Important variables which must be fixed before design of a commer-cial dryer are the following:

1. The form and particle size of product required2. The physical properties of the feed: moisture, viscosity, density,

etc.3. The maximum inlet-gas and product temperaturesTheoretical correlations of spray-dryer performance published by

Gluckert [Am. Inst. Chem. Eng. J., 8(4), 460–466 (1962)] may beemployed for the scale-up of laboratory dryers and, in some instances,for estimating dryer requirements in the absence of any tests.

Several assumptions are necessary.1. The largest droplets, which dry most slowly, are the limiting

portion of the spray. They determine ultimate chamber dimensionsand are employed for the evaluation.

2. The largest droplet in a spray population is 3 times the diame-ter of the average drop size [see Eq. (12-66)].

3. A droplet Nusselt number = 2, corresponding to pure conduc-tion (Reynolds number = 0) to infinity, is employed for evaluating thecoefficient of heat transfer.

4. Drying conditions, because of turbulence and gas mixing, areuniform throughout the chamber; i.e., the entire chamber is at the gasexit temperature—this fact has been well established in many cham-bers except in the immediate zone of gas inlet and spray atomization.

5. The temperature driving force for drying is the differencebetween the drying-gas outlet temperature and, in the case of purewater, the gas wet-bulb temperature. In the case of a solution, the adi-abatic saturation temperature of the pure saturated solution isemployed rather than the wet-bulb temperature.

Methods for calculating average and maximum drop sizes from var-ious atomizers are given by Marshall (op. cit.). For pneumatic nozzles,an expression developed by Nukiyama and Tanasawa is recom-mended:

Xwvs = + 597 1 20.45

1 21.5

(12-63)

where Xwvs = average drop diameter, µm (a drop with the same vol-ume-surface ratio as the total sum of all drops formed)

α = surface tension, dyn/cmµ = liquid viscosity, P

Va = relative velocity between air and liquid, ft/sρl = liquid density, g /cm3

1000QL}

Qa

µ}Ïαwρwlw

1920Ïαw}

VaÏρwlw

QL = liquid volumetric flow rateQa = air volumetric flow rate

For single-fluid pressure nozzles, a rule of thumb is employed:

Xwvs = 500/Ï3

∆wPw (12-64)

where ∆P = pressure drop across nozzle, lb/in2.For centrifugal disks, the relation of Friedman, Gluckert, and Mar-

shall is employed [Chem. Eng. Prog., 48, 181 (1952)]:

= 0.4 1 20.6

1 20.2

1 20.1

(12-65)

where Dvs = average drop diameter, ftr = disk radius, ftΓ = spray mass velocity, lb/(min⋅ft of wetted disk periphery)ρl = liquid density, lb/ft3

N = disk speed, r/minµ = liquid viscosity, lb/(ft⋅min)α = surface tension, lb/min2

Lw = wetted disk periphery, ft

NOTE: All groups are dimensionless. To convert dynes per squarecentimeter to joules per square meter, multiply by 10−3; to convertpoises to newton-seconds per square meter, multiply by 10−1; to con-vert feet per second to meters per second, multiply by 0.3048; to con-vert feet to meters, multiply by 0.3048; to convert pounds perminute-foot to kilograms per second-meter, multiply by 0.025; to con-vert pounds per cubic foot to kilograms per cubic meter, multiply by16.019; to convert pounds per minute squared to kilograms per sec-ond squared, multiply by 1.26 × 10−4; to convert British thermal unitsper hour to kilojoules per second, multiply by 2.63 × 10−4; and to con-vert British thermal units per hour-square foot-degree Fahrenheit perfoot to joules per square meter-second-kelvin per meter, multiply by1.7307.

Inspection of these relationships will show that the variables are dif-ficult to specify in the absence of tests except when handling pure liq-uids—which in spray drying is rare indeed. The most useful methodfor employing these equations is to conduct small-scale drying tests ina chamber under conditions in which wall impingement and stickingare incipient. The maximum particle size can then be back-calculatedby using the relationships given in the following paragraphs, and theeffects of changing atomizing variables evaluated by using the preced-ing equations:

Xwm = 3Xwvs (12-66)

where Xwm = maximum drop diameter, µm.Gluckert gives the following relationships for calculating heat trans-

fer under various conditions of atomization:Two-fluid pneumatic nozzles:

Q = !§§ (12-67)

Single-fluid pressure nozzles:

Q = Ds !§ (12-68)

Centrifugal-disk atomizers:

Q = !§ (12-69)

where Q = rate of heat transfer to spray, Btu/hKf = thermal conductivity of gas film surrounding the

droplet, Btu/(h⋅ft2)(°F⋅ft), evaluated at the averagebetween dryer gas and drop temperature

v = volume of dryer chamber, ft3

∆t = temperature driving force (under terminal conditionsdescribed above), °F

Dm = maximum drop diameter, ftws = weight rate of liquid flow, lb/hρs = density of liquid, lb/ft3

wsρt}rN

4.19Kf (Rc − r/2)2 ∆t}}}

Dm2 ρs

ρt}ρs

10.98Kf v2/3 ∆t}}

Dm2

wa + ws}

wa

ρa}waVa

ws}ρs

6.38Kf v2/3 ∆t}}

Dm2

αρlLw}

Γ2

µ}Γ

Γ}ρlNr2

Dvs}

r

SOLIDS-DRYING EQUIPMENT 12-89

TABLE 12-36 Some Materials That Have Been SuccessfullySpray-Dried in a 6-m-Diameter by 6-m-High Chamber with aCentrifugal-Disk Atomizer*

Airtemperature,

K% water Evaporation

Material In Out in feed rate, kg/s

Blood, animal 440 345 65 5.9Yeast 500 335 86 8.2Zinc sulfate 600 380 55 10.0Lignin 475 365 63 6.9Aluminum hydroxide 590 325 93 19.4Silica gel 590 350 95 16.9Magnesium carbonate 590 320 92 18.2Tanning extract 440 340 46 5.2Coffee extract 420 355 70 3.8Detergent A 505 395 50 5.0Detergent B 510 390 63 6.2Detergent C 505 395 40 2.6Manganese sulfate 590 415 50 5.5Aluminum sulfate 415 350 70 1.7Urea resin A 535 355 60 3.8Urea resin B 505 360 70 1.9Sodium sulfide 500 340 50 2.0Pigment 515 335 73 13.2

*Courtesy of NIRO, Inc.NOTE: The fan on this dryer handles about 5.2 m3/s at outlet conditions. The

outlet-air temperature includes cold air in-leakage, and the true temperaturedrop caused by evaporation must therefore be estimated from a heat balance.