To investigate the mechanism of the moisture transfer in the drying process of a bed of non-adsorptive granular and powdered materials, the drying experiments of a bed of such materials containing the dilute NaCl solution were performed. The liquid fraction of moisture transfer was defined and calculated from the experimental data. The drying mechanism during the first falling rate period was deduced from these results

HAYASHI, Shinya

TOEI, Ryozo

English

Kyoto University Research Information Repository

RIGHT:URL:CITATION:AUTHOR(S):ISSUE DATE:TITLE:The Liquid Fraction of MoistureTransfer in the Drying Process of aBed of Granular and PowderedMaterialsTOEI, Ryozo; HAYASHI, ShinyaTOEI, Ryozo ...[et al]. The Liquid Fraction of Moisture Transfer in the Drying Process of aBed of Granular and Powdered Materials. Memoirs of the Faculty of Engineering, KyotoUniversity 1965, 27(2): 218-2301965-05-20http://hdl.handle.net/2433/280626218 The Liquid Fraction of Moisture Transfer in the Drying Process of a Bed of Granular and Powdered Materials By Ryozo ToEI* and Shin ya HA y ASHI* (Received October, 1, 1964) To investigate the mechanism of the moisture transfer in the drying process of a bed of non-adsorptive granular and powdered materials, the drying experi-ments of a bed of such materials containing the dilute NaCl solution were performed. The liquid fraction of moisture transfer was defined and calculated from the experimental data. The drying mechanism during the first falling rate period was deduced from these results. 1. Introduction The drying process of bed of non-adsorptive granular and powdered materials is distinguished to three periods, i.e. constant rate period, first and second falling rate periods like the typical drying rate curve as shown in Fig. 1. It is usually accepted that the moisture is transported through the bed by liquid form during the constant rate period. It was recognized that the moisture is transported by vapor diffusion through the dried-up zone of the bed during the second falling rate period.') But the mechanism during the first falling rate period has not yet been investigated enough. It is necessary for the study of the drying mechanism during the first falling rate period to investigate whether the moisture is transported by liquid or vapor form. The coexistence of both can be supposed readily during this period. Johanson 2) suggested the idea that liquid moisture transfer and vapor transfer coexist in the drying process. Recently Luikov 3) introduced the phase transformation number in his theory of heat and mass transfer for capillary porous bodies. * Department of Chemical Engineering The Liquid Fraction of Moisture Transfer in the Drying Process of a 219 Bed of Granular and Powdered Materials 110 · 10.0 -- 90 ~ ~ 8.0 '-..., ...._ 'b 70 'Z " C ..:. nO 5.0 1.0. ''o'------~-----,1u~· -----,b~. --~ w (1/o) Fig. 1. Typical drying rate curve (Run S-3-95, sand 28~35#, t0 =95°C, H0 =0.0076, V0 =5.63 m/sec, L=3cm). There are several parameters to define the ratio of liquid moisture and vapor transfer to the total moisture transfer. The local fraction of liquid in moisture transfer f/ and the local fraction of vapor in moisture transfer fv' char2cterizing the relative intensity of internal evaporation in an infinitesimal volume are defined as follows ; f/ = j_e!_ ( 1 )' de fv'+f/=l (1)" where dev represents quantity of vapor transfer and de1 represents quantity of liquid moisture transfer in an infinitesimal volume. The sectional fraction of liquid in moisture transfer f, and the sectional fraction of vapor in moisture. transfer fv defined over the length from bottom (L) to the any section in the bed (x 1) are determined as follows; 220 Ryozo ToEI and Shinya HAYASHI Iv+ /1 = 1 ( 2) ( 2 )' ( 2 )" where R;.,' is the evaporation rate over the length x 1~L and R 1/ is the liquid moisture transfer rate over the length x1~L and R/ is the drying rate over the length X;~L. The total fraction of vapor and the total fraction of liquid in moisture transfer related to the entire volume of the bed are found :is follows; ( 3) R' f ~ I lo~ R' ( 3 )' ( 3 )" where Rv' is the total internal evaporation rate R/ is the evaporation rate at surface and R' is the total drying rate. Experimental investigations about "the phase transformation number" such as fv' and // were performed by Polonskaya•i at first. She obtained /v'=0.045 at the drying of sand bed by analysing mathematically the temperature distribution through the bed during the constant rate period. But her analysis is restricted to the constant rate period and not applied to the whole period of drying. "The phase transforma-tion number" such as fv' and // should be measured directly. Veinik and Schubin 5• 6 • 7l have made this study using the radioisotope as tracer. They investigated the influence of various factors on the values of the integral phase transformation numbers qualitatively rather than quan-titatively. The purpose of our paper is to investigate the influence of various factors on the values of the local and sectional phase transformation number such as Iv, /1, /v', ft' at the drying process of a bed of non-adsorptive granular and powdered materials which are considered as the typical capillary porous bodies. The influence of the moisture content is investigrted particularly, which is considered as a predominant factor. In this connection, the study of liquid diffusion ratio at the drying of clay has been published by Wakabayashi 8l, in which he has shown that the moisture is transported in the liquid as wall as vapor form. The Liquid Fraction of Moisture Transfer in the Drying Process of a 221 Bed of Granular and Powdered Materials 2. Experimental Equipment and Procedure The experimental equipment used for the experiment is the same as described previously 1). The cross section of the measuring part was enlarged to 43 cm width and 13 cm height in order to eliminate the difference of the drying rate with position. The experimental procedure is carried out as follows. The material to be tested is moistened with a dilute solution (0.5~ 1%) of NaCl salt to a definite initial moisture content. The prepared material is packed into the containers for measuring the weight change, temperature distributions and moisture content distributions and NaCl concentration distributions. At any desired time, one container is taken out and the container is sliced into 9 rings. The moisture content of the individual zone of the bed is mea-sured. After that the NaCl concentration is measured. The concentration of NaCl is measured by the electrical conductivity of a solution which is prepared by dispersing the material of the individual section with the definite quantity of water. The materials used for these experiments are glass beads (50~90#), sand (15~30#, 30~60#, 60~80# and 80~120#) and a fine powder of calcium carbonate. The drying conditions are changed variously ; especially, the air temperature is changed from 50°C to 100°C. 3. Calculation of the Liquid Fraction of Moisture Transfer The calculation meth')d of the sectional fraction of liquid in moisture transfer is obeyed to Wakabayashi s). At Fig. 2, the transfer rate of total moisture, R/, through the plane x=x; is given by the formula; air Fig. 2. Description of measuring sample. 222 Ryozo To El and Shiny a HAY ASH! 1 d )L R; = -- cdx dB x; ( 4) The migration rate of NaCl, R;s' is given by the formula; ( 5) The liquid moisture transfer can be traced by the migration of NaCl dis-solved in the liquid. So the liquid moisture transfer rate through the plane x=x; can be determined by the following formula; ( 6) The second term of the right hand side of eq. (6) represents the diffusion to the opposite direction due to a salt concentration gradient in the liquid. The magnitude of this term is negligibly small compared with the first term for the most part during the first falling rate period. So R;/ is determined approximately by the following formula ; ( 7) Consequently the sectional fraction of liquid in moisture transfer over the length L~x; is given by the following formula; The sectional fraction of vapor in moisture transfer Iv; is given by Iv;= 1-11; ( 8) The local fraction of liquid in moisture transfer may be determined by the following formula with above approximated situation, The alternative formula of eq. (9) is used for actual calculation ; (10) The Liquid Fraction of Moisture Transfer in the Drying Process of a 223 Bed of Granular and Powdered Materials Eqs. (8), (9) and (10) could not be used if the deposition of salt occurs. The calculation procedure is as follows. Actually the terms of :E cJx ½- ,1x :E c and :E Cs Llx "9 Llx :E Cs were calculated instead of ~:; cdx and t; csdx. Fig. 3 shows the moisture distribution curves obtained at the experiment of Run No. 11 and Fig. 4 shows the NaCl distribution curves obtained at the same experiment. Fig. 5 and Fig. 6 show the plotting the values of :E c and :E Cs zi s 1 respectively against time. From Fig. 5 and Fig. 6 the values of - f 8 ~ c ' and - f 8 ~ Cs are obtained by graphical differentiation. Then the values of ft are calculated by eq. (8) and the values of f/ are calculated by eq. (10) the values of ft. Fig. 7 shows the relation of ft from Run No. 11 versus using 20 " ~ Q() '-, ~ c:, X 15 (_) X • ·~ X <ii' ~ -.:: X • • \(;:. X X-X t:, 3 \ ( cm J Fig. 3. Moisture distribution curves (Run 11, sand, 15~30#, ta= 100°C, Ha =0.011, Va~2.5 m/sec, initial moisture content 15%, L=3cm), JQQ.--~-------------, 9.0 8.0 7.0 ~ 5.0 -., X 0 4.0 3.0 x {cm) Fig. 4. NaCl distribution curves (Run 11). I' '----.::: 1.0 QB 0.6 0.4 0.2 • 00 224 Ryozo ToEI and Shiny a HAYASHI LB 1.7 ~ ~ 1.6 "° '--- 1.5 1.4 ~ 1.3 1--.J 1.1 1.0 0,9 0.8 0.7 0.6 2 0 (hr) Fig. 5. ~c vs. 0 (Run 11). □~ X l> • sJ\o®<>□ & ti}( 41) 41) 0 • ® 0 .,, 0 .. 0 • • .,, • 0., nr. of posit ion in F;g.2 • ~0 • V/fI ., VD 0 VJ I!> V .. A JV □ ]J[ fl II X I ~2 4 6 8 10 12 14 16 18 20 22 C [1/o) Fig. 7. / 1 vs. c (Run 11). J ~ ~ 18.0.----------'><i ~ 11.0 '--- 16.0 "> ~ 15.0 c3 kJ lG.O 9.0 80 7-0 6.0 5.0 3.0 2.0 1.0 X o o~~~~-:--__..__-'--....L___J2.____, 1.0 0.8 0 [hr) Fig. 6. ~ c, vs. 0 (Run 11). □Jl;.l'\e, X t:,. 0 ..fJ .. ~ & "' 0 0 "" X 0.6 .. I!> no. of position in Fig. 2 -• V[J[ 0.4 .. VII 0 'VI I!> ·v ,A IV Q2 0 □ DI • 0 t:,. ll .. X I 0 0• .at:\ I - ,4 ' • 0 2 4 6 8 10 12 14 16 18 20 22 24 C [;½) Fig. 8. // vs. c (Run ll), I' '-.:.., -.::: The Liquid Fraction of Moisture Transfer in the Drying Process of a 225 Bed of Granular and Powdered Materials the moisture content and Fig. 8 shows the relation of // from Run No. 11 versus the moisture content. 4. Experimental Results It is observed from Fig. 7 and Fig. 8 that the value of / 1 or // is main-tained at the value of one in some range of moisture content. This fact means that all of the moisture is transfered in liquid form above the critical moisture content, 'Cf1 at which the values of / 1 or // being to decrease from one. As the experiment of Run No. 11 is performed at high initial moisture content, the experimental data at low moisture content is not reliable by the deposit of salt. So most experiments are performed at low initial moisture content in order to obtain the values of ft and // at the neighbourhood of Cf1 as truly as possible. The results described in Fig. 9 and Fig. 10 are the examples of su-::h experiments. Fig. 10 shows that the values of f/ decrease steeply with decreasing moisture content and decrease immediately from one to zero. The depen-dencies of // with c are nearly the same for any depths of bed and each value of // at any depths decreases from the same critical moisture content Cf1 with the exception of the value at suface. A similar fact is recognized in the other experiments. Fig. 11 and Fig. 12 show an example of the relation f, and // with c in the experiment of the glass beads and Fig. 13 and Fig. 14 show an example of the same relation in the experiment of CaCO3 (fine powder). I' '-'..., .... >ffi 10 □ I y 0 -~ 1.0 □ Xl0CJll'01 "' .,0 I ~ •• ,f X I OB 0 0.8 I 0 90 0.6 no. of posit ion 0.6 ~. in Fig. 2 01 ° no. of position ax " 0 in Fig. 2 • VlII 04 oOt:,. "' VII 0.4 • VlII ®' X □ VI A VII X V □ l7I • YX 0 IV X V 0.2 a " DI Q2 o IV 0 H • DI I I 0 X 0 0 H 00 • □ I I X • 00 ~00 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 C (¼) C (1/o) Fig. 9. f1 VS. C (Run 17, sand, 15~30#, Fig. 10. // vs. c (Run 17). t.=61°C, H.=0.023, V.=3.3m/sec initial moisture content 8%, L=3 cm). I ..:: !' \..'._, = 226 Ryozo ToEI and Shiny a HAY ASH! 1.0 0.8 0.6 0.4 0.2 2 3 .. 0 • ax ~ ll • 4 5 6 □ no. of posit !cm in_!_!!.}_ • VI!! A VJ! □ VI X V 0 JV • Ill 0 ff ~ 7 8 9 JO C('Yo) Fig. 11. /, vs. c (Run 1, glass beads, 50~ 90#, t0 =50°C, H0 =0.012, V0 =5.5m/sec, initial moisture content 7%, L=3 cm). 1.0 •'151~ 0 . .. D ~0 ... 0 X°"' 0.8 X A • X 0.6 □ no. of posit ion • in fig. 2 0.4 4 •VIII. D A VB □ VI • xv 0.2 D 0 JV .. JI[ ll 0 JI "'• • ~ 0 2 4 6 8 JO 12 14 16 18 20 0 C {1/o) Fig. 13. f, vs. c (CaCO3 , f 0 =60°C, H0 = 0.017, V0 =2.9 m/sec, initial moisture con-tent 15% L=3 cm). I 1.0 x~~ I QB 0 ---=-no. of position 0.6 ! D in fig. 2 □ . • VlII 0.4 .... A VB □ VI D ll X V 0 JV 0.2 0 ., III ll e II ■ I 0 A 00 2 3 4 5 6 7 8 9 JO C (1/o) Fig. 12. // VS, C (Run 1). J, ':.::' 1.0 ·~~ 0.8 0.6 no of position 0 If/. fig. 2 l1 "'x 0.4 X • VlII "' VII □ Ill XV Q2 0 JV ll .. DI • 0 II "' • 00 2 4 6 8 10 12 14 16 18 20 C r Yo J Fig. 14. // vs. c (CaCO3 , the same exp. of Fig. 13). The moisture content Cf/ at which the value of f/ reaches to zero is defined as the critical moisture content for the vapor transfer. The vapor transfer only occurs below Cf/. The values of Cf, and Cf/ are not influenced by the change of the external drying conditions; for example, cn and cf/ change scarcely by increasing the The Liquid Fraction of Moisture Transfer in the Drying Process of a 227 Bed of Granular and Powdered Materials Table I. The exprimental values of c11 and c1/• I t. I H. I v. I I L I C // I Ct/ , Material Wo (°C) (kg/kg) (m/sec) (%) (cm) I (%) (%) .. ·-sand 15~30:il' 100 0.011 2.5 15 3 60] 3.5 sand 15~30:il' 61 0.023 3.3 8 3 4.5 2.0 av. sand 30~60:il' 62 0.021 2.9 7 3 6.0 5.4 3.0 sand 80~120:!!' 62.5 0.020 2.9 7.5 3 5.0 2.5 glass bead 50~90:il' 50 0.012 5.5 7 3 4.5 3.0 CaC03 (fine powder) 60 0.017 2.9 15 3 11.0 7.0 0 air temperature from 50°C to 90°C. Then it can be recognized that the influence of the moisture content to / 1 and // is pre-dominant in the range of the experimental conditions. The values of Cf/ and Cf1 are tabulated in Table I. Fig. 15 shows the schematical curve of // vs. local moisture content c. This curve is not dependent on the external drying conditions and is characterized by the two critical values of Cf1 and Cf/. The values of // is main-tained at the value of one above the Fig. 15. C Schematic curve for f/ vs. c. moisture content Cf1 • Then // decreases suddenly and reaches to zero at the moisture content Cf/. This means that only the liquid moisture transfer occurs above Cf1 and only the vapor transfer occurs below Cf/. In the range between Cf1 and Cf/ the both transfer coexists, but this range is sufficiently small. 5. Consideration of Drying Mechanism We try to compare the value of Cf1 with the moisture content character-izing the drying process such as the surface moisture content Cse at the critical moisture content We. The surface moisture content at drying of a bed moistening with NaCl solution is not reliable by the deposition of NaCl. So the values of the surface moisture content Cse at the critical moisture con-tent We are obtained from the other drying experiments of bed not containing NaCl. The values of Cse for sand are tabulated in Table II. The values of Csc are not dependent on the particle diameter and the experimental conditions, 228 Ryozo ToEr and Shinya HAYASHI Table II. The experimental value of c,c Material I t. I Ha I v. I L I c,c I (DC) (kg/kg) (m/sec) (cm) (%) sand 10~16;1 70.5 0.012 3.30 3 5.0 sand 16~J2;i 70.7 0.012 1.80 3 6.1 sand 28~35;1 70.0 0.0076 5.63 3 6.0 sand 35~60;1 70.2 0.011 2.25 3 6.5 sand 60~80;1 70.3 0.0102 4.5 3 5.0 sand 60~80;1 80.8 0.0086 5.5 3 4.0 ---- --- --~-average value 5.4 of Csc and are found 5.4% on average. By comparing the values of Csc with the values of Cf1 in Table I, the agreement of both is fairly good. These results are consistent with the fact that during the constant rate period above the critical moisture content the moisture is transfered by liquid form and con-sequently the surface evaporation takes place, because the local moisture contents of all depths are maintained above Csc ( ~ Cf1). Below the critical moisture content the surface moisture content decreases from Csc and the plane of the moisture content Csc (½cf,) retreats into the bed. In the region between this plane and surface, the value of // is below one. So the vapor transfer appears and soon after becomes predominant in this region. This region increases continuously as the drying proceeds. Fig_ 16 shows the schematic model of drying mechanism of bed during the first falling rate period. It is considered that the rate controlling steps during the first falling rate period are the vapor transfer resistances at sur-face air film and in the region of O~.x' as shown on Fig. 16. The mechanism continues until the surface moisture content reaches C, X Fig. 16. Schematic model of drying mechanism of bed during the first falling rate period The Liquid Praction of Moisture Trans/er in the Drying Process of a 229 Bed of Granular and Powdered Materials to the equilibrium moisture content, namely, the average moisture content reaches the second critical moisture content wp. The drying mechanism during the first falling rate period will be analysed by the authors based on the present conclusion in the succeeding paper. Acknowledgement The authors wish to express their appreciations to Mr. S. Sawada and Mr. T. Fujitani for their assistances in conducting the experiments and also to Hattori Hokokai to their financial assistance in this work. Normenclature C local moisture content [?6 or g/g-dry solid] Cf1 : critical moisture content for the liquid moisture transfer [96 or g/g-dry solid] Cf/: critical moisture content for the vapor transfer [% or g/g-dry solid] Cs NaCl concentration in solid [g/g-dry solid] Cse surface moisture content at critical moisture content We f, fv R' diffusion coefficient of NaCl in bed sectional fraction of liquid in moisture transfer local fraction of liquid in moisture transfer total fraction of liquid in moisture transfer sectional fraction of vapor in moisture transfer local fraction of vapor in moisture transfer total fraction of vapor in moisture transfer depth of bed total drying rate [96 or g/g-dry solid] [cm2/hr] [-] [-] [-] [-] [-] [-] [cm] R/ : moisture transfer rate over the length x;~L of the bed [cm/hr] [cm/hr] R;/: moisture transfer rate due to liquid moisture transfer over the section (x;~L) of the bed [cm/hr] R;/: quantity of moving NaCl through a plane x=x; per unit time [cm/hr] R;/: moisture transfer rate due to vapor transfer over the section (x;~L) of the bed [cm/hr] R'. I • evaporation rate at the surface [cm/hr] R'. V • total internal evaporation rate [cm/hr] We : critical moisture content [% or g/ g-dry solid] Wp: second critical moisture content [% or g/ g-dry solid] X distance from surface [cm] 230 Ryozo ToEI and Shinya HAYASHI Literature Cited 1) R. Toei and S. Hayashi : The Memories of the Faculty of Engng., Kyoto Univ., 25, 457 (1963) 2) C. H. Johanson: Viirme Vatten Sanitat 19, 675 No, 5 (1948) 3) A. V. Luikov and Y. Mikhailov: "Theory of Energy and Mass Transfer", Prentice Hall, U. S. A. (1960) 4) F. M. Polonskaya : Zhurnal Teknicheskoi Fiziki 13, 796 (1951) 5) A. I. Veinik : Unesco/ N. S./ R. L. C., 196 (1957) 6) A. I. Veinik and A. S. Schubin : "Symposium on Heat and Mass Exchange in Capillary Porous Material" Moscow (1957) 7) A. S. Schubin : Int. J. Isotopes and Radiation 12, 110 (1957) 8) K. Wakabayashi : Chem. Eng. (Japan) 28, 12 (1964) 

The Liquid Fraction of Moisture Transfer in the Drying Process of a Bed of Granular and Powdered Materials

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The Liquid Fraction of Moisture Transfer in the Drying Process of a Bed of Granular and Powdered Materials

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