Mass transfer occurs in a number of food-processing operations such as dehydration, evaporation, concentration, distillation, solvent extraction, packaging, peeling, and leaching. Mass transfer is a common and important phenomenon in food processing and preservation. During osmotic drying of fruits, for example, sugar from a concentrated solution moves into the fruit while water leaves the fruit and migrates into the surrounding solution. By defi nition, mass transfer is the migration of matter from one location to another due to concentration or partial pressure gradient. According to this definition, the motion of air due to wind or the transport of water through a pipe by a pump is not mass transfer, because these motions occur due to either the presence of a total pressure difference (wind) or the application of mechanical work (pump).
Mass transfer subdivides into molecular mass transfer and convective mass transfer. For the former, the term diffusion is often used. Diffusion deals with the random molecular migration of matter through a medium, whereas convective mass transfer involves the migration of matter from a surface into a moving fluid or a stream of gas. Diffusion further subdivides into molecular diffusion, transitional diffusion, Knudsen diffusion, and Eddy diffusion. Among these, molecular diffusion is the most important phenomenon. It exists in most processes of mass transfer and often has a major influence when other kinds of diffusion are also present.
From the theory of molecular kinetics, it is known that when a randomly moving molecule diffuses through a capillary tube, it can move freely for some distance before a collision with another molecule or with the wall of the capillary tube occurs. If a molecule would collide with other molecules more often than it would with the wall, molecular diffusion occurs. If molecule-wall collisions are predominant, it is Knudsen diffusion. If both molecule-molecule and molecule-wall collisions are important, it is transition-type diffusion. The specific state can be determined by evaluating Knudsen's number (1). When bulk fluid motion is involved, the term Eddy diffusion applies.
Diffusion of a substance may occur in gases, liquids, or solids. Within the range of validity of the ideal gas law, the rate of diffusion in gases is affected primarily by temperature and pressure. When diffusion in liquids is considered, however, the effect of pressure is usually negligible because liquids are incompressible. Diffusion in solids is far more complex than diffusion in gases or liquids, because (1) the substance diffusing through a solid may actually be diffusing through a liquid or gas contained within the pores of the solid; and (2) many solids, such as crystals, polymeric films, and solids with capillaries, are anisotropic, in which case the molecules have a preferential direction of movement.
The general equation for all types of mass transfer is
resistance where the driving force is the partial pressure difference or the concentration gradient (depending on the transferred matter); and the resistance is a function of the properties of the medium through which the matter is transferred.
Mass transfer can occur with steady-state or unsteady-state conditions. In a steady state the concentration or partial pressure, the resistance, and the transfer rate are constant over time. In an unsteady state, all these properties vary with time. Obviously, the mathematical treatment of steady-state problems is simpler than that involving unsteady-state conditions. For this reason, the following sections shall first deal with the simple steady-state cases. It is important to remember, however, that in reality every process begins with unsteady-state conditions, which over time change to steady state.
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