Page 101 - Separation process principles 2

Chapter 3

Mass Transfer and Diffusion

Mass transfer is the net movement of a component in a barriers, such as membranes, differing species mass-transfer
mixture from one location to another where the component rates through the membrane govern equipment design.
exists at a different concentration. In many separation In a binary nzixture, molecular diffusion of component
operations, the transfer takes place between two phases A with respect to B occurs because of different potentials
across an interface. Thus, the absorption by a solvent liquid or driving forces, which include differences (gradients)
of a solute from a carrier gas involves mass transfer of the of concentration (ordinary diffusion), pressure (pressure
solute through the gas to the gas-liquid interface, across the diffusion), temperature (thermal diffusion), and external force
interface, and into the liquid. Mass-transfer models describe fields (forced diffusion) that act unequally on the different
this and other processes such as passage of a species through chemical species present. Pressure diffusion requires a large
a gas to the outer surface of a porous, adsorbent particle and pressure gradient, which is achieved for gas mixtures with a
into the adsorbent pores, where the species is adsorbed on centrifuge. Thermal diffusion columns or cascades can be
the porous surface. Mass transfer also governs selective employed to separate liquid and gas mixtures by establishing
permeation through a nonporous, polymeric material of a a temperature gradient. More widely applied is forced
component of a gas mixture. Mass transfer, as used here, diffusion in an electrical field, to cause ions of different
does not refer to the flow of a fluid through a pipe. However, charges to move in different directions at different speeds.
mass transfer might be superimposed on that flow. Mass In this chapter, only molecular diffusion caused by
transfer is not the flow of solids on a conveyor belt. concentration gradients is considered, because this is the
Mass transfer occurs by two basic mechanisms: most common type of molecular diffusion in separation
(1) molecular difision by random and spontaneous rnicro- processes. Furthermore, emphasis is on binary systems, for
scopic movement of individual molecules in a gas, liquid, or which molecular-diffusion theory is relatively simple and
solid as a result of thermal motion; and (2) eddy (turbulent) applications are relatively straightforward. Multicomponent
diffusion by random, macroscopic fluid motion. Both molecular diffusion, which is important in many applica-
molecular and/or eddy diffusion frequently involve the tions, is considered briefly in Chapter 12. Diffusion in multi-
movement of different species in opposing directions. When component systems is much more complex than diffusion in
a net flow occurs in one of these directions, the total rate of binary systems, and is a more appropriate topic for ad. anced
mass transfer of individual species is increased or decreased study using a text such as Taylor and Krishna [I].
by this bulk flow or convection effect, which may be Molecular diffusion occurs in solids and in fluids that are
considered a third mechanism of mass transfer. Molecular stagnant or in laminar or turbulent motion. Eddy diffusion
diffusion is extremely slow, whereas eddy diffusion is orders occurs in fluids in turbulent motion. When both molecular
of magnitude more rapid. Therefore, if industrial separation diffusion and eddy diffusion occur, they take place in
processes are to be conducted in equipment of reasonable parallel and are additive. Furthermore, they take place
size, fluids must be agitated and interfacial areas maximized. because of the same concentration difference (gradient).
If mass transfer in solids is involved, using small particles to When mass transfer occurs under turbulent-flow conditions,
decrease the distance in the direction of diffusion will but across an interface or to a solid surface, conditions may
increase the rate. be laminar or nearly stagnant near the interface or solid
When separations involve two or more phases, the extent surface. Thus, even though eddy diffusion may be the
of the separation is limited by phase equilibrium, because, dominant mechanism in the bulk of the fluid, the overall rate
with time, the phases in contact tend to equilibrate by mass of mass transfer may be controlled by molecular diffusion
transfer between phases. When mass transfer is rapid, because the eddy-diffusion mechanism is damped or even
equilibration is approached in seconds or minutes, and eliminated as the interface or solid surface is approached.
design of separation equipment may be based on phase Mass transfer of one or more species results in a total net
equilibrium, not mass transfer. For separations involving rate of bulk flow or flux in one direction relative to a fixed