intermittent drying of porous materials containing binary mixtures

167

Intermittent Drying of Porous Materials Containing Binary Mixtures Intermittierende Trocknung porker Gi.iter, die mit bin&-en Gemischen beladen sind

F. HEIMANN, F. THURNER* and E. U. SCHLUNDER

Universitat Karlsruhe, Institut fiir lhermische Verfahrenstechnik, Postfach 6380,750O Karlsruhe I (F.R.G.)

(Received November 25, 1985)

Abstract

The selectivity during the drying of porous materials containing binary mixtures depends on the thermodynamic equilibrium, the gas-side mass transfer and the liquid-side mass transfer. Very often the drying process is nonselective owing to the controlling liquid-side mass transfer. However, in this case at the early stages a selectivity might be expected, because the liquid-side mass transfer resistance is negligible at the beginning. This so-called initial selectivity can be extended to the whole drying process by intermittent drying. For this purpose the time required for the development of the steady state concentration profile at the beginning (transient time tT) and the time required for the degra- ation of the steady state concentration profile during recovery (relaxation time tR) had been estimated theoretically and experimentally in this work.

Kurzfassung

Bei der Trocknung von porosen Giitern, die mit einem binaren Gemisch beladen sind, hangt die Selektivitat von dem thermodynamischen Gleichgewicht, dem gasseitigen Stofftransport und dem fliissigkeitsseitigen Stofftransport ab. Infolge des dominierenden fliissigkeitsseitigen Stofftransportes verlauft der Trocknungsprozess haufig unselektiv. In diesen Fallen ist jedoch eine Selektivitat zu Beginn der Trocknung zu erwarten, da in diesem Zustand der fliissigkeits- seitige Stofftransportwiderstand vernachlassigt werden kann. Durch intermittierende Trocknung konnte diese Anfangs- selektivitat iiber den ganzen Trocknungsprozess ausgedehnt werden. Aus diesem Grund wurde in der vorliegenden Arbeit die zur Ausbildung des stationaren Zusammensetzungsprofils benotigte Zeit (Trocknungszeit tT) und die zum Abbau des stationaren Zusammensetzungsprofils benotigte Zeit (Ruhe tR) theoretisch und experimentell ermittelt.

Synopse

Die Selektivitat bei der i?ocknung von Gutern, die mit bin&en Gemischen beladen sind, hangt sowohl vom thermodynamischen Gleichgewicht als such von der Geschwindigkeit des gas- und ji’tissigkeitsseitigen Staff transpoties ab. Das thermodynamische Gleichgewicht tisst sich charakterisieren durch die relative Fluchtigkeit (GI. (I)), der gasseitige Stofftransport durch das Verhalt- nis der gasseitipen Stoffiibergarqgskoeffizienten (Gi. (2)) und der fltissigkeitsseitige Stofftransport durch das Verhaltnis der Eindringtiefe des station&en Zusammen- setzungsprofils in der FlUssigkeit (GI. (3)) zur Guts- abmessung.

*Present address: Krauss Maffei AG, Krauss-Maffei-Str. 2, 8000 Munich 50, F.R.G.

Ist die Eindringtiefe wesentlich kleiner als die Guts- abmessung, so verlhirftdie Trocknungunselektiv. Indessen ist anzumerken, Ctass zu Beginn der i?ocknung in jedem Fall eine gewisse Selektivitcit auftritt, da sich die Zusam- mensetzungsprofile in der Fki’ssigkeit stets erst noch ausbilden mussen. Diese sogenannte Anfangsselektivitat wird durch das thermodynamische Gleichgewicht und den gasseitipen Stofftrnnsport bestimmt. Ist die Eindring- tiefe sehr vie1 grosser als die Gutsabmessung, so wird die Selektivittit ebenfalls durch das thermodynamische Gleichgewicht und den gasseitigen Stofftransport bestimm t.

Unter realistischen Trocknungsbedingungen ist die Eindringtiefe vielfach sehr vie1 kleiner als die Gutsabmes- sung, d.h. die Trocknung vertift unselektiv. Es erscheint jedoch in diesem Fall miiglich, die oben erwdhnte Anfangsselektivitdt auf den gesamten ~ocknungsvor- gang auszudehnen, wenn man intermittierend trocknet.

168

Fur diesen Zweck ist es notwendig, die erforderliche Zeit fur die Ausbildung des station&en Zusammen- setzungsprofiles zu Beginn der Trocknung (Trocknungs- zeit) und die erforderliche Zeit fur den Abbau dieses station&en Zusammensetzungsprofiles wahrend der Unterbrechung der Trocknung (Ruhezeit) zu kennen. Das Ziel dieser Arbeit ist es deshalh, heide Zeiten zu ermitteln.

Betrachtet man die Verdunstung eines bin&en Gemisches aus einer geraden senkrecht zur Gutsober- f&he verlaufenden Kapillare mit unendlicher Lange (Abb. I), so lassen sich die Zusammensetzungsprofile als Funktion von Ort und Zeit durch L&en der Dtfferen- tialgleichung (Gl. (5)) unter Benicksichtigurtg der Anfangs- (Cl. (8)) und Randbedingungen (Gin. (9) und (I 0)) berechnen. Aus den fiir Isopropanol- Wasser- Gemische berechneten Zusammensetzungsprofilen (Abb. 2) ersieht man, dass die Trocknungszeit fur die Ausbildung des statiomiren Zusammensetzungsprofiles (Gl. (I 7)) in der Grossenordnung von 5 min liegt.

Fur die Berechnung der Ruhezeit wird dieselbe Kapillare mit bereits ausgebildetem Zusammensetzungs- profir betrachtet (Abb. 3). Die Zusammensetzungs- profile als Funktion von Ort und Zeit lassen sich durch Llisen der Differentialgleichung (Gl. (22)) totter Beriick- sichtigung der Anfangs- (Gl. (23)) und Randbedingungen (Gln. (24)und (2.5) J berechnen. Aus den fiir Isopropanol& Wasser-Gemische berechneten Zusammensetzungsprofilen (Abb. 4) erkennt man, dass die Ruhezeit fur den Abbau des station&en Zusammensetzungsprofiles in der Grossenordnung von 60 min liegt.

Im experimentellen Teil der Arbeit wurden porose Einzelkolper, die mit Isopropanol- Wasser-Gemischen beladen waren, in einem Trocknungskanal getrocknet (Abb. 5). Wahrend der Trocknung wurden die Konzen- trationen von Isopropanol und Wasser inder Trocknungs- abluft mittels zweier Infiarotgasanalysatoren gemessen. Die Eigenschaften des Probenmaten’als sind in der Tabelle I und die der Gutsfachte in den Abbildungen 6 und 7 dargestellt.

Aus den gemessenen Konzentrationen von Iso- propanol und Wasser in der Trocknungsabluft w&rend der kontinuierlichen Trocknung (Abb. 8) ersieht man, dass die Anfangsselektivitat etwa 2 bb 4 min anhalt, was in guter iibereinstimmung mit der berechneten Trocknungszeit ist. Bei der intermittierenden Trocknung (Abb. 9) zeigte es sich, dass es gute 60 min dauert, bis sich die Zusammensetzungsprofile in der Fltissigkeit wieder ausgeglichen haben, was in Einklang mit der berechneten Ruhezeit ist.

1. Introduction

The moisture of many materials to be dried consists of a mixture. Examples are foodstuffs, pharmaceuticals, photographic films, magnetic storage media, varnish layers, and granular synthetic materials [l]. In these cases it is important to know the selectivity during the drying process [ 2,3 J .

Thurner and Schliinder [4] showed that the selectivity during the convective drying of porous materials containing binary mixtures depends on

(1) the vapor -liquid equilibrium as given by the relative volatility

(1)

or the vapor-liquid-solid equilibrium as given by the sorption isotherm.

(2) the gas-side mass transfer as given by the ratio of the mass transfer coefficients

(2)

withm=0.58 ,..., 1,and (3) the liquid-side mass transfer as given by the ratio

of the penetration depth of the steady state concentration profile in the liquid phase

(3)

to the sample thickness L. The sample thickness is the distance between the sample surface and the centre-line of the sample or its impermeable surface.

Knowing cyrs, K, and S/L the following cases can be distinguished.

If S Q L, and after a steady state concentration profile in the liquid has been established, the drying is nonselective. The selectivity is controlled by the liquid-side mass transfer. However. a certain selectivity is always obtained at the beginning of the drying process when the concentration profiles in the liquid are developing. This kind of selectivity depends on the thermodynamic equilibrium and the gas-side mass transfer only.

If S B L the liquid-side mass transfer resistance can be neglected. The selectivity during the whole drying process is also dominated by the thermodynamic equilibrium and the gas-side mass transfer.

Under realistic drying conditions the penetration depth S is very often much smaller than the sample thickness L. i.e. the drying process is nonselective. How- ever, in this case it might be possible to extend the ahove- mentioned initial selectivity to the whole drying process by intermittent drying. For this purpose it is necessary to know the time required for the development of the steady state concentration profile at the beginning of the drying process (transition time tT) and the time required for the degradation of the steady state concentration profile during recovery (relaxation time tR).

Therefore, the objective of this work is to estimate both times for the drying of porous materials containing binary mixtures. In the theoretical part both times will he derived by solving the diffusion equation for the liquid-side mass transfer. In the experimental part these times will he ascertained experimentally.

It is expected that this analysis will provide a better insight into the unsteady state processes which occur during the intermittent drying of porous materials con- taming binary mixtures. It is further expected that some guidelines to manipulate the drying conditions in order to promote a selective drying will be obtained.

2. Theoretical part

169

The overall mass balance over the capillary is given by

tiin=tio,, + d.lV/dt

jYQi&AUQ = (ril+ &)A

UQ = @I + %)/P”Qti (4)

This means that the velocity of the capillary flow is proportional to the evaporation flux.

From a llzass balance for component 1 over a differential element of the capillary, it follows that

2.1. Concentration distribution at the beginning of the drying process

For the calculation of the concentration distribution at the beginning of the drying a straight capillary of a porous sample with infinite length and perpendicular to the sample surface filled with a binary liquid mixture is considered (Fig. 1). Component 1 is the more volatile component. The sample surface is exposed to the drying medium. Owing to the temperature gradient heat is transferred to the sample surface resulting in evaporation of the liquid. The vapor is swept off by the drying medium.

At the beginning of the drying process the concentration in the liquid is uniform. As drying proceeds a concentration profile in the liquid develops provided that the initial composition differs from the pseudo azeotrope [4]. For sufficiently long drying times a steady state concentration profile will be achieved.

For the calculation the following assumptions were made: - the evaporation of the liquid takes place at the sample

surface, and the liquid is transferred to the sample surface by capillary flow;

- the temperature inside the sample is kept constant and is equal to the wet-bulb temperature for binary mixtures [ 51 ;

- thermodynamic equilibrium is assumed at the sample surface ;

- the contact time between the sample and the drying medium is short, which means that the temperature and humidity of the drying medium are constant. The concentration distribution in the liquid as a

function of position and time may be obtained from - mass balances, - kinetic equations for mass transfer, and - the equilibrium relationship.

drying I ” I medium I I

L I

4 Ts s F t=o

/’ co t-m

91 "1

~l,S.o> -Ii

Fig. 1. Concentration distribution at the beginning of the drying process.

(5)

For the mass transfer from the sample surface to the bulk of the drying medium the linear kinetic equations can be used, because of low concentrations:

ci = P&g. i(Yi, S -yi, 02) (6) The mass transfer coefficient in this equation was calculated with the correlation for forced convection around immersed bodies [6] _

At the sample surface thermodynamic equilibrium is assumed :

In this equation the activity coefficients were calculated with the NRTL method [7] and the vapor pressures with the Antoine equation [8]. The parameters of these equations were taken from ref. 9.

The concentration distribution as a function of position and time can be calculated from this set of equations. This can be done by evaluating the solution of the differential equation (eqn. (5)) taking into account the initial and boundary conditions:

t=O: %4z, Of= 21.0 (8)

+ @I + fi2)%, s (9)

z+m: X”rf=, t’)= I,, 0 (10)

For simplification the following dimensionless variables were introduced:

4 = -‘, x fz, t+- Xl s - . < (11)

Xl. 0 - Xl, s, -

f=zlL (12)

‘i- = 6Qt/L2 (13)

The differential equation was then solved numerically using an explicit method of differences [IO].

0 OBlc-2 1.6W2 Z.L46* 3.2-1 0m2 L~fL.o.lo-* 0 l.L.16* 2.8~104 .L2.10-2 5.6.10-2 7.O.lO‘z Qf

Fig. 2. Calculated concentration distribution of the moisture of a solid brick cylinder at the beginning of drying: sample diameter d = 39.2 mm. samDle radius L = d/2 = 19.6 mm. samnle lenrth I = 95.7 mm, sample temperature Ts = 20 T, ati temperature TW = 60 r, ait _ _ velocity urn = 0.2 m SC*, air humidity Fi, _ = 0.

Figure 2 shows the calculated concentration distribution for the convective drying of a solid brick cylinder wetted with mixtures of isopropyl alcohol(l) and water(2) with air. The initial mole fractions of isopropyl alcohol are !Zl,o= 0.30 and X1.o= 0.60. In the Figures the dimensionless concentration 5 is plotted against the dimensionless coordinate 5‘. The parameter of the curves is the dimensionless time r.

A comparison between the bulk composition $+ ,, and the interface composition at steady state, Z,, s, _, reveals that for X1, ,, = 0.30 isopropyl alcohol is depleted at the interface because Kg/~12 < I [4]. For x1, o = 0.60 water is depleted because &/cY,~> i. Further, it becomes evident that a steady state concentration profile is approached for sufficiently long drying times. The magnitude of the time required to develop this steady state concentration profile is about 5 min. Its penetration depth is about 0.2 mm. That means that the liquid- side mass transfer resistance is restricted to a thin boundary layer. Consequently, the drying of a porous cylinder can be treated like the evaporation from a straight liquid- filled capillary.

If the penetration depth is much smaller than the sample thickness a steady state concentration prqjile is achieved for sufficiently long drying times. It can be calculated from the differential equation (eqn. (5)) with ax”,/at = 0:

a2gl azl 6p - t up* m - = 0

322 az (14)

Taking into account the boundary conditions

z = 0: - -- Xl - Xl, s. c-2 (I9 _ _

z-+00: Xl = XI, 0 UfJ)

integration of eqn. (14) for up, _, = constant yields

_ _ (17) Xl, 0 - Xl. s, -

ln this equation the interfnce composition Zl, s+ m can be calculated from a mass balance for component 1 over the capillary

n,, m = (ti 1,m flj*.m‘)$,o (18)

Replacing the molar fluxes by eqn. (6) and using eqn. (7) for the thermodynamic equilibrium one obtains

Xl. 0

09) From this equation the interface composition &, s, o

can be calculated by iteration. Knowing this, the velocity of the capillary flow uo, _ can be calculated from eqn. (4) by replacing the molar fluxes by eqn. (6).

The penetration depth of the steady state concentration profile is defined by

and it follows from eqn. (17) that

6P

(20)

(21)

2.2. Concentration distribution during recovery

In the foregoing section it has been shown that, for S Q L, at the beginning of the drying a certain selectivity is achieved which is controlled by the thermodynamic equilibrium and the gas-side mass transfer. However, this selectivity lasts only for a few minutes until a steady state concentration profile has been established in the liquid phase. Thereafter the drying is nonselective due to the dominating liquid-side mass transfer resistance.

For the estimation of the time required for the degradation of the steady state concentration profile during recovery (relaxation time tR) we consider a straight capillary of a porous sample with the length L

t T

t

%

Fig. 3. Concentration distribution during relaxation.

filled with a binary mixture (Fig. 3). The length of the capillary is equal to the sample radius.

At the beginning the concentration distribution in the liquid is given by eqn. (17). As time proceeds a degradation of this initial concentration profile takes place due to diffusion. For sufficiently long times the concentration in the liquid becomes uniform.

The concentration distribution as a function of position and time may be obtained from a mass balance for component 1 over a differential element of the capillary

8z a2jr,laz2 = a;r,lat (22) with the initial condition

t=o: - XlfZ, O)= Xl. s, m

VP, - -z (23)

SQ )I

and the boundary conditions

z = 0: agaz =o (24)

z=L: afcllaz = 0 (25) For simplification dimensionless variables were introduced :

E=

%fz, t+ - 21, s, m

.., .., (26)

Xl, 0 -x1. s, -

c = z/L (27)

r= 6Qt/L2 (253)

The differential equation (22) can be solved analytically. This was done by separation of the variables [l 11. A proper trial solution is

,$ = [A sin@@ + B cos(m{)] exp(-m’T) (29)

The constants in this equation can be obtained from the initial and boundary conditions. From the first boundary condition it follows that

171

A=0

and from the second

(30)

m,=O,rr,2rr,3n ,...

mi are the eigenvalues.

(31)

The values Bi are obtained from the initial condition. A least square iit between the given initial solution (eqn. (23)) and the calculated solution with the Fourier series expansion yields

BI= 1 + i [exp(-@Q)- l] (32)

Bi = ~ ~~m.2 [exp(-GQ) cos(mf) - ‘I

Q *

with the abbreviation

@‘Q = UP. c.QL/~Q (34)

The overall solution of the differential equation is then given by

C; = 2 Bi COS(mj{) eXp(-mi27)

f=1

(35)

Figure 4 shows the calculated concentration distribution for a solid brick cylinder wetted with mixtures of isopropyl alcohol(l) and water(2). The initial mole fractions of isopropyl alcohol before drying are ?r, o= 0.30 and %i, a = 0.60. The initial concentration profile is equal to the steady state concentration profile during convective drying (see Fig. 2). In the Figures the dimensionless concentration [ is plotted against the dimensionless coordinate {. The parameter of the curves is the dimensionless time r. The Figures reveal that the magnitude of the time required for the degradation of the concentration profile is about 60 min.

3. Experimental

3.1. Measuring technique

Single porous bodies wetted with mixtures of isopropyl alcohol and water were dried in a drying channel with dry air (Fig. 5). The mole fractions of isopropyl alcohol and water in the exhaust air,yrff)and y&t), respectively, were continuously recorded by two infrared gas analyzers. A detailed description of the equipment is given in ref. 4. The infrared gas analyzer is described in ref. 12.

3.2. Materials

Solid material A solid brick cylinder with a diameter of 39.2 mm

and a length of 95.7 mm was used. The properties of the brick are listed in Table 1.

0 O.&lo-' 16.10 2.L.10" 3.2.10-2 Lo.lo-2 c="

0 1.&.10-z 28.10~~ L.2.10_2 5.t3.10-'

L 5=17.0.10-z

L Fig. 4. Calculated concentration distribution of the moisture of a solid brick cylinder during relaxation: sample diameter d = 39.2 mm, sample radius L = d/2 = 19.6 mm, sample length I = 95.7 mm, sample temperature Ts = 20 “c.

balance

Q

dry\i”g channel

/ sample wetted with binary

i

-pm mixture

4

Fig. 5. Measuring technique.

TABLE 1. Properties of the solid material

Density 1800 kg me3 Porosity 0.40 Diffusion resistance factor 7 Specific heat capacity 0.84 kJ kg-l K-’ Heat conductivity 0.79 W m-l K-l

2(

al2

16

0 0.2 0.L 0.6 0.8 :, 1

Fig. 6. Relative volatility for isopropyl alcohol(l) and water(2) at 30 “C 191.

The gas-side diffusion coefficients of isopropyl alcohol and water into air at 20 “C are [13]

s s, 13 = 0.964 X 10P5 m2 s-l

6 c:. 23 = 2.540 X IO-’ m2 s-l

Moisture With m = 0.7 the characteristic number for the gas-side mass transfer becomes

A mixture of isopropyl alcohol(l) and water(Z) constituted the moisture. lsopropyl alcohol-water forms a minimum boiling azeotrope at 2, = 0.64. The relative volatility

6 m Kg= i 2fY..Z 1 = 2.0

6 g, 13

(37)

a12 = Yl Ply/Y2 p** (36) The liquid-side diffusion coefficient for isopropyl is shown in Fig. 6 as a function of the mole fraction of alcohol-water as a function of composition and temper- isopropyl alcohol 2,. ature is shown in Fig. 7.

173

0 0.5 %

1.0

Fig. 7. Liquidside diffusion coefficient and water(2) [ 141.

for isopropyl alcohol(l)

4. Results and discussion

4.1. Continuous drying

In Fig. 8 the mole fractions of isopropyl alcohol and water in the exhaust air, yift) and y&t); respectively, when continuously drying a solid brick cylinder wetted with mixtures of isopropyl alcohol and water, are plotted against the drying time t. The initial mole fraction of the isopropyl alcohol was %i, e = 0.30 and Zr* ,, = 0.60, respectively.

At the beginning, isopropyl alcohol is removed preferentially for x”i* a = 0.30, because Ka/cyra < 1. For %r+ e = 0.60 water is removed preferentially at the beginning, because K&x,~ > I. The selectivity at the beginning lasts about 2-4 min. The magnitude of this transition time for the development of the steady state concentration profile in the liquid phase is in good agreement with the calculated one (see 92.1). Thereafter the drying is nonselective (A = constant), because a steady state concentration profile will have been established. This can be attributed to the fact that the penetration depth of the steady state concentration profile (S = 0.2 mm) is much smaller than the sample radius (L = d/2 = 19.6 mm) and therefore the selectivity is controlled by the liquid-side mass transfer.

OV t. min OkF-r-T- t.min

Fig. 8. Mole fractions of isopropyl alcohol(l) and water(a) in the exhaust air continuously drying a solid brick cylinder: sample diameter d = 39.2 mm, sample length I = 95.7 mm, air temperature T, = 60 T, air velocity urn = 0.2 m s-t, air humidity& a = 0.

4.2. Intermittent d@ng

The selectivity at the beginning can be utilized if the drying process is conducted intermittently. This may occur in direct contact drying, where drying takes place only when the particles contact the heated surface and may recover when they stay in the bulk of the granular material.

In Fig. 9 the mole fraction of isopropyl alcohol in the exhaust air 9&t), when intermittently drying a solid brick cylinder wetted with a mixture of isopropyl alcohol and water, is plotted against the drying time t. The initial mole fraction of the isopropyl alcohol was Xi, o = 0.30.

The first run was performed with a fresh wetted sample. After say 10 min, the initial selectivity had com- pletely expired (jji = constant). Then the drying was interrupted and the sample was enclosed in a capsule which was kept at the expected wet-bulb temperature. After certain relaxation times the sample was dried again. The curves reveal that the required relaxation time for complete recovery is more than 60 min. This compares favorably with the calculated relaxation time (see $2.2).

t. min

Fig. 9. Mole fraction of isopropyl alcohol(l) in the exhaust air intermittently drying a solid brick cylinder: sample diameter d = 39.2 mm, sample. length I = 95.7 mm, air temperature T, = 60 “c, air velocity urn = 0.2 m s-t, air humidity yti, o. = 0.

5. Conclusions

The selectivity during convective drying of single porous bodies containing binary mixtures depends on the vapor-liquid equilibrium as given by the relative volatility olz or the vapor-liquid-solid equilibrium as given by the sorption isotherms, the gas-side mass transfer as given by the characteristic number KB, and the liquid- side mass transfer as given by the ratio of the penetration depth S of the steady state concentration profile in the liquid phase to the sample thckness L.

From the theoretical analysis and the experiments carried out in this work the following conclusions may be drawn.

If SQL a certain selectivity is obtained during a short transition period at the beginning of the drying, when a steady state concentration profile develops in

174

the liquid phase. This selectivity depends on the thermodynamic equilibrium and the gas-side mass transfer.

If S Q L and after a steady state concentration profile in the liquid phase has been established the drying becomes nonselective. The selectivity is controlled by the liquid-side mass transfer.

If the drying is interrupted after the initial selectivity expires the concentration in the liquid phase again becomes nearly uniform after a sufficient relaxation time. Therefore the initial selectivity can be extended to the whole drying process by intermittent drying. This can be realized by, for example. direct contact drying.

Acknowledgements

The financial support of the Arbeitsgemeinschaft Industrieller Forschungsvereinigungen e.V. (AIF), Cologne, which made this investigation possible, is grate- fully acknowledged.

Nomenclature

sample surface, interface, m2 sample diameter, m characteristic number for gas-side mass transfer sample radius, m sample length, m mass flux, drying rate, kg me2 s-l amount of component, kmol molar flow, kmol s-l molar flux, kmol me2 s-’ pressure, bar penetration depth, m temperature, “c time, s air velocity, m s-’ liquid velocity, m s-i mole fraction in liquid phase mole fraction in gas phase coordinate, m

relative volatility mass transfer coefficient, m ss’ activity coefficient diffusion coefficient, m2 s-’ dimensionless coordinate dimensionless concentration density, kg m-’ molar density, kmol me3 dimensionless time porosity

Subscripts

0 initial 1 more volatile component (isopropyl alcohol)

2 3 Ccl

g i

R s T

less volatile component (water) drying medium (air) bulk, steady state gaseous component i liquid relaxation interface transition

Superscripts

* equilibrium molar

References

1

2

3

4

8

Y

10

11

12

13

14

F. Churner, Selektivitat bei der Konvektionstrocknung von Giitern bei Beladung mit bin&n Gem&hen, Dissertation, IJniversitgt Karlsruhc, 1985. F. Thurner and E. U. Schhinder, Convective drying of porous materials containing binary mixtures, in J. C. Ashworth ted.), Proc. Third Int. Drying Symp., Rirrnirrghum, Vol. 2, Drying Research, Wolverhampton. U.K., 1982, pp. 3266336. F. Thurner and E. U. Schliindcr, Convective drying of porous materials containing binary mixtures, in R. Toei and A. S. Mujundar (eds.), Dry87g ‘85, Hemisphere, Washington, DC, 1985,~~. 117-125. F. Thurner and C. U. Schkinder, Progress towards under- standing the drying of porous materials wetted with binary mixtures, Chem. Erzg. Process., 20 (1986) Y-26. F. Thumer and t. U. Schliinder, Wet-bulb temperature of binary mixtures, Chem. Eng. Process., 19 (1985) 337-343. E. U. Schliinder (ed.), Heat Exchmlger Design Handbook, Vol. 2, Sect. 2.5.2, Hemisphere, Washington, DC, 1984. H. Renon and J. M. Prausnitz, Local compositions in thermodynamic excess functions for liquid mixtures, AIChE .I., 14 (1968) 135-144. M. Ch. Antoine, Tensions des vapeurs: nouvelle relation entre les tensions et les temp&atures, CR. Acad. Sci, 107 (1888) 681-685,836-837. J. Gmehling and Ii. Onken, Vapor-Liquid Equilibrium Data Collection, Chemistry Data Series, Vol. 1, Part 1, DECHEMA, Frankfurt-on-Main, 1977, p. 325. G. D. Smith, Nunwrischr Liisung van pnrtiellen Differential- gleichungen, Vieweg Verlag, Brunswick, 1970. J. N. Bronstein and K. A. Semendjajew, Taschenbuch der Mathemutik, BSB Teubner Verlagsgesellschaft, Leipzig, 19th edn., 1979. F. ‘I’hurner, S. Maul, C. Krieg and IL Breton, Restimmung der Trorknungsverlaufskurve liisungsmittelfeuchter Gitter durch kontinuierliche Messung der Abluftzusammensetzung, Vt Verfahrenstechnik, 17 (1983) 585-592. C. Krehs, Der Einiluss der Diffusion und der Gasstromver- teilung auf den gasseitigen Stoffiibergang in berieselten Pii& kiirperslulen bei der Verdunstung eines Zweistoffgemisches in ein Triigergas, Dissertation, Universitat Karlsruhe, 1982. K. C. Pratt and W. A. Wakeham. Mutual diffusion coefficient for binary mixtures of water, Proc. R. Sot. London, 342 (1975) 401-419.

intermittent drying of porous materials containing binary mixtures

Documents