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Drying has been defined as the process whereby moisture is vaporized from a material and is swept away from the surface, sometimes under vacuum, but normally by means of carrier gas which passes through or over the material [Keey (1992)]. Commonly, drying is conceived as the removal of water into a hot airstream, but drying may encompass the removal of any volatile liquid into any heated gas. For drying, so defined, to take place, the moist material must obtain heat from its surroundings by convection, radiation or conduction, or by internal generation such as dielectric or inductive heating; the moisture in the body evaporates and the vapor is received by a carrier gas. This drying process is sketched in Figure 1.

Convective drying process.

Figure 1. Convective drying process.

Drying has a number of close synonyms. Dehydration is the process of depriving a material of its water or the loss of water as a constituent. The term is often used in food-drying operations to describe processes which strive to expel moisture but retain other volatile constituents in the original material, and which are responsible for valuable aromatic and flavoring properties. Desiccation implies a more thorough removal of water. It is applied in the drying of foodstuffs to indicate almost complete dehydration of these materials for preservation. The term is also commonly used to describe the thorough removal of moisture from gases.

While heat may be used to drive off moisture from a wet substance, moisture can be severed from its host material by the action of pressure gradients. This process is known as dewatering, and is normally used as a precursor to the drying of very wet materials when the moisture-solid bonding is not strong. Dewatering may be undertaken by mechanical means, such as pressing or centrifuging. These operations are not considered in this encyclopedia since combined heat and mass transfer processes are not involved.

Water can also be removed by osmotic dehydration. Foods can be treated with concentrated solutions of salt or sugar to attain substantial removal of water with limited solute uptake. The process has been described in terms of coupled diffusion of the water and solute [Raoult-Wack et al. (1989)]. Sludges have been dewatered through the action of an external direct-current field; this is known as electro-osmosis [Yoshida and Yukawa (1992)]. These osmotic techniques also lie outside the realm of heat and mass transfer processes.

Drying is an energy-intensive operation of some significance. Estimates of energy demand range between 7 and 15% of a nation's industrial energy consumption [Keey (1992)], but a more recent survey for the United Kingdom in 1990 suggests the figure may be as high as 20%, an increase from the 12% obtained in a similar survey in 1978 [Oliver and Jay (1994)]. This difference may reflect the changing pattern of industrial activity in that country over the period.

Although the drying medium is normally considered to be air, there are advantages in using other media. If the solid being dried forms a combustible powder or the moisture itself is a flammable solvent, then the use of an inertized or inherently inert gas is advisable. Drying in steam has the added advantages of lower energy use and higher heat transfer rates. Above the so-called inversion-point temperature, drying in steam is faster than drying in perfectly dry air at the same temperature. The evolution of moisture is uniform, and this feature is observed for example in the superheated-steam drying of wood under vacuum, a process used commercially for the production of high-quality seasoned board timber with minimum degrade caused by the development of drying stresses. A closed vacuum or high-pressure vessel is not necessary for steam drying. By allowing air in the drying chamber to be displaced by water vapor as the vessel warms up and moisture evolution begins, the steam will remain in the dryer and no complex sealing arrangements are needed for the intake and discharge of solids. Steam at 100°C has only 55% of the density of air at the same temperature and thus will remain trapped inside the chamber. The patented technique is known as airless drying, and the arrangements for batch operation are shown in Figure 2. If the vented steam can be used for other purposes, such as the production of hot water, then the airless drying system can show considerable thermal economies over conventional drying in air.

An airless drying system with heat recovery. After Stubbing (1994).

Figure 2. An airless drying system with heat recovery. After Stubbing (1994).

Drying only takes place if the wet material contains more moisture than the equilibrium value for its environment. The earliest ideas on convective drying implied that liquid moisture diffuses to the exposed surface of a wet body where it evaporates, the vapor diffusing through the boundary layer into the bulk of the surrounding air. This view is clearly unsatisfactory, except for drying of homogeneous materials in which the moisture is effectively dissolved. Mechanisms of moisture movement are generally more complex. Most materials are composed of subentities, such as particles and fibres, which may be loose or held in some kind of matrix. The number and nature of the voids between these entities and the pores within them govern the quantity of moisture retained and the extent of bonding to the solids. If the openings form a capillary network, the material is said to be capillary-porous. A capillary-porous material may be nonhygroscopic: that is, the moisture held within the body exerts its full vapor pressure. This is a limiting case found in some coarse, nonporous mineral aggregates. Moisture is simply trapped between the particles. As the space between the particles becomes more confined, vapor pressure is lowered according to the Kelvin equation


where pk is the capillary-vapor pressure, p0 is the saturation vapor pressure, σ is the surface tension, ν is the molar liquid volume and dp is the capillary size.

Hygroscopicity may be related to this capillary condensation in the voids, but normally it stems from the structure of the primary entities with their finer passageways and their ability to hold moisture in a variety of ways. Material may not be simply capillary-porous, but be composed of complex arrangements of capillaries, vessels and cells, as seen with materials of vegetable origin. Some of these may be described as being both capillary-porous and colloidal, composed of a matrix colloidal by nature but developing a pore structure upon drying. Colloidal slurries of inorganic particles lose volume as moisture is driven off until the mass becomes consolidated. Colloidal material of biological origin, by contrast, does not shrink until condensed moisture in the intermiscellar spaces has been emptied. This condition is called the fibre-saturation point in woody material drying. Thereafter, as cellular moisture is expelled, the stuff shrinks as the cells shrivel.

The ratio of the moisture-vapor pressure to the saturation value at the same temperature is called relative humidity ψ. The lower the relative humidity, the more strongly is the moisture bound to the host material. The free energy ΔG required to release unit molal quantity of this moisture is given by


for an isothermal, reversible process without change of composition. Isothermal variation of the equilibrium moisture content (which is a function of this free-energy change) with relative humidity yields a moisture isotherm, and it is the desorption isotherm which is of interest in drying. Moisture isotherms are normally sigmoid in shape when plotted over the whole relative humidity range, but often a simple exponential expression can be fitted over a more limited range at higher relative humidities. The general shape of the isotherm reflects the nature of the moist material, as illustrated in Figure 3 An exception to this kind of behavior is that of inorganic crystalline solids which have multiple hydrates. With these materials, relative humidity falls in stepwise fashion with loss of moisture as each hydrate disappears.

Variation of relative humidity with equilibrium moisture content for different materials. After Keey (1978).

Figure 3. Variation of relative humidity with equilibrium moisture content for different materials. After Keey (1978).

When pores in a solid are of molecular size, moisture can only be held therein by volume filling such that the adsorbate, although highly compressed, is not considered to be a separate phase. The chemical potential of the adsorbent varies with the amount adsorbed, unlike the behavior at higher moisture contents when a separate adsorbate phase exists—with equilibrium between phases—and the chemical potential remains invariant. The fractional filling of these micropores is a complex exponential function of free-energy sorption, RT lnψ. With larger pore sizes, moisture can sorb in molecular layers on the host material. Consideration of multimolecular adsorption leads to the equation


for the equilibrium moisture content X at a relative humidity ψ, where X1 is the moisture content for a complete monolayer, k is the exp (± ΔH/RT), where ΔH is the constant enthalpy difference in adsorptive heats between the first and successive molecular layers of moisture, and C is a coefficient. When k is zero, the equation reduces to that for monomolecular adsorption. Over the range 0 < k < 1, this equation can describe the moisture-sorption behavior of materials, which appears to reach a finite moisture content as relative humidity approaches unity. This quantity is sometimes known as the maximum hygroscopic moisture content. This three-coefficient equation (with C, k and X1 as the adjustable parameters) has been tested for sorption of water vapor on 29 materials at room temperature over a wide range of relative humidity (from 0.07 to 0.97) and for some of these materials, over a narrower range of temperatures between 45 and 75%C [Jaafar and Michalowski (1990)]. In most cases, experimental data could be fitted to within ±8% up to a relative humidity of 0.7, and in some instances over the whole humidity range. To cope with the hygroscopic behavior at high relative humidities with colloidal material, which swells with increasing moisture content, Schuchmann et al. (1990) have recommended that –ln (1 – ψ) be chosen as the dependent variable rather than y itself in the correlation. It is unwise to extrapolate sorption correlations beyond their tested range of relative humidities, owing to changes in hygroscopic behavior at extremes in this range compared with that at intermediate values.

The manner in which a material dries out depends not only on its structure but also on its physical form. The drying of small wood chips is controlled essentially by moisture-vapor transport through the boundary layer; veneers and thin slats of the same wood by the dry fraction of the exposed surface; while the drying of board timber, by the internal moisture-transport mechanisms within the timber itself. Early experiments on drying materials in sample trays in an air stream have noted that initially, the drying rate was almost the same as that of a free liquid surface under the same conditions and remained relatively constant as the material dried out [Keey (1972)]. This period of drying is followed by one in which the drying rates fell off sharply as moisture content was reduced to the equilibrium value even though the drying conditions remain unchanged. This marked difference in behavior has led to the division of drying into the constant-rate period and falling-rate period, respectively. The "knee" in the drying curve between these two periods is known as the critical point. Sometimes, these periods are referred to as unhindered drying and hindered drying, respectively, to indicate whether the material itself plays a controlling role in restricting moisture loss. Appearance of the initial period can be masked by the induction effects at the start of drying as a moist solid warms up or cools to a dynamic equilibrium temperature, which is the Wet-bulb Temperature, if the surface is only heated convectively. This surface temperature is maintained as long as the surface is sufficiently wet to effectively saturate it. An example of a drying curve is shown in Figure 4.

An example of a drying curve.

Figure 4. An example of a drying curve.

The reasons for the appearance of a drying period of constant, or near-constant, drying rates are complex, particularly as it is unlikely that there exists a film of liquid moisture at the surface except in rare circumstances [van Brakel (1980)]. Indeed, a constant-rate period can be observed if the dimensions of the wet and dry patches on the surface are sufficiently small compared with the thickness of the boundary layer. The requirement is that moisture-vapor pressure at the surface maintain the saturation value at the mean surface temperature, and thus the rate of moisture loss over unit exposed surface ( ) is:


where pG is the partial pressure of the moisture vapor in the bulk of the gas and pS is the value of the gas adjacent to the moist surface. In drying calculations, it is more useful to use humidities (ratios of the mass of moisture vapor to that of dry gas), and the above expression transforms to


where βy is a mass transfer coefficient based on the humidity difference; φ is the humidity potential coefficient which effectively "corrects" for the introduction of a linear humidity driving force [Keey (1978)]; and YS and YG are the humidities at the surface and in the bulk of the gas, respectively. The falling-rate period begins when moisture movement within the solid can no longer maintain the rate of evaporation, or if moisture content at the surface falls below the maximum hygroscopic value and the partial pressure of the moisture vapor also dwindles. Clearly, a constant-rate period may never be observed in colloidal material drying that reaches unit relative humidity only at very high moisture contents.

To a first approximation, the drying kinetics in the falling-rate period may be regarded as of the first-order, and thus the drying rate is directly proportional to the difference between the mean moisture content of the wet material (X) and its equilibrium value (Xe):


Integration of this equation yields the time Δt to dry from a moisture content of X1 to X2:


where a is a coefficient which may be proportional to a moisture "diffusivity." However, the validity of this equation is no test that moisture movement is by diffusion as this expression correlates drying time for a number of materials dried in static and fluidized beds, in which diffusional processes are unlikely [van Brakel (1980)]. The appearance of first-order kinetics is sometimes referred to as the regular regime of drying.

There have been a number of attempts to provide a fundamental theoretical framework to describe drying and the development of moisture-content and temperature profiles in materials being dried. These include the use of irreversible thermodynamics to define the appropriate transport potentials [Luikov (1966)]; theories based on moisture-vapor diffusion and capillary transport of liquid in porous media [Krischer and Kast (1978)]; and volume-averaging the equations of continuity, mass and energy conservation which apply to each of the discontinuous phases within a moist porous body [Whitaker (1980)]. While these approaches have found some limited success in describing heat and mass transfer processes under certain idealized conditions, these theories are limited in application by the assumptions made to get numerical solutions.

In practice, more empirical approaches have been found which are useful in describing drying behavior of actual material under industrial conditions. One such method is based on the concept of the characteristic drying curve [Keey (1978)]. This is a generalized drying curve obtained from laboratory tests under constant drying conditions with a sample material. It is a plot of the drying rate, normalized with respect to its maximum value (mW) in the constant-rate period, against a characteristic moisture content—defined as the ratio of the freely evaporable moisture content (X – Xe) to the free moisture content at the critical point (Xcr – Xe). These nondimensional parameters thus become




respectively. An example of a characteristic drying curve is shown in Figure 5.

An example of a drying curve.

Figure 5. An example of a drying curve.

A unique characteristic drying curve is only found if the ratio of the exposed surface to the material volume is maintained constant or has a unique value at a given characteristic moisture content if the material shrinks. Strictly speaking, such a curve is only found at extremes of drying intensity, when the material's moisture content is essentially uniform (low-intensity drying) or when there is a sharp front between dried-out material close to the surface and a still-wet interior (high-intensity drying). In practice, however, over the range of practical drying conditions, characteristic drying curves appear when drying a variety of particulate and loose materials, provided the particle size is below 20 mm [Keey (1992)]. There is normally no simple relationship between the parameters f and Ф, although there are some special cases. First-order kinetics correspond to the identity f = Ф, with drying of permeable materials approximating this behavior. When drying is controlled by the dry fraction of exposed surface (with thin sheets, for example), then f = Ф2/3. Drying of impermeable materials like heartwood timber corresponds approximately to f = Ф2. If no critical point is observed in the drying experiment, a characteristic curve can be drawn up based on normalizing the moisture content with respect to the ostensible start of the falling-rate period, provided a simple algebraic relationship can be fitted to the characteristic curve. The particular advantage of the characteristic drying curve concept is that a simplified equation can be written to describe the rate of drying at any place within a dryer if the humidity potential (YW – YG) is known, where YW is the saturation humidity at the wet-bulb temperature:


Examples of the use of this expression to describe industrial drying processes are given by Keey (1978, 1992).

The intensity of drying (I) is given by the ratio of the maximum unhindered drying rate (mW) to the maximum moisture-transfer rate through the material assuming a diffusion-like process:


where D is a moisture diffusion coefficient, X0 is the initial moisture content and b is the effective thickness or radius of the material. This suggests that the product mWb is a useful property; it is called the flux parameter, F. If ln F is plotted against moisture content X, a separate curve is found for each initial moisture content X0 in the penetration period as the moisture content and temperature profiles develop within the material. In the regular regime, there is a common curve independent of initial moisture content and drying flux.

Under certain circumstances, drying curves can appear with both negative and positive gradients in drying rate as moisture is lost. The drying of layers of soluble dyestuffs can show discontinuities due to the build up and cracking of surface crusts, particularly if the crust is removed periodically. The drying of porous bodies containing a mixed volatile solvent may also show periods of falling and rising rates due to selective evaporation of the moisture with changes in relative volatility as the composition alters.


Jaafar, F. and Michalowski, S. (1990) Modified BET equation for sorption/desorption isotherms, Drying Technol. 8(4), 811-827.

Keey, R. B. (1978) Introduction to Industrial Drying Operations, Pergamon, Oxford.

Keey, R. B. (1992) Drying of Loose and Particulate Materials, Hemisphere, New York.

Krischer, O. and Kast, W. (1978) Die wissenschaftlichen Grundlagen der Trocknungstechnik, 3rd ed. Springer-Verlag, Berlin Heidelberg New York.

Luikov, A. V. (1966) Heat and Mass Transfer in Capillary-Porous Bodies, Pergamon, Oxford.

Stubbing, T. J. (1994) Airless Drying, in Proc. 9th Internat. Drying Symp., Gold Coast, Qld, 1-4 Aug.

van Brakel, J. (1980) Mass Transfer in Convective Drying, Chapter 7 in Advances in Drying, 1, (Ed. A. S. Mujumdar), Hemisphere, Washington.

Whitaker, S. (1980) Heat and Mass Transfer in Granular Porous Media, Chapter 2 in Advances in Drying, 1, (Ed. A. S. Mujumdar), Hemisphere, Washington.


  1. Jaafar, F. and Michalowski, S. (1990) Modified BET equation for sorption/desorption isotherms, Drying Technol. 8(4), 811-827. DOI: 10.1080/07373939008959916
  2. Keey, R. B. (1978) Introduction to Industrial Drying Operations, Pergamon, Oxford. DOI: 10.1002/cite.330510226
  3. Keey, R. B. (1992) Drying of Loose and Particulate Materials, Hemisphere, New York.
  4. Krischer, O. and Kast, W. (1978) Die wissenschaftlichen Grundlagen der Trocknungstechnik, 3rd ed. Springer-Verlag, Berlin Heidelberg New York. DOI: 10.1002/star.19790310113
  5. Luikov, A. V. (1966) Heat and Mass Transfer in Capillary-Porous Bodies, Pergamon, Oxford.
  6. Stubbing, T. J. (1994) Airless Drying, in Proc. 9th Internat. Drying Symp., Gold Coast, Qld, 1-4 Aug. DOI: 10.1080/07373939908917642
  7. van Brakel, J. (1980) Mass Transfer in Convective Drying, Chapter 7 in Advances in Drying, 1, (Ed. A. S. Mujumdar), Hemisphere, Washington.
  8. Whitaker, S. (1980) Heat and Mass Transfer in Granular Porous Media, Chapter 2 in Advances in Drying, 1, (Ed. A. S. Mujumdar), Hemisphere, Washington.
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