Modeling moisture absorption process of wood-based composites under over-saturated moisture conditions using two-part equations

Transcription

1 Wd Sci Technl (2009) 43: DOI /s x ORIGINAL Mdeling misture absrptin prcess f wd-based cmpsites under ver-saturated misture cnditins using tw-part equatins Sheldn Q. Shi Æ Dngfeng Wu Received: 19 Nvember 2007 / Published nline: 17 June 2008 Ó Springer-Verlag 2008 Abstract The bjective f this study was t investigate the misture absrptin prcess fr wd-based cmpsites subjected t ver-saturated misture cnditins. Tw stages are cmprised in the misture transfer prcess at the versaturated misture cnditins, an initial stage which is the misture transfer prcess mainly under fiber saturatin pint (FSP), and a secnd stage which is the misture transfer prcess beynd the FSP. A mdel was develped based n tw-part equatins t describe the prcess, frm which three cefficients (k 1,k 21, and k 22 ) can be used t quantitatively describe the misture transfer prcess under the cnditins. Tw different wd-based cmpsites, wd fiberbard and wd fiber/plymer cmpsites (plymer cntent: 30%), were used t test the mdel at fur different ambient temperatures (30, 45, 62, and 80 C). It was shwn that the tw-part equatin can accurately describe the misture absrptin prcess under ver-saturated misture cnditins. The misture absrptin rate in the initial stage was abut 30 60% greater than that in the secnd stage fr mst f the cases evaluated in this study. The higher the temperature, the greater misture absrptin parameters were btained. At bth misture absrptin stages (belw FSP and abve FSP), the calculated activatin energy fr the misture This manuscript is apprved fr publicatin as Jurnal Article N. FP 398 f the Frest and Wildlife Research Center, Mississippi State University. S. Q. Shi (&) Frest Prducts Department, Mississippi State University, Bx 9820, Mississippi State, MS 39762, USA sshi@cfr.msstate.edu D. Wu Biinfrmatics and Bistatistics Department, University f Luisville, Luisville, KY 40292, USA

2 144 Wd Sci Technl (2009) 43: absrptin rate f wd fiberbard was very clse t that f wd fiber/plymer cmpsites. Intrductin Misture mvement in wd r wd-based materials is mainly cntrlled by diffusin if the misture cntent f the wd is belw fiber saturatin pint (FSP). Skaar (1958) indicated that the misture diffusin was a cmbinatin f tw mvements: the vapr diffusin thrugh the vid structure and the bund water diffusin thrugh the cell wall. It is shwn that the misture de-srptin prcess in wd (drying) can be successfully described by the diffusin mdel based n Fick s secnd law (Skaar 1958; Avramidis and Siau 1987; Liu 1989; Chen et al. 1995). Hwever, when this diffusin mdel was applied t the misture absrptin prcess under water vapr cnditins, systematic errrs ccurred at the initial misture absrptin prcess (Shi and Gardner 2006a) thanks t the hydrxyl grups n the wd surface accelerating the misture absrptin at the initial stage f the misture absrptin prcess as ppsed t the delay during the misture de-srptin prcess. Sme researchers (Clutier and Frtin 1993; Hartley and Schneider 1993; Cai and Shang 1992; Wu and Suchsland 1996) have cnducted mdeling the misture absrptin prcess in wd-based cmpsites. Shi (2007a) develped a simple mdel describing the misture absrptin (WA) prcess as fllws: 0 1 WA e k 1t 1=2 WAðtÞ ¼@ A 1 þ WA 100 ð1þ e k 1t 1=2 where WA 11 is the equilibrium water absrptin (%), k 1 is the misture absrptin cefficient (s -1/2 ), a cnstant referred t as intrinsic relative misture absrptin rate, and t is the time (s). This equatin has been successfully applied t mdel the misture absrptin prcess under water vapr cnditins, frm which k 1 can be used t quantify the rate f the misture absrptin in wd r wd-based materials. The similar functin has als been used successfully t describe the hygrscpic thickness swelling prcess f wd-based cmpsites (Shi and Gardner 2006a, b). Over-saturated misture cnditin is that when the relative humidity in the envirnment is 100% and the misture cndensatin als ccurs n the material surface. At this cnditin, the envirnment is filled with misture mists, and the equilibrium misture cntents (EMC) f wd is higher than the FSP, but is lwer than that under full saturated cnditins (misture ccupies all the lumens and vids in wd-based material). This cnditin ften ccurs during the summer time in Gulf suth f the United States, where the weather is humid and the ambient temperature is high. The bjective f this research is t develp a mathematical mdel fr misture absrptin prcess in ver-saturated misture cnditins. In additin, thrugh applying the develped mdel, the effect f the temperature n the misture absrptin prcess f wd-based cmpsites was investigated.

3 Wd Sci Technl (2009) 43: Mdel develpment Tw-part equatin mdel Under the ver-saturated cnditins, the misture transfer in wd-based materials can be cnsidered t cnsist f tw stages. The first stage is in the initial perid f the misture transfer prcess when mst f the misture absrptin prcess is dminated by the bund water diffusin, f which the misture cntent is belw FSP. Accrding t Shi (2007b), Eq. (1) can be used t describe the prcess fr the first stage f the misture transfer prcess. The secnd stage f the misture absrptin prcess in ver-saturated cnditins is during the perid when the misture cntent f the materials is abve the FSP. Fr mdeling this prcess, the misture absrptin rate f wd-based cmpsites ( dwðtþ, in rder t shrten the scale, a square rt f time is used) can be assumed t dt 1=2 be prprtinal t the specimen weight at the initial prtin f the misture absrptin event, which is expressed as: dwðtþ dt ¼ k 21WðtÞ ð2þ 1=2 where W is the weight f the specimen, t is the time, and k 21 is the misture absrptin rate cnstant (s -1/2 ). During the secnd stage, the misture in the cell wall maybe almst saturated, and free water mvement in lumens f wd elements and vids in the cmpsites might be dminating the misture absrptin prcess. Based n this cnsideratin, ne cefficient in the mdel is sufficient t describe the misture transfer prcess. Anther cefficient (k 22 ) is intrduced in the mdel fr adjustment. Since this adjustment cefficient can be a functin f time, the initial misture absrptin rate can be expressed as: dwðtþ dt ¼ðk 1=2 21 þ k 22 t 1=2 ÞWðtÞ ð3þ where k 22 is the adjustment cefficient fr the misture absrptin rate (s -1/2 ). The relative misture absrptin rate declines linearly with an increase in the weight f the specimen. Therefre, the rate f change in specimen weight is then given by the differential equatin: dwðtþ dt 1=2 ¼ðk 21 þ k 22 t 1=2 ÞWðtÞð1 WðtÞ W 21 Þ where W 2? is the equilibrium misture cntent during the secnd stage f the misture absrptin prcess. The analytical slutin f Eq. (4) is: WðtÞ ¼ 1 þ W 21 W 0 1 W 21 e k 21t 1=2 k 22 2 t Misture absrptin f the bard can be determined by the fllwing equatin: ð4þ ð5þ

4 146 Wd Sci Technl (2009) 43: WAðtÞ ¼ WðtÞ W ð6þ W 0 Cmbine Eqs. (5) and (6), after simplificatin, the fllwing equatin is btained fr WA (t) (%): 0 1 WA e k 21t 1=2 k 22 2 t WAðtÞ ¼@ 1 þ WA e k 21t 1=2 k 22 2 t A 100 Equatin (7) is used t describe the secnd stage f the misture absrptin prcess. Therefre, the tw-part equatin mdel is a cmbinatin f Eqs. (1) and (7) f which Eq. (1) is fr the first stage f the misture absrptin prcess under versaturated cnditins, and Eq. (7) is fr the secnd stage. The ptimal pint (WA 1 ) between the Stage 1 and Stage 2 is btained frm the data set when the prgram seeks the minimum sum f square fr the data fit with the nn-linear curve fitting methd. The cefficients k 1 frm Eq. (1), and k 21 and k 22 frm Eq. (7) can als be btained. The ttal equilibrium water absrptin (WA? ) can be calculated as: WA 1 ¼ WA 1 þ WA 21 ð8þ ð7þ Experimental Fr the evaluatin f the tw-part equatin mdel, the labratry develped cmpressin mlded wd fiber based cmpsites and wd fiber/plymer cmpsites (30% plymer cntent), were used (Shi 1997). In the preparatin f wd fiber based cmpsites, hardwd fiber with 75% aspen and 25% ther hardwds were used fr the wd fiberbard manufacture. The wd fiber/plymer cmpsites were als made frm hardwd fibers and the reclaimed autmbile plymer mixtures. The plymer mixtures were prcessed frm autmbile shredder residual (ASR), als called autmbile fluff, which cntains a plymer mixture f abut 27% plyurethane, 17% plyprpylene, 12% plyvinyl chlride (PVC), 9% acrylnitrile butadiene styrene (ABS), and 35% ther plymers. The mixed plymers were grund int particles at a size f 35 mesh (0.5 mm), and blended int the hardwd fiber furnish fr making the wd fiber/plymer cmpsites. Plymeric diphenylmethane diiscyanate (pmdi) was used as a binder. The bard thickness was targeted as 3.2 mm. All the bards were prcessed at a press temperature f 130 C, a press time f 4 min, and a resin slids level f 4%. The target bard density was 900 kg/m 3. Specimens with a dimensin f mm 3 were prepared fr the misture absrptin tests. Three replicates were used fr each cmpsite type. The average f the three WA measurements was used fr the mdel evaluatin. The edges f the specimens were sealed by aluminum fil bnded with epxy t ensure misture transprt int the cmpsites in ne directin. T ensure the same misture cntent fr all the specimens, befre each test, all the specimens were ven-dried at 103 ± 2 C until a cnstant weight was reached.

5 Wd Sci Technl (2009) 43: A humidity chamber, f which the wet bulb temperature was set higher than the dry bulb temperature, was used t cntrl the misture cnditins. At this cnditin, misture mist develped and misture cndensatins were shwn in the chamber, which is cnsidered as ver-saturated misture cnditins. The water drplets were als bserved precipitating n the surface f the specimens. In rder t evaluate the effect f temperature n the misture absrptin prcess, fur different temperatures, 30, 45, 62, and 80 C, were used in the experiment. This mdel with the tw-part equatins was applied t fit the experimental data. A prgram written in S-Plus Ò sftware (Prfessinal Editin) was used t cnduct nn-linear curve fitting t the test data t find the parameters, k 1 and WA 1? f Eq. (1), and k 21,k 22, and WA 2? frm Eq. (7). The ptimal cutting pint, WA 1, was fund in the data set where t start applying the Eq. (7). Results and discussins It is seen frm Fig. 1 that the tw-part equatin mdel fits the experimental measurement very well. The predictin errr fr wd fiber plymer cmpsites is usually lwer than that fr wd fiberbard (Table 1). It is shwn in Fig. 2 that the higher the temperature, the greater the predictin errr frm the tw-part equatin mdel. This might be due t a greater measurement errr fr a higher temperature WA(%) a 30 C FB WPC WA(%) square rt f time(s^{1/2}) square rt f time(s^{1/2}) b 45 C FB WPC WA(%) c 62 C d 80 C FB WPC WA(%) FB WPC square rt f time(s^{1/2}) square rt f time(s^{1/2}) Fig. 1 Misture absrptin prcess fr wd fiberbard (FB) and wd fiber/plymer cmpsites (WPC) at different ambient temperatures. The effect f temperature n k 21 fr fiberbard (FB) and wd fiber/ plymer cmpsites (WPC)

6 148 Wd Sci Technl (2009) 43: Table 1 Calculated misture absrptin cefficients and the ther parameters frm the tw-part equatin mdel with the ptimal fit Temperature ( C) Material WA 1 (%) k 1 WA 1? (%) k 21 k 22 WA 2? (%) WA? (%) SS 30 FB WPC FB WPC FB WPC FB WPC FB wd fiberbard, WPC wd fiber-plymer cmpsites, WA 1 ptimal cutting pint in water absrptin btained frm the ptimal fit, WA 1? calculated equilibrium water absrptin frm Eq. (1), k 1 misture absrptin cefficient frm the first stage in Eq. (1), k 21 misture absrptin cefficient frm the secnd stage in Eq. (5), k 22 misture absrptin cefficient adjusted parameter frm the secnd stage in Eq. (5), WA 2? equilibrium water absrptin frm secnd stage misture absrptin prcess in Eq. (5), WA? verall equilibrium water absrptin, SS sum f square 60 Sum f Square fr the Mdel Fit FB: y = 0.82 x (R 2 = 0.96) WPC: y = 0.13 x (R 2 = 0.94) Temperature ( C) Fig. 2 The effect f temperature n sum f square fr fiberbard (FB) and wd fiber/plymer cmpsites (WPC) testing. The specimen weight measurements were taken by mving the specimens in and ut f the envirnment chamber, which wuld interrupt the misture absrptin prcess. The higher the temperature, the greater the degree f the interruptin during the measurement, and the larger the measurement errr. Figure 2 als shws that the effect f temperature n the predictin errr was mre significant fr wd fiberbard (slpe is 0.82) than that fr wd fiber/plymer cmpsites (slpe is 0.13).

7 Wd Sci Technl (2009) 43: Frm the tw-part equatin mdel, it is seen that the first equatin has ne misture absrptin cefficient (k 1 ), which is similar t the bund water diffusin prcess (first stage f the prcess) since mst f the diffusin ccurs belw fiber saturatin pint f wd-based materials. Fr the secnd equatin in the mdel, a secnd cefficient (k 22 ) was used since it is t describe the misture prcess with much mre free water mvement, in additin t having a misture absrptin cefficient (k 21 ). This secnd cefficient is the adjustment parameter which is used t adjust the predictin errrs due t the free water mvement in the lumens and vids. Fr mst cases, the misture absrptin rate at the first stage (k 1 ) is abut 30 50% greater than that at the secnd stage (k 21 ), as shwn in Table 1. This is mainly due t the nature f the misture absrptin prcess. At the initial stage f the misture absrptin prcess, the misture absrptin is faster. As the time elapses, the misture absrptin rates slw, and tend t reach 0 at equilibrium. The adjustment cefficients fr the secnd stage (k 22 ) are usually small, arund nly 1 5% f k 21. Since the first equatin is mainly describing the misture transfer belw FSP, technically, the ptimal cutting pint in water absrptin values, WA 1, btained frm the nn linear curve fitting prgram shuld be clse t the FSP f the cmpsites. As shwn in Table 1, the WA 1 values were in the range f 33 46% fr wd fiberbard and 27 37% fr wd fiber/plymer cmpsites. They were abut 9 17% higher than the FSP which is arund 24 29% fr wd fiberbard and 19 24% fr wd fiber/plymer cmpsites with 30% plymer cntent (Shi 2007b). While bund water diffusin dminates the misture absrptin prcess, sme degree f free water mvement als ccurs. This may be part f the reasn that the calculated starting pints fr the secnd misture transfer stage are higher than the FSP. As shwn in Table 1, the verall equilibrium water absrptin (WA? ) was btained as 85 89% fr wd fiberbard, and 59 66% fr wd fiber/plymer cmpsites. This was abut 60% higher than the FSP fr wd fiberbard and 40% fr wd fiber/plymer cmpsites (existing in the lumens r vids f the cmpsites as free water). It is als seen frm the equilibrium water absrptin data in Table 1, that wd fiber/plymer cmpsites prvided abut 30% less misture uptake than the wd fiberbard. This cincides with the plymer cntent used fr the wd fiber/plymer cmpsites (30%). Therefre, wd fiber is the main cntributr t the water absrptin in wd fiber/plymer cmpsites. It was als seen frm Table 1 that bth misture absrptin cefficients f tw stages changed as a functin f temperature. The higher the temperature, the greater the misture absrptin rate in the wd-based cmpsite. This prcess ccurs because water mlecules mve faster at higher temperature. As shwn in Table 1, frm 30 t 80 C, the misture absrptin rate increase fr the initial stage was 191% fr the wd fiberbard and 144% fr the wd fiber/plymer cmpsite. Fr the secnd stage, the rate was 198% fr the wd fiberbard and 169% fr the wd fiber/plymer cmpsites. This shws that temperature has a greater effect n the wd fiberbard cmpared with the wd fiber/plymer cmpsite. The Arrhenius plts in Figs. 3 and 4 shw the relatinship f ln k 1 versus 1/T and ln k 21 versus 1/T, respectively, fr bth wd fiberbard and wd

8 150 Wd Sci Technl (2009) 43: FB: E = kj/ml WPC: E = kj/ml -5 ln k /T (K -1 ) Fig. 3 The effect f temperature n k 1 fr fiberbard (FB) and wd fiber/plymer cmpsites (WPC) FB: E = kj/ml WPC: E = kj/ml ln k Excluded frm analysis /T (K -1 ) Fig. 4 The effect f temperature n k 21 fr fiberbard (FB) and wd fiber/plymer cmpsites (WPC) fiber/plymer cmpsites. The activatin energies (E a ) were calculated frm the Arrhenius equatin: k 1 r k 21 ¼ Ae E a=rt ð9þ where A is a cnstant, R is gas cnstant (8.314 J/ml K), and T is the temperature (degrees Kelvin, K).

9 Wd Sci Technl (2009) 43: E E E-05 FB: y = 2.61E-06 x k 22 -value 6.0E E E-05 WPC: y = 2E-06x Excluded frm analysis 0.0E Temperature ( C) Fig. 5 The effect f temperature n k 22 fr fiberbard (FB) and wd fiber/plymer cmpsites (WPC) It is seen frm Figs. 3 and 4 that the activatin energies calculated frm the plts f wd fiberbard and wd fiber/plymer cmpsites are similar (14.96 vs kj/ml fr k 1 and vs kj/ml fr k 21 ). This indicates that the degree f temperature effect n misture absrptin rate is similar between the wd fiberbard and wd fiber/plymer cmpsites used in this study. Figure 5 shws the effect f temperature n the adjustment cefficient (k 22 ) fr the secnd stage f the misture absrptin prcess. This adjustment cefficient was higher at higher temperature frm experimental measurements in this study except fr that at 80 C. This difference may be due t the fact that higher temperature may give mre predictin errr n the misture absrptin rate, which needs a greater adjustment cefficient. Cnclusin The tw-part misture absrptin mdel develped in this study can accurately describe the misture absrptin prcess under ver-saturated misture cnditins. The mdel can be used t quantitatively cmpare the misture absrptin rates f different wd-based materials. Fr the tw different wd-based cmpsites used in the study, wd fiberbard and wd fiber/plymer cmpsites (plymer cntent: 30%), the misture absrptin rate in the initial stage is abut 30 60% greater than that in the secnd stage fr mst f the specimens used in this study. The higher the temperature, the greater misture absrptin cefficients were btained. The calculated activatin energies are very clse between the wd fiberbard and wd fiber/plymer cmpsites at bth absrptin stages (belw FSP and abve FSP).

10 152 Wd Sci Technl (2009) 43: References Avramidis ST, Siau JF (1987) An investigatin f the external and internal resistance t misture diffusin in wd. Wd Sci Technl 21: Cai L, Shang D (1992) Mdeling pf the misture transfer prcess in particlebard. Hlz Rh Werkst 50: Chen Y, Chng ET, Wetzel DM (1995) Evaluatin f diffusin cefficient and surface emissin cefficient by an ptimizatin technique. Wd Fiber Sci 27(2): Clutier A, Frtin Y (1993) A mdel f misture mvement in wd based n water ptential and determinatin f the effective water cnductivity. Wd Sci Technl 27: Hartley LD, Schneider MH (1993) Water vapur diffusin and adsrptin characteristics f sugar maple (Acer saccharum, Marsh.) wd plymer cmpsites. Wd Sci Technl 27: Liu JY (1989) A new methd fr separating diffusin cefficient and surface emissin cefficient. Wd Fiber Sci 21(2): Shi SQ (1997) Cmpsites prcessed frm wd fibers and autmbile plymer fluff. PhD dissertatin, Michigan Technlgical University Shi SQ (2007a) Diffusin mdel based n Fick s secnd law fr the misture absrptin prcess in wd fiber-based cmpsites: is it suitable r nt? Wd Sci Technl 41(8): Shi SQ (2007b) A simple mdel fr misture absrptin prcess in wd-based cmpsite and wdplymer cmpsites under water vapr cnditins. Frest Prducts Sciety 61st Internatinal Cnventin, Knxville, Tennessee, USA, June Shi SQ, Gardner DJ (2006a) Hygrscpic thickness swelling rate f cmpressin mlded wd fiberbard and wd fiber/plymer cmpsites. Cmps A Appl Sci Manufact 37(9): Shi SQ, Gardner DJ (2006b) Effect f density and plymer cntent n the hygrscpic thickness swelling rate f cmpressin mlded wd fiber/plymer cmpsites. Wd Fiber Sci 38(3): Skaar C (1958) Misture mvement in beech belw the fiber saturatin pint. Frest Prd J 8: Wu Q, Suchsland O (1996) Predictin f misture cntent and misture gradient f an verlaid particlebard. Wd Fiber Sci 28(2):