part i general principles

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Historical Background

For thousands of years, man has sun dried foods to

sustain him in off-season periods. The following are

some recorded examples of the very early application of

sun drying. As far back as 20,000 BC meat was cut into

strips and sun dried in Russia. Around 10,OOO BC salt

was produced by sun drying seawater. American Indians

made dried mashed potatoes about 3500 BC. The

potatoes were frozen overnight and trampled to express

out the juices. This process was repeated before the

mash was dried. In ancient Egypt (2800-2300 BC) fruit

such as apples, grapes and apricots were sun dried.

Around 500 BC, dry-salted fish was produced.

Tea was dried in India in 300-400 AD . In the period

710-785 AD, large quantities of sun-dried foods were

produced in Japan including fruits, vegetables, fish and

shellfish, meat and poultry. The dried products were

stored in warehouses. Around 900 AD, fish was sun

dried in Norway. The Mongolian army used sun dried

powdered milk in 1240AD. Around 1650AD colonists

in North America dried boiled Indian corn over !ires.

In 1780AD, the first patent on vegetable drying was

taken out in America. The vegetables were boiled in salt

water, and kept for 20-30 hours. The quality was poor.

In 1795 AD, in France, sliced vegetables were dried in

air at W C , pressed, and sealed in foil. Enzyme activity

occurred and vitamin C was destroyed.

Dried vegetables were shipped to the British troops

during the Crimean war (1854-1856) and were also used

by the Union troops in the American Civil War

(1861-1865). In 1865AD, a patent for producing dried

egg was taken out. In 1872, Samuel Percy took out a

patent on “Improvements in Drying and Concentrating

Liquid Substances by Atomizing”, i.e. spray drying/

concentrating. Dried vegetables, produced in Canada,

were used by British troops during the Boer war

Developments accelerated in the 20th century. In

1901, Robert Stauffpatented a spray drier for blood and

milk. This featured an upward-spraying nozzle and

perforated plate air disperser. In 1902, Just Hatmaker

(1899-1902).

developed a drum drier. Merrel Soul, an American

company, purchased the Stauff patent in 1905 and

developed a spray drier for producingmilk powder. Thiswas a box-type, horizontal-concurrent drier which was

operated on a batch principle. In 1912, George Krauss

developed the centrifugal spray drier and in 1913 Grey

and Jensen developed a conical spray drier. This type of

spray drier was used extensively for many years. Dried

vegetables were supplied to British and American troops

during World War I (1914-1918). During that period,

there was considerable expansion in vegetable-drying

facilities in Europe, including cabinet, tunnel and

conveyor driers. Research on vacuum drying of foods

was also undertaken. C. E. Rogers introduced the

continuous box-type, horizonal-concurrent, spray-drier

in 1917. The jet-spray drier was developed by Coulter in

1940. Before and during World War II (1939-1945) a

whole range of dried products was developed, including

drum-dried soup mixes and tomato flakes, spray-dried

milk and egg products, vacuum-dried fruits, and air-

dried onions and garlic. In the period 1939-1945 a huge

expansion in drying facilities occurred in Europe and

America and dried foods were used extensively by the

troops of al l the parties to the conflict. In 1945, Flosdorf

first used vacuum freeze drying for foods. Considerable

research into freeze drying was undertaken in the UK in

the early 1950s which led to the development of the

accelerated freeze drying (AFD) method. Freeze-drying

plants for meat, fish and vegetables were set up in many

countries, notably Ireland. However, mainly because of

the costliness of the process, interest in freeze drying of

such products waned over the next decade.

The first instantizedmilk was introduced by Peebles

in 1954. The BIRS drier was introduced in 1962 but it

did not receive widespread application. In 1965, the first

patent on instant coffee was taken out. Since then

considerable advances have been made in improving the

organoleptic quality and reconstitution properties of

instant beverages. In 1960, the first freeze-dried instant

coffee was produced. The production of freeze-dried

3



4 HistoricalBackground and General Principles

instant coffee grew rapidly in the late 1970s and 1980s.Pneumatic drying of small particulate foods came intouse in the early 1960s. This was followed by theintroduction of fluidized-bed driers. These have foundincreasing application to food dehydration in the lasttwenty years. They are also used as agglomerators forspray-dried powders. The spouted bed drier, a variationon the fluidized bed, has also found some useful

applications, particularly for larger-sized particles,greater than 5 mm. A novel application for the spouted-beddrier is for drying liquid foods. The liquid is sprayedonto a spouted bed of inert solid particles. Thisapplication is still under investigation. The toroidal-beddrier is another variation on the fluidized bed. This wasfirst introduced in the 1980s and is still being eval-uated.

The advantages of multistage drying became recog-nized in the 1970s and it is now widely practised.Conveyor, fluidized-bed and pneumatic drying may becarried out in two or more stages. Powder from spray

driers may receive secondary drying in fluidized beds.

Spray-drying systems featuring multistage drying in oneunit were introduced in the 1980s and are findingincreasing application.

The need for energy conservation became a priority inthe 1980s and has led to improvements in the thermalefficiency of drying systems and in m ethods of recover-ing heat from the exhaust air from d rying chambers. Theuse of microwave heating for the purpose of drying has

so far found only limited application. However, this isbeing researched and is likely to find wider applicationin the near future.

Hand-in-hand with developments in drying equipme ntand techniques over the last fifty years, our under-standing of d rying processes has increased.A great dealof research into the mechanisms of heat and masstransfer during drying has been undertaken and, in recentyears, models for the prediction of drying time andtemperaturdmoisture distribution within food piecesduring drying, has been developed (Van Arsdel et al,1973a; Hayash i, 1989; Dalgleish, 1990; Masters, 1991).



General Principles of Dehydration

Many authors use the teim ‘drying’ to describe theremoval of moisture by exposure to the sun and the term‘dehydration’ to moisture removal by the application ofother heating m ethods. In this text, no such distinction ismade. Both terms are used interchangeably to describethe unit operation in which nearly a l l the water normallypresent in a foodstuff is removed by evaporation orsublimation as a result of the application of heat. Thusmechanical de-watering methods, such as filtration,centrifugation or expression are not included. Osmoticdrying and azeotropic drying are treated briefly eventhough they do not fall within the definition givenabove.

Usually, the main objective of dehydrating food is to

prolong its shelf life beyond that of the fresh material.This is achieved by reducing the water activity (a,) ofthe food to a value which will inhibit the growth anddevelopment of pathogenic and spoilage microorgan-isms, significantly reducing enzy me activity and the rateat which undesirable chemical reactions occur. Theinfluence of a, on such changes is discussed underWater activity and food quality (page 129). By this

adjustment of a, and the use of appropriate packaging,the shelf life of the food can be extended without theneed for refrigerated storage. Th e removal of most of thewater from the food reduce s the weight to be carried perunit food value. This can lead to substantial savings inthe costs of handling and transporting the dried productas compared with the fresh material. A reduction involume of the dried m aterial, as compared with the fresh,can lead to savings in the cost of storage and transport.The maxim um reduction in bulk is attained when diluteliquid foods are dried to powders, particularly if thepowd er is then compressed into blocks o r tablets. On theother hand, little or no change in volume occurs whensolid pieces of food are freeze dried. In between theseextremes, varying deg rees of shrink age occur, dependingon the food, the method of drying and the drying

conditions.

Drying can also bring about undesirable changes infoods. The size and shape of solid food pieces change

during drying, due to the shrinkage discussed above.Wh en reconstituted, they may not return to their originalshape and size. Colour changes may also occur due tothe removal of water or as a result of exposure to hightemperatures during drying. Again, the colour of thereconstituted product may differ from that of the freshmaterial. The texture of the reconstituted material maybe less acceptable than that of the fresh because ofchanges in structure due to shrinkage and/or excessiveexposure. to heat. The capacity of dried food pieces toreabsorb water may be limited which would alsocontribute to their poor texture. In the case of food

powders, it is usually desirable that they reconstituterapidly and completely in hot or cold liquid, as

appropriate. The extent to which this occurs depends onthe drying method and conditions (see under Recon-stitutability of dried food powders, page 91). Changes inflavour may also occur as a result of drying. These maybe due to the loss of volatile flavour compounds duringdrying and/or to the development of an undesirablecooked flavour because of exposure to high tem-peratures. The extent of these changes depends on the

drying method. Freeze-dried products generally exhibitthe least changes in flavour. Spray drying and otherrapid drying methods bring about moderate changes.Drying techniques in which the food is exposed torelatively high temperatures, e.g. drum drying, and/orwhich entail relatively long drying times, e.g. in cabinetdriers, are likely to bring about important changes inflavour.

Chan ges in the nutritional quality of foods may occuras a result of drying. Considerable losses of water-soluble nutrients m ay occurduring the preparation of thefood prior to dehydration, i.e. during cleaning, peeling,blanching or cooking. Similar losses would be encoun-tered when preparing foods prior to freezing o r canning.

During the drying o peration itself, the loss of water- and

5



6 Historical Background and General Principles

lipid-soluble nutrients will depend on the drying methodand conditions. Exposure of the food to a hightemperature at a m oisture content intermediate betweenthat of the fresh material and the dried product is likelyto lead to high losses. Such conditions should be

minimizedby careful selection of the drying method andconditions and good control of the drying operation. Ingeneral, drying should result in high retention of

nutrients with the exceptions of vitamins C and A.Vitamin C losses in drying are usually somew hat higherthan in canning and much higher than in freezing.Vitamin A losses in drying can be very much higher thanin canning or freezing. Vitamin B losses in drying arerelatively low, comparable with freezing an d lower than

As a result of a considerable amount of research inrecent years, many modem dehydrated foods have goodorganoleptic characteristics and reconstitute rapidly.Consequently, they constitute a significant component ofthe convenience food market.

Dehydration is a simultaneous heat-and-mass transferoperation. The necessary sensible and latent heat ofevaporation, or sublimation, must be supplied to thefood, while water or water vapour must mov e within thefood to the evaporating surface and the water vapourmust transfer from that surface to the surroundingatmosphere. The mechanisms whereby heat is trans-ferred to food provide a convenient way of classifyingthe many drying m ethods used today. On this basis, thereare three categories of drying methods as follows:

In group I heated air is the drying medium. The food isplaced in a current of heated air. Most of the heat issupplied to the food by convection from the air. Suchmethods are also known as convective or convectiondrying methods.

In group 2 the food is placed in contact with a heatedsurface, usually a metal surface. Most of the heat istransferred to the food by conduction from the hotsurface. Such methods are also known as conductive orconduction drying methods.

In group 3 the food is exposed to radiant heat, andradiation is the m ain mechanism of heat transfer. Thesemethods are also known as radiative drying methods.

Sun drying fits into this category.

In addition to these three main categories, the use ofmicrowave and dielectric energy for the purposes ofdrying should be considered, as well as freeze dryingwhich involves a freezing and a drying stage.

in canning.

Drying in heated air

(i) SolidsDuring the drying of a wet solid in heated air, the air

supplies the necessary sensible and latent heat and alsoacts as a carrier for the water vapour formed, moving it

away from the drying surface and permitting furtherevaporation to occur. Consider a wet solid in the form ofa thin slab positioned in a current of heated air flowing

parallel to one of its large faces. Assume that dryingtakes place from this large face only. The slab consists of

an inert solid, wetted with pure water, and the tem-perature, humidity and velocity of the air remainconstant. Assume that all the heat is transferred byconvection from the air. If the moisture content of thematerial is monitored throughout drying and the datapresented in the form of curves as shown in Figure 1.1,

it can be seen that the drying cycle can be considered toconsist of a number of stages or periods as follows:

Period A-B. This represents a 'settling down' orequilibration period during which the solid surfaceconditions come into equilibrium with the drying air.The length of this period is usually small compared tothe overall drying time.

Period B-C.During this period the rate of dryingremains constant. Hence it is known as the constant rateper iod. During this period the surface of the solid issaturated with water. As water evaporates from the

surface it is replaced with water which migates fromwithin the solid to the surface. The rate of evaporation ofwater from the surface balances the rate of heat transferto the surface, from the air, and so a state of equilibriumexists at the surface. Throughout this period the surfacetemperature remains constant at a value which corre-sponds to the wet-bulb temperature of the drying air.This is understandable if one com pares the conditions atthe surface to those which prevail at the wick of a w et-bulb thermometer. This state of equilibrium persists as

long as the movement of water to the surface is sufficientto m aintain it in a saturated condition. Water evaporates

into the air stream as a result of a water-vapour pressuregradient between the surface of the solid and the mainstream of the air. The rate of mass transfer (-dwldt) maybe described by an expression such as:

where K g = mass transfer coefficient; A = drying area; p s

= water vapour pressure at the surface of the solid (i.e.the vapour pressure of water at surface temperature,since the surface is saturated); p a = water vapourpressure in the main stream of the air.

Equation (I) may also be written as:dw -Kg'A(H, - H a )

dt

where Kg'= mass transfer coefficient; H , = absolutehumidity at the surface of the solid (i.e. saturationhumidity of the air at surface tem perature); Ha= absolutehumidity in the main stream of the air.

The rate of heat transfer to the surface of the solid(dQldr) may be described by an expression such as:

92 = h J ( 0 , - 0,)

drwhere h, = heat transfer coefficient for convectionheating: 8, = dry-bulb temperature of the air; 0, =



General principles of Dehydration 7

the air does not flow parallel to the drying surface andfor through-flow of air.W hen a significant proportion ofthe heat of drying is supplied by conduction, e.g. fromthe metal tray on which the food is placed, and/or byradiation, e.g. fro m the walls of the drying chamber, anoverall heat transfer coefficient, taking this into account,must be used in the above equations. In such circum-stances, the surface temperature may remain constant

during the constant rate period of drying, but its valuewill be between the wet-bulb temperature of the air andthe boiling point of the water. In most practical dryingsituations, some heat transfer by conduction and radia-tion will occur in addition to convection. Drying underconstant rate conditions can be advantageous when heatsensitive foods are being dried, as high rates ofevaporation may be accomplished at relatively lowproduct temperatures. Some solid foods do exhibitconstant-rate drying but the length of that period-isusually only a small proportion of the total drying time.In the case of many foods no constant rate period of

drying is evident.A s drying continues, a point is reached at which the

rate of migration of m oisture to the surface is no longeradequate to m aintain the surface in a saturated condition(point C in Figure 1.1).From this point on, the rate ofdrying is no longer constant but falls progressivelythroughout the rest of the drying cycle. Point C is knownas the critical point, the moisture content at that point -W,, the critical moisture conte nt and the drying periodbeyond that point - C-D, the falling-rate period.

In period C-D, thefulling-rate period, the temperatureat the surface of the solid rises as drying proceeds and

approaches a value corresponding to the dry-bulbtemperature of the air as the material approachesdryness. Many authors have reported the Occurrence oftw o or more falling rate periods, i.e. points of inflexionin the falling-rate curve (Figure l . l ( c ) ) .Attempts havebeen made to explain such curves in terms of what ishappening within the solid. One such explanation is as

follows: jus t beyond the critical point the surface beginsto dry out but moisture is still evaporating from thesurface. At some point E (Figure I. l(c)) he plane ofevaporation moves down into the solid. The vapourarising from this plane has to pass through a layer of dry

solid which further reduces the rate of drying. Thisbehaviour could account for a two-stage falling-rateperiod, but there is little experimental evidence toco nf im this. Other explanations relate to the mechanismof moisture movement within the solid (see below).Usually, in food dehydration o perations, a large propor-tion of the drying takes place under falling rateconditions.

Very many mathematical models have been proposedto represent drying under falling-rate conditions. Thesecan be put into two categories: (a) those that relate to themechanisms of moisture movement within the solid and

(b) those that are empirical and are obtained by fittingexpressions to drying curves constructed from experi-mental data.

temperature at the surfam of the solid (i.e. the wet-bulbtempera- of the air).

Since a state of equilibrium exists at the surface of th esolid, and if sensible heat changes are neglected, the

rates of mass and heat transfer may be related as

follows:

(Jww dQ-Ls = - -dr dr

where L , = latent heat of evaporation at 8,.

Thus, the rate of mass transfer (i.e. the rate of drying )may be expressed in terms of a h eat transfer coefficientand temperature difference as follows:

the drying rate may also be expressed in terms of the rateof change of moisture content thus:

where -dW/dr = the rate of change of moisture content(dwb); A' = effective drying surface area per unit massof dry solids.

If the thickness (depth) of the slab is I and the bulkdensity of the m aterial ps. the rate of change of moisturecontent may be expressed thus:

If Wo is the mois ture content of the wet material at thestart of the constant rate period (dwb) and W, its

moisture content at the end of that period (dw b) then theconstant-rate drying time r , is:

Thus, the factors w hich control the rate of drying duringthe constant-rate period are the drying surface area, thedifference in temperature or humidity between the air

and the drying surface and the mass or heat transfercoefficients. The velocity of the air and the dimensionsof the system also influence drying rate by affecting thetransfer coefficients. For example, the following rela-

tionship often holds:

U Ph, =-,"

where G = the mass velocity of the air, D, =

characteristic dimension of the system; a, n and m areconstants. D, has been represented as the equivalentdiameter of the flow chann el (cross-sectional area X 4 +perimeter) or the length of the drying surface parallel tothe direction of flow of the air. For most tray-dryingcalculations the equivalent diameter is used. Values of nin the range 0.35-0.80 have been reported in the

literature. Where no specific data are available, a valueof 0.80 is often used in calculations. Alternativeexpressions for h, are available to use in situations where




(a) Several modes of transfer of moisture within the

solid have been proposed. These include liquid diffusion

resulting from concentration gradients; vapour diffusion

due to partial pressure gradients; liquid movement

Flpr,1.1Model drying cu~ycs:a) moisture content (dwb)Mh e , (b) rate of change of moisture content vs time,

(c) rate of h g e f moisture content vs naoishue content

caused by capillary forces; diffusion in liquid layers

adsorbed at solid interfaces; vapour flow as a result of

differences in total pressure; flow caused by pressure

gradients brought about by shrinkage; movement by a

vaporizationandensation mechanism. The mechanism

which has received the widest acceptance is diffusion

due to concentration gradients. Such diffusion may be

represented by Fick's second law:

(XI

where W = moisture content (dwb); t = time; 1 =distance; D = liquid Ws iv it y. A well-known solution

to this equation for a slab-shaped solid, drying from one

large face only is:

dW d2W

dr d l 2

_ - D -

w - we = 8 exp [-Dt (Gr]w, - we 112

+ .9 exp [-9Dt (ir]]X I )where W = average moisture content at time t (dwb); We= equilibrium moisture content (dwb); W, =_moisture

content at the start of the falling-rate period (dwb), i.e.critical moisture content; I = depth of slab. For large

values of t equation ( X I ) may be reduced to:

k-%8 exp [-Dt ( (XII)

This expression holds for values of (W-We)/(W, - We)

less than 0.6.Direct application of equation (XII) assumes that D

remains constant throughout the falling-rate period.

There is considerable evidence that this is not the case

and that D varies with moisture content. Many authors

who have reported two or more falling-rate stages have

found that the diffusion equation could be applied to

each stageprovided that a different value of D was used.As far back as 1958, Jason found this behaviour when

drying fish muscle under laboratory conditions. He

presented the results during the falling-rate period in the

form of a curve shown in Figure 1.2. In this figure,

the difference between the weight at time t, W and theequilibrium weight, We, is plotted on a logarithmic scale

as a function of time, t. The resultsare seen to fall on two

straight lines LL andMM, ver most of the curve. The

diffusion equation could be fitted to both of these lines ifa lower value of D was used for line MM s compared

with LL.More recently, in a project in which thisauthor

participated (Gutierrez-Lopez, 1989), a food model

comprised of glucose syrup, agar, glucose and sucrose

with an initialmoisture content of 0.27 (dwb), was driedunder carefully controlled conditions. Some of the dataare shown in Figure I.J(u). Three falling-rate stages

were detected. When the diffusion equation was appliedto each stage three values of D were calculated,

decreasing as drying pmxeded. Similar experiments

w, - we 7F2



General Principles of Dehydration 9

Figure 1.2 Amount of free water remaining in a fish fillet

piece as a function of time (Jason, 1958)

were carried out with pasta, with similar results (Figure

1.3@)). his researcher obtained values of D for the foodmodel and pasta by differential scanning calorimetry

@SC), which agreed well with those calculated from

data obtained from laboratory drying experiments. More

recently still, data collected by Wang (1992) when

drying potato, exhibited a two-stage falling-rate pat-

tern.

If a relationship between D and moisture content is

known it can be incorporated into equation (XI) which

then becomes a non-linear differential equation. One

method of determining D at different moisture contents

was reported by Saravacos (1967).A term known as the

halfequilibrium time was defined as the time required to

reach a moisture content halfway between the moisture

content at the start of the falling-rate period and

equilibrium moisture content. Equation (XI) may be

written in a more general form as:

8 10.5=1-- c

Figure 1.3 Dimensionless moisture content,X, s a functionof time. x E (w W ~ Y W C - W ~or (a) a food model and@) pasta ( G u t i e r r e z - ~ z ~989)

at various humidities or moisture contents in which the

diffusivity is assumed to remain constant.

In diffusion equations, the drying time is proportional

to 1’. In the literature, the dryiig time for food materials

is generally reported as being proportional to 1 9 with

values of n ranging from 1.40 to 1.99. For example,

Jason (1958) reports a value of 1.80 for fish muscle,

Gutierrez-Lopez (1989) 1.94 to 1.98 for a model food

and Wang and Brennan (1992) 1.78 to 1.88 for potato.

The existence of external mass transfer resistances is one

reason suggested in the literature for values of n of less

than 2. This is most likely when air velocity is low.

When high air velocity is used such resistances are less

likely to occuT.~nuch c~cumstancesvaccaremnd

Chirife (1978) suggested that a heat effect may be

responsible for low values of n and they developed a

model for the calculation of material temperature as a

function of drying time. Wang and Brennan (1992) used

this model to calculate a c omted value of n for potato,which was 1.93.

m

exp(-(2n+l)’Dt( ET]71’ “d) (h 1)’

( ~ m )

If the first term only of th is equation is used, it reduces

to:

0.1941’W)

where t(o.5) is the half-equilibium time. Approximate

values of D can be obtained by applying equation (XW)

D = -

‘(0.5)



10 Historical Background and GeneralPrinciples

Diffusivity varies with temperature. The usual rela- where u and b = material constants. Equation (XVI) ay

be integrated to the form:ionship is an Arrhenius typemodel of the form:

w - we-= exp ( - K A (mm)

(xv) w c - wee = Doexp --

An expression of this type has been said to represent

drying when capillary movement of moisture takes place

within the solid. In this case K, is related to the drying

rate in the constant rate period as follows:

( I3where De = average effective diffusivity; Do = tem-

perature independent constant; Q = energy of activation

for diffusion;R = gas constant; T = absolute temperature.An example of such a relationship is shown in Figure1.4 where the values of In D for the three falling-rate

stages in the drymg of pasta are linearly related to 1/T

gax)

Thus by combining equations (W ) and (XVIII) the

drying time in the falling-rate period, from an initial

moisture content W, (dwb) to a final moisture content W(dwb) is given by:

(=)

-(3(Gutierrez-Lopez, 1989). K , =2(b) Numerous mathematical models to represent falling-

rate drying have been proposed, which were largely

derived from experimental data. One of the earliest,

proposed by Lewis (1921), took the form:

wc - we

(m)P J J (W , - We) ln (WC - We)

z )-K,(W - We)

f r = w, 0, ) (W - We)where dW/dt= drying rate at moisture content W during

the falling-rate perid and K c = drykg constanL which

came to be knownas the -s transfer coeficient and

was related to temperature by an expression of the

form:

(m)

There is not much experimental evidence to show that

such an expression does depict capibry movement of

moisture.

Equation ONm) above was used to describe the

drying of agricultural materials but it did not apply to the

whole falling-rate curve. The introduction of an empiri-

cal exponent n to give the expression:, = u exp ($)

Fleon 1.4 Li+d diffusivity,D , 88 a functionofabsolute tempmturc, T,for the three stages of drying of pasta

(GU~~CITCZ-L~~~Z,989)



General Rindplea of Dehydration 11

Spray drying is by far the most common method used for

drying food liquids in heated air. The liquid is converted

into a fine mist or spray (atomized)which is brought into

contact with heated air in a drying chamber. Very rapid

drying takes place and the spray is converted into a

powder. Drying times are short, less than 20", and

evaporative cooling maintains a relatively low product

te throughout most of the drying cycle. If thepowder is removed quickly from the drying chamber

heat damage should be limited.

If it is assumed that drying takes place under constant

rate conditions, the time, t, for a spherical droplet to dry

from an initial moisture content W, (dwb) to a final

moisture content wd (dwb) may be expressed thus:

(U) Liquids- we-- - exp ( - K , f )

wc - weis said to have widened its applicability. This last

equation gave good results when applied to drying

shelled corn and soya beans (Sharaf-Elden et al, 1979).

It was later applied successfully to experimental data

from thin-layer drying of sunflower seeds and in-shell

pecans.Many other empirical expressions to represent falling-

rate drying have been reported. Some of these were

reviewed by Sharaf-Elden et al(1979). In general, such

equations are usually applicable only under conditions

close to those used when obtaining the experimental

data. Many are specfic to a particular food material or

closely related materials. Within these limitations, they

can be useful for predicting drying times.

Alvarez and Legues (1986) developed a model for the

drying of seedless grapes which had both empirical and

analytical elements. They defined an effective diffusion

coefficient, De, as follows:

(rnwhere Do and b are constants and Fois a dimensionless

number accounting for variations of diffusivity with time

thus:

De = Do(1 - Fo)b

The full expression proposed was as follows:

m

W - W e 6 1 n 2 d

w, - we 7 r2-

c sex+=n = l

'I11 + Fo)(' + b, - 1

This model was simplified by taking only the first

exponential term of the equation to give:

w - we

w c - we

(1 + F0)(' + ') - 1-

(=v)

Equations ( XX IV ) and ( XXV ) fitted well to experi-mental data obtained for seedless grapes.

Hot air drying systems for solidsVarious systems for drying solids in heated air are

discussed elsewhere in this text. These include:

Kiln drier

Cabinet drier

Conveyor drier

Bin drier

Fluidized-bed drier (including spouted-bed and toroidal-

bed)Pneumatic drier

Rotary drier

where r = the radius of the droplet and p1 = the density

of the liquid.

In practice not all the moisture is removed underconstant rate conditions. Much more detailed accounts

of drying behaviour of droplets in spray driers have been

published (Kerkhof and Schoeber, 1974; Masters,

1991).

The principles of spray drying are discussed else-

where in this text and so also are &/powder separators,

atomization and spray-drying chambers.

Drying by direct contact with a heated surfaceIf a wet material is placed in contact with a heated

surface the necessary sensible and latent heat of

evaporation is transferred to the material by conductionand drying can take place. The pattern of drying is

similar to that of hot air drying in that drying takes place

mainly in two stages. During the initial constant rate

period the material temperature is close to its boiling

point at the prevailing pressure. During this period the

rates of drying will be higher than those attainable in air

at the same temperatureas the heated surface. When the

rate of movement of moisture to the evaporating surface

falls below the rate of evaporation, the falling rate period

commences and the temperature of the material rises

towards that of the heated surface. Assuming that drying

takes place from one large face only and that shrinkageis negligible, the rate of drying may be expressed in

terms of an overall heat transfer coefficient and tem-

perature gradient as follows:

where dwldt = rate of change of weight (drying rate);

dQ/dt rate of heat transfer by conduction; Le= latent heat

of evaporation at Be; U = overall heat transfer coeffi-

cient; A = drying area; 8, = temperature of the heated

surface (wall temperature); ee = evaporating tem-

perature.As drying proceeds (e, - e,) decreases. If K, is an

overall heat transfer coefficient for the complete drying



12 Historical Background and GeneralPrinciples

cycle (allowing for the decrease in (0, - 0,)) then dw/&

m a y be written as:

dt r,OOrwI)

The overall dryiig rate for a complete cycle may be

expressed as:

dw KcA(O, - 0,)- = -

dw (W, - Wf)M

dt t

_ -

where W, = initial moisture content of the material

(dwb); Wf =finalmoisture content of the material (dwb);

M = the mass of dry solid on heated surface; t = total

drying time.

From the two above equations comes the relation-

ship:

(xxx)w, - Wf)M - K c w , - 0,)-

t L,

from which t can be calculated.If drying is carried out at atmospheric pressure than 0,

will be in excess of 100°C. In order to achieve

reasonable drying times and to dry to low moisture

contents, 0, needs to be appreciably higher than this.

Towards the end of drying, the material temperature may

be quite high and heat damage may occur. To imit such

damage, when drying at atmospheric pressure, the

material may be applied in a thin layer onto the heated

surface resulting in short drying times. The drum drier

operates in this way. Alternatively, drying may be carried

out under reduced pressure so that relatively low values

of 8, prevail and hence low values of 8, may be used.Such low temperatures are used in vacuum-shelf and

vacuum-band driers.Drum driers and vacuum driers are

discussed elsewhere in this text.

I 1 f /

Radio waves / Infrared

Drying by the application of radiant (inh.ared) heat

In Figure 1.5 the types of electromagnetic radiation are

presented. Infrared radiation, which is em i W by hot

objects, occupies the wavelength range 0 . 7 ~o300pn. The rate of emission of infrared energy from a

heated surface, dQ/dt, is given by:

9 = uAT14u (mdt

where A = the area from which the radiation is emitted,

TI = the absolute temperature of the surface;u = Stefan-

the emissivity of the surface. Substances that are good

emitters of radiation are also good absorbers of it. The

rate of absorption of radiation by a surface, dQ'/dt, is

given by:

Boltzmann constant (= 5.7 X lo-* J s-l m-2 K4 ; € =

y-rays and X-rays

mQ'- O L A T ~ ~ Udt

where OL = absorptivityof the surface. The absorptivity

value of a surface is numerically equal to the emissivityvalue. Thus, for a surface exposed to infrared radiation

the net rate of heat transfer by radiation to the surface is

given by:

dtde" = e A(TI4- T24)u

where Tl and T2 = the absolute temperatures of the

emitting surface and the absorbing surface, respec-

tively.

Complex relationships exist between the physical,

thermal and optical properties of foods and their

influence on the absorptionof infrared radiation. Each ofthe major components of food, protein, fat and carbohy-

drate exhibits its own characteristic absorption pattern.

In addition to this, the absorption characteristicsof water

Wavelength

Frequency (Hz)

Figure 15 Electromagnetic radiation spectrum (Lewis, 1987)




heat. The power, P ( W C ~ - ~ ) ,bsorbed by the food is

given by:

(=

wheref= the frequency of the radiation (Hz); Ef the

field strength (Vcm-'); E" = dielectric loss factor of the

food. This factor is an important property of the food

which will affect its heating rate. The loss factor for a

given food will vary with its moisture content, tem-perature and whether it is frozen or not. It also depends

on the frequency of the radiation.

The depth of penetration of radio waves into the food,

D, ay be expressed thus:

(XXxV)

in the liquid, vapour or frozen state affects the overall

absorption by the food. In general, shorter wavelength

radiation penetrates further than the longer waves.

However, shorter wavelength radiation is more readily

reflected. Consequently, it is difficult to predict the

optimum wavelength to promote maximum transfer of

heat to a given material.

It is, therefore, difficult to promote uniform heating of

foods exposed to infr;lred radiation and to control theheating rate. Infrared heating is generally not used for

removing water in bulk from foods. However, it has

been applied to removing small amounts of moisture

from granular materials such asbreadcrumbs, spices and

starches. Infrared driers are further discussed elsewhere

cabinet and band driers and in freeze driers. These driers

arediscussed elsewhere in this text. Radiant heat emitted

from hot surfaces also plays a part in supplying the heat

of evaporation in hot-air driers, even though the main

mechanism of heat transfer is convection.

Approximately 48% of solar energy falls within theinfrared range of frequencies. Solar drying is widely

practised where sufficient sunlight is available. The

applications for direct and indirect solar drying are

discussed elsewhere in this text.

P = 55.61 X 10-'4fEfzr"

in the text. Infrared heating is also used in vacuum- D = X ,2T(€")"n

where A, = wavelength in free space.

To date the use of dielectridmicrowaveheating as the

major source of energy for dehydration has been limited

to removing small amounts of moisture from low-

moisture products such as biscuits and cereals. It mayalso be employed in vacuum-cabinet and band driers and

in freeze driers (Fellows, 1988; Lewis, 1989; B r e ~ a nt

al, 1990). Microwave drying is further discussed else-

where in this text.

Freeze dryingMicrowave and dielectric heating in food This method of drying involves freezing the material and

dehydration subsequently subliming the ice from the frozen state to

The position of microwave and dielectric radiation in the give a dried product. Sublimationoccurs when the water

electromagnetic spectrum can be seen in Figure 1.5. vapour pressure in the immediate surroundings of the

Dielectric radiation is at a lower frequency (1-100 MHz) frozen material is less than that at the ice front within the

than microwave radiation (300MHz-300GHz). The material. In commercial operations, this water vapourphenomena of dielectric heating and microwave heating pressure gradient is achieved by placing the frozen food

are essentially the same. Both are radio waves. The in a vacuum cabinet and reducing the pressure in the

differences are in the frequencies used which determine cabinet to levels of the order of 13.5-270 N m-2

the extent of the energy penetration. The higher (0.1-2.Otorr). The main components of a batch freeze

frequency, shorter wavelength microwaves penetrate drier are shown in Figure 1.6. The function of the

further than those in the dielectric range. By inter- condenser is to remove the water vapour formed by

national agreement, the frequencies used for microwave sublimation from the atmosphere so as to maintain the

heating are 915MHz (896MHz in Europe) and low water vapour pressure in the cabinet. The vacuum

2450MHz.When food is located in the path of radio system removes the non-condensible gases from the

waves, distortions and deformations of the molecular chamber. Heat may be applied from above or below the

structure occur and the applied energy is converted into sample or from both directions. Once sublimation has

commenced, the main factors which affect the rate ofdrying are the rate at which water vapour moves through

the dry layer and the rate at which heat is transferred to

the ice front. Consider the case where a slab-shaped

solid is being freeze dried from its upper surface only

and where heat is supplied from above only, Le. water

vapour and heat move countercurrently through the dry

layer (Figure 1.7(a)).The mass flow rate of water

vapour through the dry layer, dw/dt, may be expressed

(=VI)

as:

dw Ab@i - p d )

dt 1

_ -

where A = drying area normal to the direction of flow of

the vapour;b = the permeability of the dry layer to watergttre 1.6 Main componentsof a batch freeze drier




Figure 1.7 A slab-shaped solid being freeze dried: (a) with heat supplied through the dry layer, (b ) with heat supplied throughthe frozen layer.

vapour; pi = the water vapour pressure at the ice front at

the prevailing temperature(ei,see below); p d = the water

vapour pressure at the top surface of the dry layer; I = the

thickness of the dry layer.

Combining equations (XXXVIII) and (XL) we get the

relationship:

dw Akd(ed - ei) - A b b i - Pd)-- -The rate of heat transfer to the ice front through the dt LJ 1

dry layer, dQldt, may be expressed as:dl

= APS(W0 - Wf) - (=I)(=w dt

_ -Q k&@d - ei)

dt 1-

where kd = thermal conductivity of the dry layer;Od

=temperature at the top surface of the dry layer; Bi = integrating within the limits t =0,1 = 0; = tt,

1=

1~

P M O - Wf)1,2

- LSPS(W0 - WfV:

temperature at the ice front. t, =An energy balance combining equations (XXXVI) b@i - pdl2

and (XXXW)gives:

(XLII)

where tt = total drying time to Wf; It = total thicknessof

the slab.

If heat is applied through the frozen layer only while

water vapour escapes through the dry layer, Figure

1.7(b), then the equation becomes:

-

kd(ed - ei)2XXXVIII)&(ed - ei) Ldb@ip d )= -

1 I

where Ls = heat of sublimation at Oi.

The vapour pressure at the ice front,pi, is given by:

pi = pd +-d (ed - ei) (1bLS

Note that 1 cancels out so that this relationship isdw w(e - e i)P (=m-ndependent of the extent of the drying. e, and pi are

related thermodynamically. If the dried surface tem- dt LA4 - operature and chamber Pressureare fixed* he iCe surface

where 4 = thermal conductivity of the frozen material;

8, = temperature of the surface of the frozen material in

ice kont, pi, now becomes:

temperature is also fixed.

into the slab, that the frozen layer is at its initial moisture

content,W, dwb), and the dry layer at its final moisture

slab, dw/dt, may be expressed as:

If it is assUmedthat the ice front recedesunifodYcontact with the hated plate. The vapour pressure at the

(8, - ei) (=wontent, Wf (dwb). the rate of change of weight of the 41

bLS(4 - oi = p d +

dw dl-ApAWo - Wf) &dt

(=) As theratio U(1,- I)

changes as drying proceedsso

does

pi and hence Bi. If pi is expressed as a function of 1 then

to calculate the total drying time, tt, the followinghere ps = density of the dried solid.




Similar expressions may b e derived to represent the casewhere heat is applied through the dry layer and thefrozen layer simultaneously (Karel, 1974; Brennan et d ,

1990).The principles of freeze drying are discussed further

elsewhere in this text as well as batch and continuousfreeze drying equipment.

equation must be solved by analytical or numericalmethods:

part i general principles

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