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Moisture transformation and transport during the drying process for Radix Paeoniae Alba slices
Accepted Manuscript Moisture transformation and transport during the drying process for Radix Paeoniae Alba slices Ran Li, Chuanping Liu, Chenwei Zhang, Jianbiao Shen, Li Wang, Chao Jia PII: DOI: Reference:
S1359-4311(16)31482-X http://dx.doi.org/10.1016/j.applthermaleng.2016.08.123 ATE 8922
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
27 May 2016 16 August 2016 21 August 2016
Please cite this article as: R. Li, C. Liu, C. Zhang, J. Shen, L. Wang, C. Jia, Moisture transformation and transport during the drying process for Radix Paeoniae Alba slices, Applied Thermal Engineering (2016), doi: http:// dx.doi.org/10.1016/j.applthermaleng.2016.08.123
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Moisture
transformation
and
transport
during the drying process for Radix Paeoniae Alba slices Ran Lia, Chuanping Liua,b,*, Chenwei Zhanga, Jianbiao Shena, Li Wanga,b, Chao Jiaa a
School of Mechanical Engineering, University of Science and Technology Beijing, Beijing, 100083, China
b
Beijing Engineering Research Centre of Energy Saving and Environmental Protection, Beijing, 100083, China
*
Email: [email protected]
Abstract: The moisture-binding type and change in moisture content of Radix Paeoniae Alba (RPA) slices were determined during their drying process. Water in RPA slices exists in two types: bound water (BW) and free water (FW). During the drying process, FW diffuses from inside the sample to outside it; simultaneously, it is mutually transformed with BW. The drying rate (R) exhibits a nonlinear relationship with the moisture content (M) of RPA slices, and the slope of R (dR/dM) changes non-monotonically with M. When the diffusion law of FW as well as the mutual transformation between FW and BW are considered, the drying process of the slices can be divided into three stages: FW drying, mix-drying, and BW-drying periods. Mutual transformation between FW and BW is simplified as a reversible conversion process, and a drying model is established for RPA slices based on Fick’s second law. Keywords: drying characteristics; drying model; free water and bound water; NMR
1 Introduction Radix Paeoniae Alba (RPA), which is a typical rootstock medical herb, is an important crop valued as a medicinal plant in China. It is used to gain health benefits, such as blood nourishment, pain relief, and suppression of hyperactive liver. RPA is typically cut into slices and then dried with hot air. Its medicinal component is mainly influenced by drying temperature, and thus, an efficient drying operation can enhance its quality and appearance. Many experiments have been performed to study the effects of drying conditions on various [1]
[2]
[3]
[4]
biological products, such as kiwi slices , grape seed , organic apple slices , eggplant slices , [5]
and peach slices , among others. Accordingly, numerous mathematical models
[6,7,8,9]
, including
theoretical, semi-empirical, and purely empirical models, have been developed to describe the drying process quantitatively. Drying gas temperature and slice thickness have been identified as the main factors that affect drying rate. Increasing temperature or decreasing thickness will shorten the drying period, and the curve of the drying rate versus the decrease in moisture content
1
[4]
will exhibit a gradual decline. The results of the experiments of Ertekin
and Zhu
[5]
showed that
drying could also be accelerated by increasing gas velocity in a convective dryer. For some products such as RPA, the internal resistance to moisture movement of samples is considerably higher than the resistance on the surface; therefore, the influence of the relative humidity and [ ]
velocity of drying gas is insignificant 10 . Moisture within biological products can be generally divided into two types: free water (FW) and bound water (BW). FW exists in tissues or cells and can flow freely, whereas BW is bound to biological macromolecules via one or more hydrogen bonds. Martin et al.[11] proposed that the amount of water bound to macromolecules in food items was an important parameter because it could determine optimal drying (to allow rehydration in a reversed manner). They also demonstrated the occurrence of a “bound” water–“weakly bound” water exchange phenomenon at an intermediate rate in wheat starch suspensions. Sharaf-Eldeen et al.
[ 12 ]
observed two
declining-rate periods in the drying curves of corn ears. These periods could be attributed to the change in moisture state during drying, i.e., from capillary moisture (strong liquidity, similar to [13]
FW) to cellular water (weak liquidity, similar to BW). Lu et al.
reported that the drying process
of unsaturated porous media with BW included the convection and capillary transport of FW, the diffusion of BW, as well as the convection and diffusion of gas. A strong bonding force enables BW to negatively and directly influence water movement during drying. Recently, the nuclear magnetic resonance (NMR) technique has been widely used in the literature to measure the contents of BW and FW in samples
[14,15,16,17]
. This technique can
nondestructively and non-invasively distinguish water in different types of bond with macromolecules in accordance with the chemical environment of protons. In the current study, the drying characteristics of RPA slices are experimentally determined, and the moisture transformation between FW and BW is investigated during the drying process by applying the NMR technique.
2 Experiment methods and results The RPA root used in the following experiments were grown to maturity in experimental plots located in Bozhou, Anhui Province. RPA root is a white or pale red/brown cylinder with a smooth and clearly layered cutting surface. Its radial texture is that of xylem wood. To get closer texture, smoother slice type and shorter drying time, the clean roots are usually boiled in boiling water, which also makes it easier to be peeled. After many tests, 10-15min is proved to be the optimum boiling time for RPA roots used in our research, as too long boiling time may result in hollow interior and weight reduction of the samples, too short cooking time may lead to the black center of roots after drying. A stout root without a white heart and fissure is preferred. The RPA root was harvested in March and carefully washed to remove the soil on its surface. Both ends of the root were then cut. The clean root was boiled for 10–15 min, and then immediately cooled in cold 2
water. After the outer covering was peeled, the root was placed on a table to be used for the experiment. We chose an RPA root with a diameter (d) of 25±3.0 mm, and then sliced the root into pieces with varying thickness ( = 4±0.5, 8±0.5, and 12±0.5 mm). The samples were horizontally arranged on the bottom of a tray and dried using a rapid moisture meter (Model: MA150, Sartorius, Germany) according to the national standard GB/T 5009.3 2010 18
. The tray
was heated electrically at different temperatures (T = 50, 60, 70, and 80 °C), and the samples were observed. During the drying period, the samples were measured continuously using the rapid moisture meter until their mass stopped changing. The dimensionless moisture ratio (MR), which ranges from 0 to 1, is defined as follows: MR
M , M0
(1)
where M is the moisture content of the samples during the drying procedure, and M0 is the initial moisture before drying. The drying rate (R) is defined as the moisture change in unit time that characterizes the speed of the drying process, as follows: R
M t t M t . t
(2)
At different times during the drying process, the samples were removed from the rapid moisture meter and their moisture-binding types (including the contents of FW and BW) were tested using an NMR spectrometer (MiniMR-60, Niumag, China). Five tests were performed for each condition, and the average values of the results were used as the experimental data. 2.1 Effects of drying air temperature and sample thickness Fig.2(a) shows the change in dimensionless moisture content (MR) of the RPA slices during the drying process at different temperatures, whereas Fig.2(b) shows that the RPA slices have varying thickness. As drying proceeded, MR decreased and its variation tendency (which corresponded to the drying rate) also gradually decreased. Finally, drying reached a steady state, and MR remained at the equilibrium moisture content (Me). Drying rate can be accelerated and the period during which the equilibrium moisture content is reached will be shortened by increasing drying temperature or decreasing slice thickness. Notably, the equilibrium moisture content of the slices decreases with increasing temperature [Inset, Fig.2(a)], but is hardly influenced by the thickness of the slices [Fig.2(b)]. The final equilibrium moisture contents are the same for varying slice thickness. Fig.3 shows the relation between the drying rate (R) and moisture content (M) of a slice. While the slices are drying, the moisture content decreases and the corresponding drying rate also
3
decreases. However, the changes in drying rate and moisture content do not exhibit a linear relationship. As shown in Fig.3(a), the relation between drying rate and moisture content (R–M) for 4 mm-thick slices exhibits a super-line function when a slice has high moisture content and a sublinear function when a slice has low moisture content. That is, dR/dM changes nonmonotonically with M. When moisture content is approximately 0.28, a turning point is observed on the R–M curve, at which dR/dM achieves a minimum value. The moisture content at this point is defined as the critical moisture content (Mc). The drying rate and the correspondence relation between drying rate and moisture content both change with the variation in drying temperature, as shown in Fig.3(a). With increasing drying temperature, the R–M curve becomes increasingly nonlinear, the decrease in critical moisture content Mc becomes increasingly evident. When the temperature is below 60 °C, the turning point on the R–M curve is no longer evident. In addition to gas temperature, the drying rate is also influenced by slice thickness, as shown in Fig.3(b). As thickness increases, the drying rate of a slice decreases. The turning point on the R–M curve is no longer evident when a slice is thicker than 12 mm; however, the value of the critical moisture content (Mc) remains nearly unchanged. The main factor that affects the drying kinetics is the diffusion behavior of internal moisture. A rapid decline on drying rate curve after the turning point indicates the increasing in the internal moisture diffusion resistance. In addition to the organizational structure of the sample, the moisture diffusion behavior is also related to moisture content and different water-binding types. Therefore, we test the contents of FW and BW individually during drying. 2.2 Moisture transformation during drying In the fresh RPA samples, the initial moisture contents of FW and BW are 86% and 14% of the total moisture content, respectively; that is, FW accounts for a larger proportion than BW. FW can easily emerge, whereas removing BW directly during drying is nearly impossible. Fig.4(a) shows the contents of FW and BW in 4 mm-thick RPA slices and the drying rate varying with the total moisture content during drying at 80 °C. As the total moisture content decreases, the FW content rapidly declines at the beginning, and then slows down until its value has dropped to zero. By contrast, the BW content increases during initial drying, this indicates that a certain percentage of FW is transforming into BW during this stage. The BW content begins to
4
decline gradually after reaching the maximum value, which indicates that BW is starting to transform into FW. The experimental results at 70 °C are similar to those at 80 °C. However, when the temperature decreases to 60 °C, the BW content remains nearly unchanged during the entire drying process, and no evident rising or falling tendency are observed, as shown in Fig.4(b). The results at 50 °C are similar to those at 60 °C. Therefore, we conclude that, in addition to FW diffusion, mutual transformation
[11]
between FW and BW also occurs during the drying process
for RPA slices. FW diffusion and mutual transformation simultaneously affect the drying rate of the samples, causing the nonmonotonic change in dR/dM versus M. The high drying temperature is conducive to achieving mutual transformation between BW and FW. We have established a drying model for RPA slices based on the preceding analysis. The model demonstrates both the transformation and transport mechanisms of internal moisture.
3 Model and discussion The drying of RPA is a complex process that involves heat and mass transfer[19]. In this work, a drying model is established according to the following assumptions. ① The thermophysical parameters of the samples are the functions of local temperature and humidity. ② The evaporation of moisture and the flow of water vapor in the sample can be disregarded. ③ The lateral heat transfer within the sample can be disregarded. ④ The thickness of a slice is significantly smaller than its width, and the samples are regarded as continuous with a regular finite flat shape. ⑤ The preheating process of the samples is fast, and their temperature remains constant during drying. ⑥ Only FW can emerge from the samples during drying, BW merely participates in the mutual transformation with FW. The dimensionless moisture contents of FW and BW are defined as MRF = MF/M0 and MRB = MB/M0, respectively, where MF and MB denotes the moisture contents of FW and BW, respectively. FW diffusion follows Fick’s second law, and its diffusion rate can be expressed as RD D
2 MRF x 2
,
(3)
where D is the diffusion coefficient that is dependent on drying temperature[20]. This coefficient follows Arrhenius equation[21]: D D0e
Ed RT
,
(4)
where D0 denotes the Arrhenius constant, and Ed represents the activation energy for moisture 5
diffusion. The mutual transformation between FW and BW is considered reversible conversion. In this study, the transformation of BW into FW is defined as forward conversion, the rate of which is described as RBF. Meanwhile, the transformation of FW into BW is defined as reverse conversion, the rate of which is described as RFB. Up to now, there is no literature related to the dynamics research on mutual transformation between free water and bound water in the internal of plant. Here, mutual transformation was analogous to a reversible chemical. Herein, RBF and RFB were defined by referencing reversible reaction kinetic equation, which are related to the moisture content and drying temperature of the RPA slice, as shown in the following expressions: RBF k BF MRBa ,
(5a)
RFB k FB MRFa ,
(5b)
where a is the exponential coefficient; and kBF and kFB are the reaction rate constants of forward and reverse conversions, respectively, which follow Arrhenius equation:
E BF RT
E FB RT
k BF CBF e k FB CFB e
,
(6a)
,
(6b)
where CBF and CFB are the Arrhenius factors; and EBF and EFB are the activation energy for the forward and reverse conversions, respectively. Therefore, the total consumption rate of FW can be expressed as RF
MRF 2 MRF D k FB MRFa k BF MRBa . 2 t x
(7)
RPA slices were arranged horizontally on the tray. The tray was placed in air with temperature T and moisture content ME. The contact surface of the tray was considered adiabatic [Fig.1]. The initial moisture content is uniformly distributed in the RPA slices; hence, the adiabatic and convective boundary conditions are expressed as MRF ( x,0) MRF 0 ,
(8a)
MRF (0, t ) 0, x
(8b)
K ( MRF ( , t ) M E ) D
MRF ( , t ) , x
(8c)
where x is the position along the height of the slice; t is the drying time; MRF0 is the initial moisture content of FW; and K is the mass transfer coefficient, which has been modeled using an Arrhenius-type relation to obtain its functional relationship with the sample temperature as
6
follows: K K 0e
Ek RT
(9)
,
where K0 is the Arrhenius constant and Ek is the activation energy for convective mass transfer. Finite volume method (FVM) was applied to get the numerical solution of Eq.(7). The profile that MRF changes with x was considered to be stepwise; the first derivative was considered to changes over time t in an explicit step way and the final discrete equation is given as:
MRF nt t 1 2Dt MRF nt Dt MRF nt 1 MRF nt 1 - kFB MRF nt
a
x
x
a k BF MRB nt t
(10) where subscript n is the nth calculation cell, n-1 and n+1 are last and next calculation cell respectively; Δt and Δx are time and space step, respectively. The drying rate of the FW and BW content versus drying time can be obtained from Eq.(10) solved by iterations through an explicit method using a simulation program. The parameters and properties used in the model are shown in Table1. Fig.5 shows the dimensional moisture content and drying rate obtained for a 4 mm-thick slice at 80 °C. As shown in Fig.5(a), the BW content increases at the beginning and then decreases after it reaches the maximum value, which signifies the occurrence of mutual transformation between FW and BW in the slices. Moreover, the change in dR/dM versus M is nonmonotonic. The modeling results coincide with the experimental results shown in Fig.4(a). Fig.5(b) shows the diffusion rate of FW (RD) and the transformation rate from BW to FW (RT = RBF–RFB, hereafter referred to as transformation rate) against the moisture content of a material during drying. The points of RT that is equal to 0 (BW content has reached the maximum value) and RT that reaches the maximum value (the evident turning point occurs on the drying rate curve) are selected to divide the drying process into three stages: FW-drying, mix-drying, and BW-drying periods [Figs. 4(a) and 5]. During the FW-drying period, the drying rate is determined from the rate of FW diffusion and transmission. During the mix-drying period, the drying rate is affected by both diffusion and mutual transformation. By contrast, the drying rate is only influenced by the conversion rate of BW to FW during the BW-drying period. At the beginning of drying, the temperature of the samples was raised rapidly and the balance between the FW and BW contents of the samples before drying was upset. RBF and RFB increased 7
simultaneously, which resulted in RFB>RBF because the content of FW was higher than that of BW. The apparent result of the mutual transformation between FW and BW was the conversion of FW into BW, which increased BW content. The diffusion rate of FW (RD) was relatively high because of its high content, and the water that diffused across the interface was immediately removed with hot air. The simultaneous occurrence of diffusion and transformation led to a rapid reduction in the FW content, and which resulted in the rapid decline of RD. During this stage, the drying rate of the samples was determined via the diffusion rate of FW. The downward trend of the drying rate is similar to the decline of the FW content, i.e., the FW-drying period. As the drying process proceeded, the FW content was reduced rapidly, whereas the BW content was increased gradually, which decreased RBF and increased RFB. The two rates approached each other until they were equal. During this moment, RT was reduced to 0 and the BW content reached the maximum value; the drying process entered the mix-drying period. During this period, the apparent result of mutual transformation between the two types of moisture was the conversion of BW into FW given that RT>0. The BW content began to decrease, and both RFB and RBF were reduced. However, RT exhibited an uptrend because of the faster reduction of the FW content than the BW content, i.e., RFB was reduced faster than RBF. Except diffusing some content out, FW gained the content conversed from BW at mean time, so that the decreasing speed of FW content was lower than before, and thus, the decline of RD was slower compared with the previous speed. During this stage, both FW and BW contents were reduced. The drying rate was simultaneously affected by the diffusion rate of FW (RD) and the transformation rate (RT), i.e., the mix-drying period. As drying continued, the FW content was further reduced at a low speed, which caused the reverse conversion rate RFB to decrease slowly until its decrement was relatively less compared with that of the forward conversion rate RBF. RT reached the maximum value, and the evident turning point appeared on the drying rate curve, i.e., the drying process entered the BW-drying period. During this stage, RD decreased gradually and drew close to RT. FW that dried out almost completely obtained from the transformation of BW. Moreover, the FW content that could be detected within the samples was at an extremely low level. The effect of the reverse conversion rate RFB on the total drying rate could be negligible; hence, the total drying rate of the samples was only affected by the transformation rate (RT). The downward trend of the total drying rate is 8
similar to the decline of the BW content, i.e., the BW-drying period. As shown in Figs.3(a) and 6(a), the drying rate curve of the 4 mm-thick RPA slice tends to flatten gradually with decreasing drying temperature. When drying temperature was reduced to below 60 °C, the turning point disappeared. Combined with Fig.4(b), these results showed that no apparent mix-drying period and BW-drying period occurred during the drying experiments. Therefore, we can conclude that mutual transformation between FW and BW cannot be achieved at a low temperature (50 °C and 60 °C). Moreover, the diffusion rate is relatively lower at low temperatures (i.e., 50 °C and 60 °C) compared with that at high temperatures (70 °C and 80 °C). No water or only an extremely small amount of water obtained from BW transformation was necessary for the supply. The total drying rate of the samples was determined using only the diffusion rate of FW and gradually decreased following the decline of the total water content of the sample without any evident turning point on the curves. As shown in Figs.3(b) and 6(b), evident turning points appeared on the drying rate curves at 80 °C, and three complete stages could be recognized when the samples were 4 mm and 8 mm thick. By contrast, no turning point could be observed on the drying rate curve of the 12 mm-thick samples. The increase in the thickness of RPA slices widened the moisture axial transmission path; therefore, moisture gradient decreased as moisture content remained unchanged, which reduced the diffusion rate. When the thickness is 8mm, FW can emerge rapidly from the samples only at a high temperature (80 °C) because of relatively large diffusion rate. When the thickness of the sample was increased to 12 mm, the excessive thickness of the RPA slices led to an extremely low moisture gradient within the samples at the same moisture content. Even at high temperatures of 80 °C, the diffusion rate was still too small. FW could not emerge rapidly and its content decreased slowly, no supplement from BW transformation was required. Consequently, the overall drying rate of the samples declined gradually and smoothly without a turning point. The goodness of fit of this model was evaluated using the standard error (SE), the root mean square error (RMSE) and the chi-square (χ2). The lower the value of SE, RMSE and χ2, the better is the goodness of the fit. These statistical values in dimensionless moisture content are defined as:
1 RMSE N
1
2 ( MR pre,i MRexp,i ) 2 , i 1 N
9
(11a)
N
2
(MR
pre,i
MRexp,i ) 2
(11b)
i 1
,
N f N
SE
(MR
pre, i
MRexp,i ) 2
(11c)
i 1
,
N 1
where MRexp,i and MRpre,i are the ith experimentally and calculated dimensionless mean moisture content, N is the number of observations and f is the number of constants
[22]
.These statistical
parameters were given in Table 2 for different experimental conditions. It is clear that, RMSE, χ2 and SE values were very low. This model represented the experimental values satisfactorily.
4 Conclusions The results showed that both the temperature and slice thickness affect obviously the changes in moisture content and drying rate of samples, increasing the drying temperature or/and decreasing the slice thickness may improve the drying rate and shorten the drying time. Throughout the drying process, the diffusion of FW and the mutual transformation between FW and BW simultaneously influence the total RPA sample drying rate, which results in nonmonotonic changes in the drying rate versus their moisture content. In particular, when samples with low thickness are dried at a high temperature, an evident turning point appears on the drying rate curve. Accordingly, the drying process can be divided into three stages: the FW-drying, mix-drying, and BW-drying periods. Only at high drying temperatures and with thin sample thickness, three stages can be all recognized during drying, lowering the temperature and/or increasing the thickness of samples may result in inconspicuousness or disappearance of mix-drying and BW-drying periods. A transformation and transport rate model combining different water-binding types and their contents is established. Mutual transformation between FW and BW was simplified as reversible conversion and transport rate model of FW was made by assuming and deducting on the basic of Fick's second law. The modeling results coincide with experiments.
10
Acknowledge The authors are grateful for the supports of the National Natural Science Foundation of China (Nos. 51506006, 51476009), the Fundamental Research Funds for the Central Universities (No. FRF-SD-15-018A3) and the National Basic Research Program of China (973 Program, No. 2012CB720406).
References [1] Chin S K, Siew E S, Soon W L. Drying characteristics and quality evaluation of kiwi slices under hot air natural convective drying method. International Food Research Journal, 2015, 22(6): 2188-2195. [2] Gracielle J, Maraisa Lopes de Menezes, Nehemias C P, Edson Antonio da Silva. Comparing models to Neumann and dirichlet conditions in grape seed drying. Applied Thermal Engineering, 2016, 93: 865-871. [3] Sacilik K, Elicin A K. The thin layer drying characteristics of organic apple slices. Journal of Food Engineering, 2006, 73(3): 281-289. [4] Ertekin C, Yaldiz O. Drying of eggplant and selection of a suitable thin layer drying model. Journal of Food Engineering, 2004, 63(3): 349-359. [5] Zhu A, Shen X. The model and mass transfer characteristics of convection drying of peach slices. International Journal of Heat and Mass Transfer, 2014, 72: 345-351. [6] Ayensu A. Dehydration of food crops using a solar dryer with convective heat flow. Solar Energy, 1997, 59(4): 121-126. [7] Hutchinson D, Otten L. Thin‐layer air drying of soybeans and white beans. International Journal of Food Science & Technology, 1983, 18(4): 507-522. [8] Yaldýz O, Ertekýn C. Thin layer solar drying of some vegetables. Drying Technology, 2001, 19(3-4): 583-597. [9] Özdemir M, Devres Y O. The thin layer drying characteristics of hazelnuts during roasting. Journal of Food Engineering, 1999, 42(4): 225-233. [10] Henderson S M, Pabis S. Grain drying theory: IV. The effect of air flow rate on the drying index. Journal of Agricultural Engineering Research, 1962, 7(2): 85-89. [11] Le B D, Martin C, Colonna P, et al. Quantitative determination of bound water in wheat starch by time domain NMR spectroscopy. Carbohydrate Research, 1998, 308(1–2):29-36. [12] Sharaf-Eldeen Y I, Blaisdell J L, Hamdy M Y. A model for ear corn drying. Transactions of the ASAE, 1980, 23(5): 1261-1265. [13] Lu T, Jiang P, Shen S. Numerical and experimental investigation of convective drying in unsaturated porous media with bound water. Heat and Mass Transfer, 2005, 41(12): 1103-1111. [14] Garnczarska M, Zalewski T, Kempka M. Changes in water status and water distribution in maturing lupin seeds studied by MR imaging and NMR spectroscopy. Journal of Experimental Botany, 2007, 58(14): 3961-3969. [15] Rathjen J R, Strounina E V, Mares D J. Water movement into dormant and non-dormant wheat (Triticum aestivum L.) grains. Journal of Experimental Botany, 2009, 60(6): 1619-1631. [16] Ghosh P K, Jayas D S, Smith E A, et al. Mathematical modelling of wheat kernel drying with input from moisture movement studies using magnetic resonance imaging (MRI), Part I: Model development and comparison with MRI observations. Biosystems Engineering, 2008, 100(3): 389-400. [17] Xing H, Takhar P S, Helms G, et al. NMR imaging of continuous and intermittent drying of pasta. Journal of Food Engineering, 2007, 78(1): 61-68.
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[18] GB/T 5009. 3－2010. National food safety standard. Determination of moisture in foods, China. [19] Akpinar E K, Toraman S. Determination of drying kinetics and convective heat transfer coefficients of ginger slices. Heat and Mass Transfer, 2015: 1-11. [20] Bialobrzewski I, Markowski M. Mass transfer in the celery slice: Effects of temperature, moisture content, and density on water diffusivity. Drying Technology, 2004, 22(7): 1777-1789. [21] Tripathy P P, Kumar S. A methodology for determination of temperature dependent mass transfer coefficients from drying kinetics: Application to solar drying. Journal of Food Engineering, 2009, 90(2): 212-218. [22] San Martin M B, Mate J I, Fernandez T, et al. Modelling adsorption equilibrium moisture characteristics of rough rice. Drying technology, 2001, 19(3-4): 681-690.
12
T
d
Tray bottom
Fig.1 Experiment setup: d = 25 mm and = 4, 8, and 12 mm
=4mm
1.0
0.6
Me(-)
T=50℃ T=60℃ T=70℃ T=80℃
0.8
MR (-)
0.12 0.09 0.06 50
0.4
60
70
(a)
0.2 0.0 1.0
(b)
0.8
MR (-)
80
T (℃)
T=80℃
=4mm =8mm =12mm
0.6 0.4 0.2 0.0
0
200
400
600
800
1000
1200
Drying time (min) Fig.2 Moisture change in the samples during the drying process
13
=4mm
R (1/min)
15
T=50℃ T=60℃ T=70℃ T=80℃
10
5
(a)
0
T=80℃ =4mm
R (1/min)
15
=8mm =12mm
10
5
(b)
0 0.0
0.5
1.0
1.5
M (kg water/kg dry matter) Fig.3 Drying rate of the RPA slices 1.0 FW-drying
Mix-drying
0.6
12 FW BW Drying rate
0.4 0.2
4
(a)
0.0 1.0
MR（ -）
0.8
8
FW BW Drying rate
0 20 16
0.6
12
0.4
8
0.2
4
(b)
0.0 0.0
R (1/min)
16
0.5
1.0
R (1/min)
MR（ -）
0.8
20 BWdrying
0
1.5
M（ kg water/kg dry matter）
Fig.4 Moisture content and drying rate during the drying process for a 4 mm-thick RPA slice: (a) 80 °C and (b) 60 °C
14
BW-drying Mixing-
0.8 MR（ -）
FW-drying 15
drying
0.6
10 MR of FW MR of BW Drying rate
0.4
R (1/min)
1.0
5
0.2
(a)
0.0
0
15
R (1/min)
10 Diffusion rate of FW Transformation rate from FW to BW
5 0 -5
-10 0.0
(b) 0.5
1.0
1.5
M（ kg water/kg dry matter）
Fig5. Moisture content and drying rate obtained from the drying model for the 4 mm-thick RPA slice at 80 °C
=4mm
R (1/min)
15
T=50℃ T=60℃ T=70℃ T=80℃
10
5
(a)
0
=80℃
=4mm =8mm =12mm
R (1/min)
15
10
5
(b)
0 0.0
0.5
1.0
1.5
M (kg water/kg dry matter)
Fig.6 Drying rate of the RPA slices obtained from the simulation
15
Table1 Parameters and properties used in the model Parameters and properties
Values
the number of grids
600/1200/1800
Ed/R
2701.8
Ek/R
6.210
EFB
21694
EBF
20763
D0
21.09
k0
0.0023
CFB
2.94×1024
CBF
1.75×1023
a
0.33
Table2 Results of statistical error analysis of the model at different drying conditions Drying temperature
Thickness of samples
(℃)
(mm)
50
standard error
root mean square error
chi-square
(SE)
(RMSE)
(χ2)
4
0.004272
0.046208
0.002135
60
4
0.002057
0.022255
0.000495
70
4
0.003692
0.039946
0.001596
80
4
0.003665
0.03965
0.001572
80
8
0.002375
0.025695
0.000660
80
12
0.003232
0.034964
0.001222
16
Graphical abstract
0.8
20 BWdrying
FW-drying
Mix-drying
16
0.6
12 FW BW Drying rate
0.4
8
0.2
4
0.0
0
0.0
0.5
1.0
Drying rate R (1/min)
Moisture content MR（ -）
1.0
1.5
M（ kg water/kg dry matter）
Moisture content and drying rate during the drying process for a 4 mm-thick RPA slice under 80℃. The drying rate (R) exhibits a nonlinear relationship with the moisture content (M) of RPA slices, and the slope of R (dR/dM) changes non-monotonically with M. When the diffusion law of FW as well as the mutual transformation between FW and BW are considered, the drying process of the slices can be divided into three stages: FW drying, mix-drying, and BW-drying periods. During the FW-drying period, the drying rate is determined from the rate of FW diffusion and transmission. During the mix-drying period, the drying rate is affected by both diffusion and mutual transformation. By contrast, the drying rate is only influenced by the conversion rate of BW to FW during the BW-drying period.
17
Highlights
The drying rate shows a nonlinear relationship with the moisture content. Free water is mutually transformed with bound water during drying. A drying model combining different water-binding types is established. The drying process can be divided into three stages.
18
S1359-4311(16)31482-X http://dx.doi.org/10.1016/j.applthermaleng.2016.08.123 ATE 8922
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
27 May 2016 16 August 2016 21 August 2016
Please cite this article as: R. Li, C. Liu, C. Zhang, J. Shen, L. Wang, C. Jia, Moisture transformation and transport during the drying process for Radix Paeoniae Alba slices, Applied Thermal Engineering (2016), doi: http:// dx.doi.org/10.1016/j.applthermaleng.2016.08.123
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Moisture
transformation
and
transport
during the drying process for Radix Paeoniae Alba slices Ran Lia, Chuanping Liua,b,*, Chenwei Zhanga, Jianbiao Shena, Li Wanga,b, Chao Jiaa a
School of Mechanical Engineering, University of Science and Technology Beijing, Beijing, 100083, China
b
Beijing Engineering Research Centre of Energy Saving and Environmental Protection, Beijing, 100083, China
*
Email: [email protected]
Abstract: The moisture-binding type and change in moisture content of Radix Paeoniae Alba (RPA) slices were determined during their drying process. Water in RPA slices exists in two types: bound water (BW) and free water (FW). During the drying process, FW diffuses from inside the sample to outside it; simultaneously, it is mutually transformed with BW. The drying rate (R) exhibits a nonlinear relationship with the moisture content (M) of RPA slices, and the slope of R (dR/dM) changes non-monotonically with M. When the diffusion law of FW as well as the mutual transformation between FW and BW are considered, the drying process of the slices can be divided into three stages: FW drying, mix-drying, and BW-drying periods. Mutual transformation between FW and BW is simplified as a reversible conversion process, and a drying model is established for RPA slices based on Fick’s second law. Keywords: drying characteristics; drying model; free water and bound water; NMR
1 Introduction Radix Paeoniae Alba (RPA), which is a typical rootstock medical herb, is an important crop valued as a medicinal plant in China. It is used to gain health benefits, such as blood nourishment, pain relief, and suppression of hyperactive liver. RPA is typically cut into slices and then dried with hot air. Its medicinal component is mainly influenced by drying temperature, and thus, an efficient drying operation can enhance its quality and appearance. Many experiments have been performed to study the effects of drying conditions on various [1]
[2]
[3]
[4]
biological products, such as kiwi slices , grape seed , organic apple slices , eggplant slices , [5]
and peach slices , among others. Accordingly, numerous mathematical models
[6,7,8,9]
, including
theoretical, semi-empirical, and purely empirical models, have been developed to describe the drying process quantitatively. Drying gas temperature and slice thickness have been identified as the main factors that affect drying rate. Increasing temperature or decreasing thickness will shorten the drying period, and the curve of the drying rate versus the decrease in moisture content
1
[4]
will exhibit a gradual decline. The results of the experiments of Ertekin
and Zhu
[5]
showed that
drying could also be accelerated by increasing gas velocity in a convective dryer. For some products such as RPA, the internal resistance to moisture movement of samples is considerably higher than the resistance on the surface; therefore, the influence of the relative humidity and [ ]
velocity of drying gas is insignificant 10 . Moisture within biological products can be generally divided into two types: free water (FW) and bound water (BW). FW exists in tissues or cells and can flow freely, whereas BW is bound to biological macromolecules via one or more hydrogen bonds. Martin et al.[11] proposed that the amount of water bound to macromolecules in food items was an important parameter because it could determine optimal drying (to allow rehydration in a reversed manner). They also demonstrated the occurrence of a “bound” water–“weakly bound” water exchange phenomenon at an intermediate rate in wheat starch suspensions. Sharaf-Eldeen et al.
[ 12 ]
observed two
declining-rate periods in the drying curves of corn ears. These periods could be attributed to the change in moisture state during drying, i.e., from capillary moisture (strong liquidity, similar to [13]
FW) to cellular water (weak liquidity, similar to BW). Lu et al.
reported that the drying process
of unsaturated porous media with BW included the convection and capillary transport of FW, the diffusion of BW, as well as the convection and diffusion of gas. A strong bonding force enables BW to negatively and directly influence water movement during drying. Recently, the nuclear magnetic resonance (NMR) technique has been widely used in the literature to measure the contents of BW and FW in samples
[14,15,16,17]
. This technique can
nondestructively and non-invasively distinguish water in different types of bond with macromolecules in accordance with the chemical environment of protons. In the current study, the drying characteristics of RPA slices are experimentally determined, and the moisture transformation between FW and BW is investigated during the drying process by applying the NMR technique.
2 Experiment methods and results The RPA root used in the following experiments were grown to maturity in experimental plots located in Bozhou, Anhui Province. RPA root is a white or pale red/brown cylinder with a smooth and clearly layered cutting surface. Its radial texture is that of xylem wood. To get closer texture, smoother slice type and shorter drying time, the clean roots are usually boiled in boiling water, which also makes it easier to be peeled. After many tests, 10-15min is proved to be the optimum boiling time for RPA roots used in our research, as too long boiling time may result in hollow interior and weight reduction of the samples, too short cooking time may lead to the black center of roots after drying. A stout root without a white heart and fissure is preferred. The RPA root was harvested in March and carefully washed to remove the soil on its surface. Both ends of the root were then cut. The clean root was boiled for 10–15 min, and then immediately cooled in cold 2
water. After the outer covering was peeled, the root was placed on a table to be used for the experiment. We chose an RPA root with a diameter (d) of 25±3.0 mm, and then sliced the root into pieces with varying thickness ( = 4±0.5, 8±0.5, and 12±0.5 mm). The samples were horizontally arranged on the bottom of a tray and dried using a rapid moisture meter (Model: MA150, Sartorius, Germany) according to the national standard GB/T 5009.3 2010 18
. The tray
was heated electrically at different temperatures (T = 50, 60, 70, and 80 °C), and the samples were observed. During the drying period, the samples were measured continuously using the rapid moisture meter until their mass stopped changing. The dimensionless moisture ratio (MR), which ranges from 0 to 1, is defined as follows: MR
M , M0
(1)
where M is the moisture content of the samples during the drying procedure, and M0 is the initial moisture before drying. The drying rate (R) is defined as the moisture change in unit time that characterizes the speed of the drying process, as follows: R
M t t M t . t
(2)
At different times during the drying process, the samples were removed from the rapid moisture meter and their moisture-binding types (including the contents of FW and BW) were tested using an NMR spectrometer (MiniMR-60, Niumag, China). Five tests were performed for each condition, and the average values of the results were used as the experimental data. 2.1 Effects of drying air temperature and sample thickness Fig.2(a) shows the change in dimensionless moisture content (MR) of the RPA slices during the drying process at different temperatures, whereas Fig.2(b) shows that the RPA slices have varying thickness. As drying proceeded, MR decreased and its variation tendency (which corresponded to the drying rate) also gradually decreased. Finally, drying reached a steady state, and MR remained at the equilibrium moisture content (Me). Drying rate can be accelerated and the period during which the equilibrium moisture content is reached will be shortened by increasing drying temperature or decreasing slice thickness. Notably, the equilibrium moisture content of the slices decreases with increasing temperature [Inset, Fig.2(a)], but is hardly influenced by the thickness of the slices [Fig.2(b)]. The final equilibrium moisture contents are the same for varying slice thickness. Fig.3 shows the relation between the drying rate (R) and moisture content (M) of a slice. While the slices are drying, the moisture content decreases and the corresponding drying rate also
3
decreases. However, the changes in drying rate and moisture content do not exhibit a linear relationship. As shown in Fig.3(a), the relation between drying rate and moisture content (R–M) for 4 mm-thick slices exhibits a super-line function when a slice has high moisture content and a sublinear function when a slice has low moisture content. That is, dR/dM changes nonmonotonically with M. When moisture content is approximately 0.28, a turning point is observed on the R–M curve, at which dR/dM achieves a minimum value. The moisture content at this point is defined as the critical moisture content (Mc). The drying rate and the correspondence relation between drying rate and moisture content both change with the variation in drying temperature, as shown in Fig.3(a). With increasing drying temperature, the R–M curve becomes increasingly nonlinear, the decrease in critical moisture content Mc becomes increasingly evident. When the temperature is below 60 °C, the turning point on the R–M curve is no longer evident. In addition to gas temperature, the drying rate is also influenced by slice thickness, as shown in Fig.3(b). As thickness increases, the drying rate of a slice decreases. The turning point on the R–M curve is no longer evident when a slice is thicker than 12 mm; however, the value of the critical moisture content (Mc) remains nearly unchanged. The main factor that affects the drying kinetics is the diffusion behavior of internal moisture. A rapid decline on drying rate curve after the turning point indicates the increasing in the internal moisture diffusion resistance. In addition to the organizational structure of the sample, the moisture diffusion behavior is also related to moisture content and different water-binding types. Therefore, we test the contents of FW and BW individually during drying. 2.2 Moisture transformation during drying In the fresh RPA samples, the initial moisture contents of FW and BW are 86% and 14% of the total moisture content, respectively; that is, FW accounts for a larger proportion than BW. FW can easily emerge, whereas removing BW directly during drying is nearly impossible. Fig.4(a) shows the contents of FW and BW in 4 mm-thick RPA slices and the drying rate varying with the total moisture content during drying at 80 °C. As the total moisture content decreases, the FW content rapidly declines at the beginning, and then slows down until its value has dropped to zero. By contrast, the BW content increases during initial drying, this indicates that a certain percentage of FW is transforming into BW during this stage. The BW content begins to
4
decline gradually after reaching the maximum value, which indicates that BW is starting to transform into FW. The experimental results at 70 °C are similar to those at 80 °C. However, when the temperature decreases to 60 °C, the BW content remains nearly unchanged during the entire drying process, and no evident rising or falling tendency are observed, as shown in Fig.4(b). The results at 50 °C are similar to those at 60 °C. Therefore, we conclude that, in addition to FW diffusion, mutual transformation
[11]
between FW and BW also occurs during the drying process
for RPA slices. FW diffusion and mutual transformation simultaneously affect the drying rate of the samples, causing the nonmonotonic change in dR/dM versus M. The high drying temperature is conducive to achieving mutual transformation between BW and FW. We have established a drying model for RPA slices based on the preceding analysis. The model demonstrates both the transformation and transport mechanisms of internal moisture.
3 Model and discussion The drying of RPA is a complex process that involves heat and mass transfer[19]. In this work, a drying model is established according to the following assumptions. ① The thermophysical parameters of the samples are the functions of local temperature and humidity. ② The evaporation of moisture and the flow of water vapor in the sample can be disregarded. ③ The lateral heat transfer within the sample can be disregarded. ④ The thickness of a slice is significantly smaller than its width, and the samples are regarded as continuous with a regular finite flat shape. ⑤ The preheating process of the samples is fast, and their temperature remains constant during drying. ⑥ Only FW can emerge from the samples during drying, BW merely participates in the mutual transformation with FW. The dimensionless moisture contents of FW and BW are defined as MRF = MF/M0 and MRB = MB/M0, respectively, where MF and MB denotes the moisture contents of FW and BW, respectively. FW diffusion follows Fick’s second law, and its diffusion rate can be expressed as RD D
2 MRF x 2
,
(3)
where D is the diffusion coefficient that is dependent on drying temperature[20]. This coefficient follows Arrhenius equation[21]: D D0e
Ed RT
,
(4)
where D0 denotes the Arrhenius constant, and Ed represents the activation energy for moisture 5
diffusion. The mutual transformation between FW and BW is considered reversible conversion. In this study, the transformation of BW into FW is defined as forward conversion, the rate of which is described as RBF. Meanwhile, the transformation of FW into BW is defined as reverse conversion, the rate of which is described as RFB. Up to now, there is no literature related to the dynamics research on mutual transformation between free water and bound water in the internal of plant. Here, mutual transformation was analogous to a reversible chemical. Herein, RBF and RFB were defined by referencing reversible reaction kinetic equation, which are related to the moisture content and drying temperature of the RPA slice, as shown in the following expressions: RBF k BF MRBa ,
(5a)
RFB k FB MRFa ,
(5b)
where a is the exponential coefficient; and kBF and kFB are the reaction rate constants of forward and reverse conversions, respectively, which follow Arrhenius equation:
E BF RT
E FB RT
k BF CBF e k FB CFB e
,
(6a)
,
(6b)
where CBF and CFB are the Arrhenius factors; and EBF and EFB are the activation energy for the forward and reverse conversions, respectively. Therefore, the total consumption rate of FW can be expressed as RF
MRF 2 MRF D k FB MRFa k BF MRBa . 2 t x
(7)
RPA slices were arranged horizontally on the tray. The tray was placed in air with temperature T and moisture content ME. The contact surface of the tray was considered adiabatic [Fig.1]. The initial moisture content is uniformly distributed in the RPA slices; hence, the adiabatic and convective boundary conditions are expressed as MRF ( x,0) MRF 0 ,
(8a)
MRF (0, t ) 0, x
(8b)
K ( MRF ( , t ) M E ) D
MRF ( , t ) , x
(8c)
where x is the position along the height of the slice; t is the drying time; MRF0 is the initial moisture content of FW; and K is the mass transfer coefficient, which has been modeled using an Arrhenius-type relation to obtain its functional relationship with the sample temperature as
6
follows: K K 0e
Ek RT
(9)
,
where K0 is the Arrhenius constant and Ek is the activation energy for convective mass transfer. Finite volume method (FVM) was applied to get the numerical solution of Eq.(7). The profile that MRF changes with x was considered to be stepwise; the first derivative was considered to changes over time t in an explicit step way and the final discrete equation is given as:
MRF nt t 1 2Dt MRF nt Dt MRF nt 1 MRF nt 1 - kFB MRF nt
a
x
x
a k BF MRB nt t
(10) where subscript n is the nth calculation cell, n-1 and n+1 are last and next calculation cell respectively; Δt and Δx are time and space step, respectively. The drying rate of the FW and BW content versus drying time can be obtained from Eq.(10) solved by iterations through an explicit method using a simulation program. The parameters and properties used in the model are shown in Table1. Fig.5 shows the dimensional moisture content and drying rate obtained for a 4 mm-thick slice at 80 °C. As shown in Fig.5(a), the BW content increases at the beginning and then decreases after it reaches the maximum value, which signifies the occurrence of mutual transformation between FW and BW in the slices. Moreover, the change in dR/dM versus M is nonmonotonic. The modeling results coincide with the experimental results shown in Fig.4(a). Fig.5(b) shows the diffusion rate of FW (RD) and the transformation rate from BW to FW (RT = RBF–RFB, hereafter referred to as transformation rate) against the moisture content of a material during drying. The points of RT that is equal to 0 (BW content has reached the maximum value) and RT that reaches the maximum value (the evident turning point occurs on the drying rate curve) are selected to divide the drying process into three stages: FW-drying, mix-drying, and BW-drying periods [Figs. 4(a) and 5]. During the FW-drying period, the drying rate is determined from the rate of FW diffusion and transmission. During the mix-drying period, the drying rate is affected by both diffusion and mutual transformation. By contrast, the drying rate is only influenced by the conversion rate of BW to FW during the BW-drying period. At the beginning of drying, the temperature of the samples was raised rapidly and the balance between the FW and BW contents of the samples before drying was upset. RBF and RFB increased 7
simultaneously, which resulted in RFB>RBF because the content of FW was higher than that of BW. The apparent result of the mutual transformation between FW and BW was the conversion of FW into BW, which increased BW content. The diffusion rate of FW (RD) was relatively high because of its high content, and the water that diffused across the interface was immediately removed with hot air. The simultaneous occurrence of diffusion and transformation led to a rapid reduction in the FW content, and which resulted in the rapid decline of RD. During this stage, the drying rate of the samples was determined via the diffusion rate of FW. The downward trend of the drying rate is similar to the decline of the FW content, i.e., the FW-drying period. As the drying process proceeded, the FW content was reduced rapidly, whereas the BW content was increased gradually, which decreased RBF and increased RFB. The two rates approached each other until they were equal. During this moment, RT was reduced to 0 and the BW content reached the maximum value; the drying process entered the mix-drying period. During this period, the apparent result of mutual transformation between the two types of moisture was the conversion of BW into FW given that RT>0. The BW content began to decrease, and both RFB and RBF were reduced. However, RT exhibited an uptrend because of the faster reduction of the FW content than the BW content, i.e., RFB was reduced faster than RBF. Except diffusing some content out, FW gained the content conversed from BW at mean time, so that the decreasing speed of FW content was lower than before, and thus, the decline of RD was slower compared with the previous speed. During this stage, both FW and BW contents were reduced. The drying rate was simultaneously affected by the diffusion rate of FW (RD) and the transformation rate (RT), i.e., the mix-drying period. As drying continued, the FW content was further reduced at a low speed, which caused the reverse conversion rate RFB to decrease slowly until its decrement was relatively less compared with that of the forward conversion rate RBF. RT reached the maximum value, and the evident turning point appeared on the drying rate curve, i.e., the drying process entered the BW-drying period. During this stage, RD decreased gradually and drew close to RT. FW that dried out almost completely obtained from the transformation of BW. Moreover, the FW content that could be detected within the samples was at an extremely low level. The effect of the reverse conversion rate RFB on the total drying rate could be negligible; hence, the total drying rate of the samples was only affected by the transformation rate (RT). The downward trend of the total drying rate is 8
similar to the decline of the BW content, i.e., the BW-drying period. As shown in Figs.3(a) and 6(a), the drying rate curve of the 4 mm-thick RPA slice tends to flatten gradually with decreasing drying temperature. When drying temperature was reduced to below 60 °C, the turning point disappeared. Combined with Fig.4(b), these results showed that no apparent mix-drying period and BW-drying period occurred during the drying experiments. Therefore, we can conclude that mutual transformation between FW and BW cannot be achieved at a low temperature (50 °C and 60 °C). Moreover, the diffusion rate is relatively lower at low temperatures (i.e., 50 °C and 60 °C) compared with that at high temperatures (70 °C and 80 °C). No water or only an extremely small amount of water obtained from BW transformation was necessary for the supply. The total drying rate of the samples was determined using only the diffusion rate of FW and gradually decreased following the decline of the total water content of the sample without any evident turning point on the curves. As shown in Figs.3(b) and 6(b), evident turning points appeared on the drying rate curves at 80 °C, and three complete stages could be recognized when the samples were 4 mm and 8 mm thick. By contrast, no turning point could be observed on the drying rate curve of the 12 mm-thick samples. The increase in the thickness of RPA slices widened the moisture axial transmission path; therefore, moisture gradient decreased as moisture content remained unchanged, which reduced the diffusion rate. When the thickness is 8mm, FW can emerge rapidly from the samples only at a high temperature (80 °C) because of relatively large diffusion rate. When the thickness of the sample was increased to 12 mm, the excessive thickness of the RPA slices led to an extremely low moisture gradient within the samples at the same moisture content. Even at high temperatures of 80 °C, the diffusion rate was still too small. FW could not emerge rapidly and its content decreased slowly, no supplement from BW transformation was required. Consequently, the overall drying rate of the samples declined gradually and smoothly without a turning point. The goodness of fit of this model was evaluated using the standard error (SE), the root mean square error (RMSE) and the chi-square (χ2). The lower the value of SE, RMSE and χ2, the better is the goodness of the fit. These statistical values in dimensionless moisture content are defined as:
1 RMSE N
1
2 ( MR pre,i MRexp,i ) 2 , i 1 N
9
(11a)
N
2
(MR
pre,i
MRexp,i ) 2
(11b)
i 1
,
N f N
SE
(MR
pre, i
MRexp,i ) 2
(11c)
i 1
,
N 1
where MRexp,i and MRpre,i are the ith experimentally and calculated dimensionless mean moisture content, N is the number of observations and f is the number of constants
[22]
.These statistical
parameters were given in Table 2 for different experimental conditions. It is clear that, RMSE, χ2 and SE values were very low. This model represented the experimental values satisfactorily.
4 Conclusions The results showed that both the temperature and slice thickness affect obviously the changes in moisture content and drying rate of samples, increasing the drying temperature or/and decreasing the slice thickness may improve the drying rate and shorten the drying time. Throughout the drying process, the diffusion of FW and the mutual transformation between FW and BW simultaneously influence the total RPA sample drying rate, which results in nonmonotonic changes in the drying rate versus their moisture content. In particular, when samples with low thickness are dried at a high temperature, an evident turning point appears on the drying rate curve. Accordingly, the drying process can be divided into three stages: the FW-drying, mix-drying, and BW-drying periods. Only at high drying temperatures and with thin sample thickness, three stages can be all recognized during drying, lowering the temperature and/or increasing the thickness of samples may result in inconspicuousness or disappearance of mix-drying and BW-drying periods. A transformation and transport rate model combining different water-binding types and their contents is established. Mutual transformation between FW and BW was simplified as reversible conversion and transport rate model of FW was made by assuming and deducting on the basic of Fick's second law. The modeling results coincide with experiments.
10
Acknowledge The authors are grateful for the supports of the National Natural Science Foundation of China (Nos. 51506006, 51476009), the Fundamental Research Funds for the Central Universities (No. FRF-SD-15-018A3) and the National Basic Research Program of China (973 Program, No. 2012CB720406).
References [1] Chin S K, Siew E S, Soon W L. Drying characteristics and quality evaluation of kiwi slices under hot air natural convective drying method. International Food Research Journal, 2015, 22(6): 2188-2195. [2] Gracielle J, Maraisa Lopes de Menezes, Nehemias C P, Edson Antonio da Silva. Comparing models to Neumann and dirichlet conditions in grape seed drying. Applied Thermal Engineering, 2016, 93: 865-871. [3] Sacilik K, Elicin A K. The thin layer drying characteristics of organic apple slices. Journal of Food Engineering, 2006, 73(3): 281-289. [4] Ertekin C, Yaldiz O. Drying of eggplant and selection of a suitable thin layer drying model. Journal of Food Engineering, 2004, 63(3): 349-359. [5] Zhu A, Shen X. The model and mass transfer characteristics of convection drying of peach slices. International Journal of Heat and Mass Transfer, 2014, 72: 345-351. [6] Ayensu A. Dehydration of food crops using a solar dryer with convective heat flow. Solar Energy, 1997, 59(4): 121-126. [7] Hutchinson D, Otten L. Thin‐layer air drying of soybeans and white beans. International Journal of Food Science & Technology, 1983, 18(4): 507-522. [8] Yaldýz O, Ertekýn C. Thin layer solar drying of some vegetables. Drying Technology, 2001, 19(3-4): 583-597. [9] Özdemir M, Devres Y O. The thin layer drying characteristics of hazelnuts during roasting. Journal of Food Engineering, 1999, 42(4): 225-233. [10] Henderson S M, Pabis S. Grain drying theory: IV. The effect of air flow rate on the drying index. Journal of Agricultural Engineering Research, 1962, 7(2): 85-89. [11] Le B D, Martin C, Colonna P, et al. Quantitative determination of bound water in wheat starch by time domain NMR spectroscopy. Carbohydrate Research, 1998, 308(1–2):29-36. [12] Sharaf-Eldeen Y I, Blaisdell J L, Hamdy M Y. A model for ear corn drying. Transactions of the ASAE, 1980, 23(5): 1261-1265. [13] Lu T, Jiang P, Shen S. Numerical and experimental investigation of convective drying in unsaturated porous media with bound water. Heat and Mass Transfer, 2005, 41(12): 1103-1111. [14] Garnczarska M, Zalewski T, Kempka M. Changes in water status and water distribution in maturing lupin seeds studied by MR imaging and NMR spectroscopy. Journal of Experimental Botany, 2007, 58(14): 3961-3969. [15] Rathjen J R, Strounina E V, Mares D J. Water movement into dormant and non-dormant wheat (Triticum aestivum L.) grains. Journal of Experimental Botany, 2009, 60(6): 1619-1631. [16] Ghosh P K, Jayas D S, Smith E A, et al. Mathematical modelling of wheat kernel drying with input from moisture movement studies using magnetic resonance imaging (MRI), Part I: Model development and comparison with MRI observations. Biosystems Engineering, 2008, 100(3): 389-400. [17] Xing H, Takhar P S, Helms G, et al. NMR imaging of continuous and intermittent drying of pasta. Journal of Food Engineering, 2007, 78(1): 61-68.
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[18] GB/T 5009. 3－2010. National food safety standard. Determination of moisture in foods, China. [19] Akpinar E K, Toraman S. Determination of drying kinetics and convective heat transfer coefficients of ginger slices. Heat and Mass Transfer, 2015: 1-11. [20] Bialobrzewski I, Markowski M. Mass transfer in the celery slice: Effects of temperature, moisture content, and density on water diffusivity. Drying Technology, 2004, 22(7): 1777-1789. [21] Tripathy P P, Kumar S. A methodology for determination of temperature dependent mass transfer coefficients from drying kinetics: Application to solar drying. Journal of Food Engineering, 2009, 90(2): 212-218. [22] San Martin M B, Mate J I, Fernandez T, et al. Modelling adsorption equilibrium moisture characteristics of rough rice. Drying technology, 2001, 19(3-4): 681-690.
12
T
d
Tray bottom
Fig.1 Experiment setup: d = 25 mm and = 4, 8, and 12 mm
=4mm
1.0
0.6
Me(-)
T=50℃ T=60℃ T=70℃ T=80℃
0.8
MR (-)
0.12 0.09 0.06 50
0.4
60
70
(a)
0.2 0.0 1.0
(b)
0.8
MR (-)
80
T (℃)
T=80℃
=4mm =8mm =12mm
0.6 0.4 0.2 0.0
0
200
400
600
800
1000
1200
Drying time (min) Fig.2 Moisture change in the samples during the drying process
13
=4mm
R (1/min)
15
T=50℃ T=60℃ T=70℃ T=80℃
10
5
(a)
0
T=80℃ =4mm
R (1/min)
15
=8mm =12mm
10
5
(b)
0 0.0
0.5
1.0
1.5
M (kg water/kg dry matter) Fig.3 Drying rate of the RPA slices 1.0 FW-drying
Mix-drying
0.6
12 FW BW Drying rate
0.4 0.2
4
(a)
0.0 1.0
MR（ -）
0.8
8
FW BW Drying rate
0 20 16
0.6
12
0.4
8
0.2
4
(b)
0.0 0.0
R (1/min)
16
0.5
1.0
R (1/min)
MR（ -）
0.8
20 BWdrying
0
1.5
M（ kg water/kg dry matter）
Fig.4 Moisture content and drying rate during the drying process for a 4 mm-thick RPA slice: (a) 80 °C and (b) 60 °C
14
BW-drying Mixing-
0.8 MR（ -）
FW-drying 15
drying
0.6
10 MR of FW MR of BW Drying rate
0.4
R (1/min)
1.0
5
0.2
(a)
0.0
0
15
R (1/min)
10 Diffusion rate of FW Transformation rate from FW to BW
5 0 -5
-10 0.0
(b) 0.5
1.0
1.5
M（ kg water/kg dry matter）
Fig5. Moisture content and drying rate obtained from the drying model for the 4 mm-thick RPA slice at 80 °C
=4mm
R (1/min)
15
T=50℃ T=60℃ T=70℃ T=80℃
10
5
(a)
0
=80℃
=4mm =8mm =12mm
R (1/min)
15
10
5
(b)
0 0.0
0.5
1.0
1.5
M (kg water/kg dry matter)
Fig.6 Drying rate of the RPA slices obtained from the simulation
15
Table1 Parameters and properties used in the model Parameters and properties
Values
the number of grids
600/1200/1800
Ed/R
2701.8
Ek/R
6.210
EFB
21694
EBF
20763
D0
21.09
k0
0.0023
CFB
2.94×1024
CBF
1.75×1023
a
0.33
Table2 Results of statistical error analysis of the model at different drying conditions Drying temperature
Thickness of samples
(℃)
(mm)
50
standard error
root mean square error
chi-square
(SE)
(RMSE)
(χ2)
4
0.004272
0.046208
0.002135
60
4
0.002057
0.022255
0.000495
70
4
0.003692
0.039946
0.001596
80
4
0.003665
0.03965
0.001572
80
8
0.002375
0.025695
0.000660
80
12
0.003232
0.034964
0.001222
16
Graphical abstract
0.8
20 BWdrying
FW-drying
Mix-drying
16
0.6
12 FW BW Drying rate
0.4
8
0.2
4
0.0
0
0.0
0.5
1.0
Drying rate R (1/min)
Moisture content MR（ -）
1.0
1.5
M（ kg water/kg dry matter）
Moisture content and drying rate during the drying process for a 4 mm-thick RPA slice under 80℃. The drying rate (R) exhibits a nonlinear relationship with the moisture content (M) of RPA slices, and the slope of R (dR/dM) changes non-monotonically with M. When the diffusion law of FW as well as the mutual transformation between FW and BW are considered, the drying process of the slices can be divided into three stages: FW drying, mix-drying, and BW-drying periods. During the FW-drying period, the drying rate is determined from the rate of FW diffusion and transmission. During the mix-drying period, the drying rate is affected by both diffusion and mutual transformation. By contrast, the drying rate is only influenced by the conversion rate of BW to FW during the BW-drying period.
17
Highlights
The drying rate shows a nonlinear relationship with the moisture content. Free water is mutually transformed with bound water during drying. A drying model combining different water-binding types is established. The drying process can be divided into three stages.
18