but with a “dispersion” coefficient
will appear to be homogeneous. replacing the diffusion coefficient. In still others cases,
The process responsible for the movement of the cop- where there is transport across some type of interface, the
per sulfate is diffusion, the basic phenomenon in this arti- mixing is described as “mass transfer” and correlated with
cle. Caused by random molecular motion, diffusion leads a “mass transfer coefficient.” Mass transfer coefficients

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