Page 114 - Separation process principles 2

3.2 Diffusion Coefficients 79

Table 3.9 Experimental Diffusivities of Large Biological Proteins in Aqueous Solutions

Diffusivity, DAB,
Protein MW Configuration Temperature, "C cm2/s x lo5
Bovine serum albumin 67,500 globular 25
y -Globulin, human 153,100 globular 20
Soybean protein 361,800 globular 20
Urease 482,700 globular 25
Fibrinogen, human 339,700 fibrous 20
Lipoxidase 97,440 fibrous 20

crystalline, or amorphous; and the type of solid material, mechanisms or combinations thereof may take place:
whether it be metallic, ceramic, polymeric, biological, or 1. Ordinary molecular diffusion through pores, which
cellular. Crystalline materials may be further classified ac-
present tortuous paths and hinder the movement of
cording to the type of bonding, as molecular, covalent, ionic,
large molecules when their diameter is more than 10%
or metallic, with most inorganic solids being ionic. How-
of the pore diameter
ever, ceramic materials can be ionic, covalent, or most often
a combination of the two. Molecular solids have relatively 2. Knudsen diffusion, which involves collisions of diffus-
ing gaseous molecules with the pore walls when the
weak forces of attraction among the atoms or molecules. In
covalent solids, such as quartz silica, two atoms share two or pore diameter and pressure are such that the molecular
more electrons equally. In ionic solids, such as inorganic mean free path is large compared to the pore diameter
salts, one atom loses one or more of its electrons by transfer 3. Surface diffusion involving the jumping of molecules,
to one or more other atoms, thus forming ions. In metals, adsorbed on the pore walls, from one adsorption site to
positively charged ions are bonded through a field of elec- another based on a surface concentration-driving force
trons that are free to move. Unlike diffusion coefficients in 4. Bulk flow through or into the pores
gases and low-molecular-weight liquids, which each cover a
When treating diffusion of solutes in porous materials
range of only one or two orders of magnitude, diffusion co-
where diffusion is considered to occur only in the fluid in the
efficients in solids cover a range of many orders of magni-
tude. Despite the great complexity of diffusion in solids, pores, it is common to refer to an effective diffusivity, Def,
Fick's first law can be used to describe diffusion if a mea- which is based on (1) the total cross-sectional area of the
sured diffusivity is available. However, when the diffusing porous solid rather than the cross-sectional area of the pore
solute is a gas, its solubility in the solid must also be known. and (2) on a straight path, rather than the pore path, which
may be tortuous. If pore diffusion occurs only by ordinary
If the gas dissociates upon dissolution in the solid, the
concentration of the dissociated species must be used in molecular diffusion, Fick's law (3-3) can be used with an
Fick's law. In this section, many of the mechanisms of diffu- effective diffusivity. The effective diffusivity for a binary
sion in solids are mentioned, but because they are exceed- mixture can be expressed in terms of the ordinary diffusion
ingly complex to quantify, the mechanisms are considered coefficient, DAB, by
only qualitatively. Examples of diffusion in solids are con-
sidered, together with measured diffusion coefficients that
can be used with Fick's first law. Emphasis is on diffusion of
gas and liquid solutes through or into the solid, but move- where E is the fractional porosity (typically 0.5) of the solid
ment of the atoms, molecules, or ions of the solid through it- and T is the pore-path tortuosity (typically 2 to 3), which is
self is also considered. the ratio of the pore length to the length if the pore were
straight in the direction of diffusion. The effective diffusivity
is either determined experimentally, without knowledge of
Porous Solids
the porosity or tortuosity, or predicted from (3-49) based on
When solids are porous, predictions of the diffusivity of measurement of the porosity and tortuosity and use of the
gaseous and liquid solute species in the pores can be made. predictive methods for ordinary molecular diffusivity. As an
These methods are considered only briefly here, with details example of the former, Boucher, Brier, and Osburn [13] mea-
deferred to Chapters 14, 15, and 16, where applications are sured effective diffusivities for the leaching of processed soy-
made to membrane separations, adsorption, and leaching. This bean oil (viscosity = 20.1 cP at 120°F) from 1116-in.-thick
type of diffusion is also of great importance in the analysis and porous clay plates with liquid tetrachloroethylene solvent.
design of reactors using porous solid catalysts. It is sufficient The rate of extraction was controlled by the rate of diffusion
to mention here that any of the following four mass-transfer of the soybean oil in the clay plates. The measured value of