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Infrared drying of water based varnish coated on elastomer substrate
International Journal of Thermal Sciences 79 (2014) 103e110
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International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
Infrared drying of water based varnish coated on elastomer substrate Nadine Allanic a, *, Pascal Le Bideau b, Patrick Glouannec b, Alain Bourmaud b a b
LUNAM Université, IUT de Nantes, CNRS, GEPEA, UMR 6144, BP 539, 44475 Carquefou Cedex, France Laboratoire d’Ingénierie des Matériaux de Bretagne, Université Européenne de Bretagne, BP 92116, 56321 Lorient Cedex, France
a r t i c l e i n f o
a b s t r a c t
Article history: Received 4 August 2012 Received in revised form 17 September 2013 Accepted 14 January 2014 Available online 14 February 2014
This study deals with the drying and curing of polyurethane water based varnish by infrared radiation. The varnish is thinly coated on rectangular elastomer substrates. After characterizing their main thermophysical properties, the curing rate is linked to the thermal behavior of varnish. A laboratory setup is developed to retrieve mass and temperature evolutions. First, drying experiments with a constant infrared radiation inferior to 20 kW m2 are performed. The thermal and hydric behaviors of the product are analyzed in term of drying time and heating rate. Then, several experiments with modulated infrared radiation are carried out. The impact of drying conditions on curing rate of varnish is then discussed. Ó 2014 Elsevier Masson SAS. All rights reserved.
Keywords: Experiment Nanoindentation Calorimetric analysis Numerical model Inverse method Crosslinking
1. Introduction In industry, rubber profiles designed for the automotive sector are produced on extrusion lines. During its manufacturing, the extruded product successively undergoes many thermal operations. One of them consists in drying and reticulating a thin film of varnish applied on the profile surface. The reticulated varnish protects the profile of its environment (light, humidity), increases its water tightness, accentuates the product brilliance or increases the abrasion protection. The topical environmental challenges encourage industries to use water based varnishes instead of organic based varnish [1,2]. Thus, the drying step needs a larger amount of energy. A classical solution is to add in the industrial process a superficial radiative heat source, such as infrared technologies [3,4]. Previous works [5,6] have shown the difficulty to dry aqueous polymer solution or dispersion without forming an impermeable skin at the surface of the solution. The use of superficial heating, in case of thin polymer film drying such as varnishes, needs a good control of energy inputs to avoid material deterioration. This work deals with the infrared heating of a water based varnish containing polyurethane, coated on an elastomer substrate. Due to several physical phenomena involved in the drying (evaporation, shrinkage, crystallization, crosslinking.) [7,8], the product * Corresponding author. Tel.: þ33 (0) 2 28 09 20 26; fax: þ33 (0) 2 28 09 20 17. E-mail address: [email protected] (N. Allanic). 1290-0729/$ e see front matter Ó 2014 Elsevier Masson SAS. All rights reserved. http://dx.doi.org/10.1016/j.ijthermalsci.2014.01.013
is very sensitive to energy inputs. Thus, to understand well the product’s behavior, an experimental laboratory setup, enabling to obtain the drying kinetics of thin coat during drying under infrared radiation, is involved. First, the influence of level of infrared radiation on the heat and mass transfers during the drying is studied. In parallel, a comparison of drying with short-wave and mediumwave infrared radiations is performed. After examining the results, an experimental investigation which consists in modulating the infrared irradiation to dry the product at a constant level of temperature is presented. The final state of crosslinking is linked with the mechanical properties of the varnish by a nanoindentation method, which confirms the possibility to improve the quality of the final product by the control of the infrared inputs. 2. Material and techniques 2.1. Experimental dryer and procedure The experimental dryer enables to perform experiments with infrared heating combined with natural convection (Fig. 1). The infrared emitters are placed at the upper side of the chamber. Experiments were performed separately with short-wave and medium-wave infrared emitters having a low thermal inertia. The nominal powers of the lamps are respectively of 2 kW for shortwave infrared lamp and 1.5 kW for medium-wave infrared lamp. Each lamp is fitted out with a parabolic reflector to obtain a homogenous radiation on the product surface. A power controller unit
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N. Allanic et al. / International Journal of Thermal Sciences 79 (2014) 103e110
Fig. 1. Experimental setup.
operating in syncopated wave train controls the electrical power supplied to the emitter [9]. This unit is controlled by an input voltage (0e10 V). The infrared radiation received by the product is measured using a sensor developed at the laboratory for both kinds of emitters [10]. The laboratory dryer was designed in order to measure the evolutions of mass and temperatures. Thus, the substrate is placed on a weighting system, located in the chamber. Several precautions are necessary to limit disturbances of mass measurements during the drying stage. Two glass plates are located between the emitters and the sample to avoid convection phenomena involved by emitters’ fan inside the chamber. It is also important to avoid the increase of air temperature around the sample during drying. Thus, the chamber is a closed enclosure, whose walls are cooled down with a water circulation. The sample is surrounded with a plate cooled down with the same water circulation. The sample, schematized in Fig. 1, is constituted of an elastomer plate of dimensions 100 50 4 mm. A spray gun is used to apply a thin film of varnish, corresponding to a thickness of 80 mm, at the upper surface of the substrate. In order to record the temperature evolutions of the substrate, three K-type thermocouples of diameter 200 mm are placed inside the elastomer: at the surface (T1), 2 mm-deep (T2) and 4 mm-deep (T3). An optical pyrometer measures the surface temperature (Tsurf) of the varnish. The emissivity is assumed to be constant and equal to 0.93. The measurement of air temperature is also performed by a K-type thermocouple inserted in a cylindrical radiative shield. All sensors are connected to an acquisition system. Despite the significant precautions taken to avoid it, a drift of the weighting caused by the increase of the air temperature inside the chamber is observed. Thus, before each experiment, a no-load test (substrate without varnish and without thermocouples) is performed to correct it. Then, at each level of infrared radiation, an experiment is performed with a first instrumented coated substrate to measure the temperature evolutions. A second experiment is performed using a coated substrate without thermocouples to
avoid disturbances on the mass measurement. Using this configuration, the precision on mass measurement is estimated to 30 mg.
2.2. Material description A water-based black varnish containing polyurethane is studied. A thermogravimetric analysis (TGA), performed at 2 C/min, showed that water is not the only volatile constituent of the varnish [11]. Several weight losses were observed before 100 C, corresponding to an evaporation of solvent. The density of its dried and reticulated base, measured with a pycnometer, is rvd ¼ 1120 kg m3. The varnish density is expressed by Ref. [12]:
rv ¼ rvd
1þW 1 þ jW
(1)
with W the moisture content in dry basis.
Fig. 2. Calorimetric analysis of dried varnish from 20 C to 240 C at heating rate of 20 K/min.
N. Allanic et al. / International Journal of Thermal Sciences 79 (2014) 103e110
To characterize the curing phenomena, a differential scanning calorimetry analysis (DSC) was investigated on samples of varnish dried three hours at 80 C. Two thermal cycles were carried out in a temperature range of 20 Ce240 C at a heating rate of 20 C/min. Product can be assumed to be not cured during the first temperature cycle and cured during the second one. Fig. 2 presents the obtained heat flows. Below 120 C, the observed peaks correspond to evaporation of residual solvent. The comparison of the first and second increases of temperature shows several exothermic peaks after 120 C, corresponding to curing. Moreover, the peak centered around 115 C is present at the first and second temperature cycle, which is characteristic of the crystallization of one of the constituents of the varnish. Therefore, the crosslinking reaction was studied by means of a second calorimetric analysis, performed on varnish with its initial moisture content. The varnish was heated from the ambient temperature to 180 C according to a temperature increase of 10 C/min. Then, the temperature remains constant during 10 min. Two temperature cycles were performed. During the first cycle, the varnish is dried and reticulated. Fig. 3 presents a zoom of this analysis after the evaporation stage of water and solvents. The difference of heat flow levels between both temperature cycles is mainly due to the reticulation reaction. After 10 min with a constant temperature of 180 C, the heat flows become equivalent. The varnish is thus totally reticulated. This analysis shows that the kinetic of the reticulation may be deduced from the temperature evolution of the product during drying. The isotherm desorption (water activity of a product) of the product was measured at a temperature of 60 C. Varnish was introduced in a dish of 30 mm and placed into a climatic room, which humidity and temperature were regulated [4]. Fig. 4 shows that the evolution of water activity decreases for low moisture content. Indeed, the critical moisture content is located between WC ¼ 0.1e0.15 kg kg1. The isotherm desorption was expressed using a GAB model [13e15]:
W ¼
Wm CKaw ð1 Kaw Þð1 Kaw þ CKaw Þ
(2)
with the fitted parameters Wm ¼ 0.0152, C ¼ 0.6139 and K ¼ 0.9887. The studied elastomer contains about 28 wt% EPDM gum, 39 wt % reinforcing agent (carbon black, chalk.) and about 33 wt% of other components (oil, sulfur, activators, accelerators, antioxidant.). Its properties were previously determined [9] and are given in Table 1.
105
Fig. 4. Isotherm desorption (water activity) of varnish measured at 60 C.
2.3. Nanoindentation measurements Nanoindentation tests were investigated, involving the contact of an indenter on the samples surface and its penetration to a specified load or depth. Using the load versus penetration depth responses, effective elastic modulus and hardness were calculated [16,17]. Indentation tests were performed with a commercial nanoindentation system (Nanoindenter XP, MTS Nano Instruments) at room temperature (23 1 C) with a continuous stiffness measurement (CSM) technique. In this technique, an oscillating force at controlled frequency (70 Hz) and amplitude (3 nm) was superimposed onto a nominal applied force. After the indenter made contact with the surface, it was driven into the material with a constant strain rate, 0.05 s1 to a depth of 5000 nm; the load was held at its maximum value for 60 s; finally, the indenter was withdrawn from the surface with the same rate as loading until 10% of the maximum load was reached. The modulus values have been obtained from the unloading segment according to the work of Oliver and Pharr. [18]. 2.4. Mathematical modeling Model is briefly presented here since it was previously described [4,23]. Mass transfers are unidirectional and varnish temperature is homogenous. Inside the product, only liquid diffusion is considered. The evaporation (Fm) is located at the product’s surface and involves a linear shrinkage (j). By assuming a local thermodynamical equilibrium [19,20], the drying rate Fm is usually given by Refs. [21,22]:
Fm ¼ km
Pt Mv Pt Pv ðTÞ ln Pt aw Pvsat ðTÞ RT
(3)
Governing equations are expressed in a dimensionless form and in a fixed base linked to the dried product (0 < x < ed) to ease numerical resolution. Thus, the mass balance is written [4]:
vW * v ¼ * vt * vx
D* ðW; TÞ
vW *
! (4)
2 * vx 1 þ jW0 W *
with D* ¼ D/D0, W* ¼ W/W0, t* ¼ tD0/e2d, and x* ¼ x/ed. Table 1 Thermophysical properties of elastomer substrate.
Fig. 3. Calorimetric analysis of varnish.
l (W m1 K1)
r (kg m3)
Cp (J kg1 K1)
0.32
0.73 T þ 1215
2.73 T þ 1420
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N. Allanic et al. / International Journal of Thermal Sciences 79 (2014) 103e110
The mass diffusion coefficient is expressed as follows [23,24]: ERTa
DðW; TÞ ¼ D1 þ D2 e
eW b
(5)
with D1, D2, Ea and b constant values. The parameter D1 was introduced in the expression in order to avoid the divergence of numerical solving when the moisture content tends to zero (end of the drying). The mass transfer boundary condition at the varnish surface is expressed by:
x* ¼ 1 Fm ð1 þ JWÞ2 ¼ r0v D* D0
W0 vW
(6)
*
ed vx
The assumption of impermeable substrate results in the following boundary condition:
vW *
x* ¼ 0
*
vx
¼ 0
(7)
The heat balance for the varnish is given by:
D0 vT *
rv cp;v e
e2d vt *
*4 ¼ hc Ta* T * þ εs Tw T *4 þ
1 ðf Tl T0 s
þ av EIR Fm Lv Þ (8) with T* ¼ T T0/Tl T0, Ta* ¼ Ta T0 =Tl T0 and * ¼ T T =T T . Tw w 0 l 0 Tl corresponds to a limit temperature and ɸs is the conductive heat transfer at the substrate/varnish interface. T0 is the initial temperature of the varnish. An efficient heat capacity of dried varnish cp,vd is deduced from calorimetric analysis and introduced into the model (Fig. 2). Thus, the heat capacity of varnish cp,v is expressed by:
cpv ¼ cp;vd
1 W þ cp;w 1þW 1þW
(9)
Due to its radiative properties [11], the infrared radiation av EIR is assumed absorbed at the varnish surface. Thus, the transfer of energy inside the substrate is mainly due to conductive transfer. The experimental temperature (T3) is introduced as a boundary condition inside the model for the bottom face. However, numerical studies conducted in parallel have shown that this temperature can be numerically determined by assuming that the substrate is a semi-infinite medium. The initial conditions are:
t* ¼ 0
W* ¼ 1
T* ¼ 0
3.1. Preliminary drying experiments In this experimental investigation, samples were exposed to infrared radiation until their temperature reached the limit temperature Tl ¼ 180 C. Considering the calorimetric analysis (Figs. 2 and 3), the varnish is partially cured at this temperature. Fig. 5 presents the experimental drying kinetics obtained with a short infrared irradiation of Esw1 ¼ 10.2 kW m2. In order to analyze the impact of varnish presence on the thermal response, the measured temperature of the substrate without varnish (noted “no varnish” on Fig. 5) for the same solicitation (Esw1) is also reported. Moreover, the evolution of air temperature inside the chamber, which progressively increases to reach 36 C at the end of experiment, is also given. During the first 20 s, the temperature of product remains constant, which corresponds to the period before starting the emitters. Ten seconds after, the gradient of temperature inside the product, varnished or not, reaches 25 C. For the substrate without varnish, the elastomer surface temperature, measured with thermocouple T1 and optical pyrometer (Tsurf), are similar. The temperature difference stays lower than 1 K. In the case of varnished substrate, due to the energy used for water evaporation, the surface temperature remains relatively constant while mean moisture content begins to considerably decrease. This step corresponds to a water activity product close to 1 (Fig. 4). During this step, both temperatures Tsurf and T1 are similar. Then, one observes a difference less than 1 K which progressively increases and reaches 10 K at 250 s. This result shows that the surface temperature is certainly underestimated. Indeed, in this work, the emissivity of the product is assumed to be constant. In fact, it decreases all along the drying due to water evaporation which has a consequence on measured temperature by optical pyrometer. In another way, it is possible that the thermocouple T1 receives a part of infrared irradiation and thus gives an overestimated temperature. In the elastomer, the product temperature at the middle position (T2) and on the bottom face (T3) is progressively lower for the varnished substrate compared to not varnished substrate. At the end of the experiment, the gaps are respectively of 5 C for T2 and 7 C for T3. After 70 s, the mean moisture content of varnish begins to slowly decrease, which corresponds to the third stage of drying, when activity is lower. Thus, the surface temperature increases to reach a value close to the case of substrate heated without varnish. Thus, the experimental curves are used to determine the global absorptivity of varnish towards emitters infrared radiation. At the beginning of heating, the substrate can be considered as a semi-
(10)
A control volume method is used to spatially integrate the differential equations. All the equations were simultaneously solved by means of a predictorecorrector method with a high order. The coupling and the nonlinearity of equations were solved by a Newton method. Forty control volumes were considered in the varnish (only for mass balance) and twenty control volumes in the elastomer substrate. The time step was variable to ensure the convergence of calculations. 3. Results and discussion Several configurations of drying have been tested and are now discussed. A mass of 415 35 mg is applied on substrate, which corresponds to a thickness of 80 7 mm.
Fig. 5. Evolution of temperature obtained for substrate with and without varnish for short-wave infrared with Esw1 ¼ 10 kW m2.
N. Allanic et al. / International Journal of Thermal Sciences 79 (2014) 103e110
107
infinite medium, with constant thermophysical properties. We assume that convective and long wave radiative exchanges are negligible comparable to incident infrared radiation. Knowing substrate absorptivity (as ¼ 0.57) [9], varnish absorptivity is estimated using the temperature evolutions of substrate with and without varnish thanks to the following relation:
av ¼ as
v =dt dTsurf s =dt dTsurf
(11)
Mean absorptivity av calculated during the period t ¼ 5 s and t ¼ 20 s is av ¼ 0.64. A similar analysis carried out on dried product gives an identical value. 3.2. Curing with short-wave and medium-wave infrared radiation The influence of the spectral domain of the emitters (short-wave and medium-wave) is now studied. Indeed, it avoids moving the emission spectrum to medium-wave infrared wavelengths. Experiments were performed with infrared irradiation of Esw1 ¼ 10.2 kW m2 and Esw2 ¼ 15.4 kW m2 corresponding respectively to 40% and 60% of control voltage. For medium-wave infrared lamps, the infrared radiations tested are Emw1 ¼ 10 kW m2 and Emw2 ¼ 13 kW m2, corresponding respectively of 70% and 100% of control voltage. Fig. 6 presents the evolutions of product temperature (6a and 6b), mean moisture content and drying rate (6c), obtained for the four tests previously described. Experiments were stopped when the product temperature reached 180 C to avoid its deterioration. First, the comparison of evolution of short-wave infrared radiation (6a) and medium-wave infrared irradiation (6b) shows a quicker setting period for short-waves emitters. For each test, the three steps in heating previously described are also observed. For the same infrared irradiation, even if the varnish temperature increases slightly quicker with short-wave infrared than with medium-wave infrared, the behavior of varnish is globally the same. When the drying rate decreases, differences begin to appear between the two drying kinetics. At 350 s, when the drying can be considered as over, the moisture content is W ¼ 0.78 kg kg1 for Esw1 and W ¼ 0.98 kg kg1 for Emw1. Esw1 ¼ 10.2 kW m2 is slightly higher than Emw1 ¼ 10 kW m2. Thus, the surface temperature increases slightly higher in the first case. At the end of drying, Tsurf is equals to 180 C with Esw1 and only 175 C with Emw1. The consequence of this temperature increase could be a lower final moisture content. However, the precision on mass measurements was estimated to Dm ¼ 30 mg, which involves an uncertainty on moisture content lower than DX ¼ 0.25 kg kg1. Thus, it is difficult to interpret further the difference observed between both mass evolutions at the end of drying. Considering the drying rate, it clearly appears that the level of radiation is the essential element in short-wave and mediumwave infrared. Indeed, the higher drying rate is obtained with the infrared irradiation Esw2. 3.3. Drying experiments with a temperature set point Drying experiments are performed by regulating the surface temperature at different set points. The maximum of infrared irradiation is limited at 10.2 kW m2 and is controlled using a proportional corrector. The aim is to obtain samples with different final moisture content to be analyzed by nanoindentation method. Table 2 gives the condition of experiments performed for three levels of bound temperature (130 C, 150 C and 180 C). Fig. 7a shows the incident irradiation variations during the heating step and the corresponding evolutions of surface temperature. We notice the thermal responses are similar during the first 150 s (i.e.
Fig. 6. Evolutions of product temperatures and infrared irradiation in the case of shortwave infrared emitters (a), evolutions of product temperatures and infrared irradiation in the case of medium-wave infrared emitters (b), evolution of moisture content and drying rate obtained with short-wave and medium-wave infrared emitters (c).
the infrared irradiation set point equals to 10.2 kW m2). Mainly due to the initial varnish mass, which is not exactly the same (Table 2), the mean moisture content evolutions differed during this first stage (Fig. 7b). Finally, the samples have a final moisture content varying from 0.4 kg kg1 to 0.75 kg kg1. During the varnish crosslinking, the mechanical properties, like elastic modulus or hardness, are supposed to be increasing. In order Table 2 Results of drying experiments with a temperature set point. Test Tsp Initial varnish ( C) mass (mg)
Final moisture content (kg kg1)
Mean modulus from unload (MPa)
RMS (MPa)
1 2 3
0.75 0.6 0.4
39.4 32.7 24.6
3.5 2.8 2.6
180 451 150 425 130 435
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N. Allanic et al. / International Journal of Thermal Sciences 79 (2014) 103e110 Table 3 Simulated results of diffusion coefficients estimated parameters. D1 (m2 s1)
D2 (m2 s1)
Ea (kJ mol1) b
Research intervals 1017e1013 5 107e5 105 20e40 Estimated values 1014 105 25.065
0.05e6 4.65
From these measurements, we could conclude that the crosslinking is incomplete for the tests performed at 130 C and 150 C. Indeed, the corresponding moduli are inferior to those obtained with the full crosslinking (180 C). 3.4. Comparison of simulated and experimental results An equivalent Cp taking into account crystallization peak is deduced of calorimetric analysis (Fig. 2) and introduced into the
Fig. 7. Drying results for three bound temperature (130 C, 150 C and 180 C) e surface temperature and infrared irradiation (a), moisture content and drying rate (b).
to characterize its state of curing after the drying and reticulation tests, we measured the elastic modulus of thin varnish film. The load-penetration curves are presented in Fig. 8 and Table 3 presents the different modulus values and their root mean squares. The measured stiffnesses are included between 24.6 and 39.4 MPa. A good agreement is found between our Young’s modulus values and literature. For example, Ferencz et al. [25] evidenced an EPDM Young’s modulus from 30 to 48 MPa by using AFM nanoindentation. In another study, Yusoh and Song [26] studied the mechanical behavior of polyurethane elastomer/organoclay composites; they evidenced some stiffness values closed to 14 MPa for the virgin elastomer. As expected, our values could present an overestimate due to the varnish presence.
Fig. 8. Load-penetration curves resulting of nanoindentation tests.
Fig. 9. Confrontation of experimental and simulated results for three infrared irradiations (a) Esw1 ¼ 10.2 kW m2, (b) Esw2 ¼ 15.4 kW m2, (c) Esw3 ¼ 20.3 kW m2.
N. Allanic et al. / International Journal of Thermal Sciences 79 (2014) 103e110
model. For the simulations; the limit temperature Tl ¼ 180 C is considered. In this study, the values of D1 and D2 are fixed. At the opposite, the parameters Ea and a are estimated by inverse method. The minimization is performed on mass and surface temperature evolutions, obtained for low infrared irradiation [23]. Thus, an experiment with short-wave infrared irradiation Esw1 ¼ 10.2 kW m2 is used for the estimation procedure. Tests are performed for several values of D1 and D2 and boundary values of parameters. The retained set of parameters is given in Table 3. Fig. 9 compares experimental results (noted exp) and simulated results (noted sim) for three short-wave infrared irradiations Esw1 ¼ 10.2 kW m2, Esw2 ¼ 15.4 kW m2 and Esw3 ¼ 20.3 kW m2. For each case, the gap between simulated and experimental moisture content remains lower than 0.25 kg kg1. This value corresponds to the uncertainty on mass measurement. In parallel, we can note that the mean squares between experimental and simulated surface temperature of varnish are respectively 2.6 C for Esw1, 8 C for Esw2 and 14 C for Esw3. These gaps are mainly due to an overestimation of simulated temperature during the second stage of drying, when the drying rate is highest and activity close to one. These results show the necessity to improve the determination of water activity. Moreover, it can be interesting to introduce reticulation energy before estimating mass diffusion coefficient. Despite of this fact, the final substrate temperatures are well described in the three cases: this denotes a good description of thermal and radiative properties of materials. 4. Conclusion In this work, the behavior of water based varnish exposed to infrared radiation was analyzed with an adapted instrumentation of temperature sensors inside the substrate and the measurement of weight loss in continuous. The experimental investigation showed the influence of infrared irradiation on drying rate and heating rate. The analysis performed on varnish showed the necessity to control the infrared irradiation and to perform experiments with low infrared irradiation with well-known mechanisms to improve numerical parameters determination. The study has also enabled to determine the methodology to link the state of reticulation with the varnish mechanical properties. In the following steps, the experimental and numerical tools could be used to define quality criteria and determine optimal temperature and moisture content evolutions to obtain a fixed final reticulated stage. References [1] R. Dhib, Infrared drying: from process modelling to advanced process control, Dry. Technol. 25 (2007) 97e105. [2] Z. Ul-Islam, R. Dhib, Y. Dahman, Modeling of infrared drying of polymer solutions, Chem. Prod. Process Model. 5 (2010) 1. Article 21. [3] P. Dufour, Control engineering in drying technology: review and trends, Dry. Technol. 24 (2006) 889e904. [4] N. Allanic, P. Salagnac, P. Glouannec, Convective and radiant drying of a polymer aqueous solution, Heat Mass Transfer 43 (10) (2007) 1087e1095. [5] A. Overbeek, Polymer heterogeneity in waterborne coatings, J. Coat. Technol. Res. 7 (1) (2010) 1e21. [6] I. Ludwig, W. Schabel, P. Ferlin, J.C. Castaing, M. Kind, Drying, film formation and open time of aqueous polymer dispersions, Eur. Phys. J. Spec. Top. 166 (2009) 39e43. [7] J.Z. Lai, Y.C. Chang, J.T. Yeh, K.N. Chen, Single component self-curable aqueousbased PU system with new aziridinyl curing agent, J. Appl. Polym. Sci. 91 (2004) 1997e2007. [8] J.Z. Lai, P.J. Chen, J.T. Yeh, K.N. Chen, A cross self-curing system for an aqueousbased PU hybrid, J. Appl. Polym. Sci. 97 (2005) 550e558. [9] P. Le Bideau, J.P. Ploteau, P. Dutournie, P. Glouannec, Experimental and modelling study of superficial elastomer vulcanization by short wave infrared radiation, Int. J. Therm. Sci. 48 (2009) 573e582.
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[10] J.P. Ploteau, P. Glouannec, H. Noël, Thermoelectric flux-meters for infrared radiation measurements, Appl. Therm. Eng. 27 (2e3) (2007) 674e681. [11] N. Allanic, P. Salagnac, P. Glouannec, J.P. Ploteau, Experimental study of the drying and curing of water based varnishes by infrared radiation, in: A.S. Mujumdar (Ed.), 16th International Drying Symposium, Hyderabad, India, 9e12 November 2008, 2008, pp. 1219e1224. [12] S. Khalloufi, C. Almeida-Rivera, P. Bongers, A fundamental approach and its experimental validation to simulate density as a function of moisture content during drying processes, J. Food Eng. (2010) 177e187. [13] J. Frias, J.C. Olivieira, K. Schittkowski, Modelling and parameter identification of a maltodextrin DE 12 drying process in a convection oven, Appl. Math. Model. 25 (2001) 449e462. [14] S. Basu, U.S. Shivhare, A.S. Mujumdar, Models for sorption isotherms for foods: a review, Dry. Technol. 24 (2006) 917e930. [15] A. Belghit, A. Bennis, Experimental analysis of the drying kinetics of cork, Energy Convers. Manage. 50 (2008) 618e625. [16] X. Li, B. Bhushan, A review of nanoindentation continuous stiffness measurement technique and its applications, Mater. Charact. 48 (1) (2002) 11e36. [17] I.B. Topcu, T. Bilir, Experimental investigation of drying shrinkage cracking of composite mortars incorporating crushed tile fine aggregate, Mater. Des. 31 (9) (2010) 4088e4097. [18] W.C. Oliver, G.M. Pharr, An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments, J. Mater. Res. 7 (1992) 1564e1583. [19] A. Erriguible, P. Bernada, F. Couture, M.A. Roques, Simulation of vaccum drying by coupling models, Chem. Eng. Process. (2007) 1274e1285. [20] A.S. Mujumdar, Handbook of Industrial Drying, third ed., Taylor & Francis, Philadelphia, 2007. [21] F.P. Incropera, D.P. De Witt, Fundamentals of Heat and Mass Transfer, fourth ed., John Wiley & Sons Inc., 1996. [22] R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, second ed., John Wiley & Sons, Inc., 2002. [23] N. Allanic, P. Salagnac, P. Glouannec, B. Guerrier, Estimation of an effective water diffusion coefficient during infrared-convective drying of a polymer solution, AIChE J. 55 (9) (2009) 2345e2355. [24] P. Navarri, J. Andrieu, High-intensity infrared drying study. II. Case of thin coated films, Chem. Eng. Process. 32 (1993) 319e325. [25] R. Ferencz, J. Sanchez, B. Blümich, W. Herrmann, AFM nanoindentation to determine Young’s modulus for different EPDM elastomers, Polym. Test. 31 (3) (2012) 425e432. [26] K. Yusoh, J. Jin, M. Song, Subsurface mechanical properties of polyurethane/ organoclay nanocomposite thin films studied by nanoindentation, Prog. Org. Coatings 67 (2) (2010) 220e224.
Nomenclature
Symbols aw: water activity b: water diffusion coefficient parameters C: water activity parameter Cp: specific heat capacity, J kg1 K1 D: water diffusion coefficient, m2 s1 D1, D2: water diffusion coefficient parameters, m2 s1 hc: heat convective exchange coefficient, W m2 K1 e: thickness, m E: infrared radiation, W m2 Ea: activation energy, J mol1 Fm: evaporation rate, kg m2 s1 K: water activity parameter km: mass transfer coefficient, m s1 Lv: latent heat of vaporization, J kg1 Mv: molecular weight, kg mol1 Pt: atmospheric pressure, Pa Pv: water vapor pressure, Pa R: gas constant, J mol1 K1 T: temperature, K T1, T2, T3: thermocouple measures, K t: time, s W: moisture content in dried basis, kg1 kg1 Wm: water activity parameter Greek letters
a: infrared absorptivity ε: product emissivity x: spatial coordinate, m ɸ: heat flow, W m2 l: thermal conductivity, W m1 K1 r: density, kg m3
110
j: linear shrinkage coefficient s: StefaneBoltzmann constant, W m2 K4 Subscripts a: ambient d: dried product IR: infrared l: limit
N. Allanic et al. / International Journal of Thermal Sciences 79 (2014) 103e110 s: substrate sat: saturated sp: set point surf: surface sw: short waves mw: medium waves 0: initial value *: dimensionless v: varnish
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International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
Infrared drying of water based varnish coated on elastomer substrate Nadine Allanic a, *, Pascal Le Bideau b, Patrick Glouannec b, Alain Bourmaud b a b
LUNAM Université, IUT de Nantes, CNRS, GEPEA, UMR 6144, BP 539, 44475 Carquefou Cedex, France Laboratoire d’Ingénierie des Matériaux de Bretagne, Université Européenne de Bretagne, BP 92116, 56321 Lorient Cedex, France
a r t i c l e i n f o
a b s t r a c t
Article history: Received 4 August 2012 Received in revised form 17 September 2013 Accepted 14 January 2014 Available online 14 February 2014
This study deals with the drying and curing of polyurethane water based varnish by infrared radiation. The varnish is thinly coated on rectangular elastomer substrates. After characterizing their main thermophysical properties, the curing rate is linked to the thermal behavior of varnish. A laboratory setup is developed to retrieve mass and temperature evolutions. First, drying experiments with a constant infrared radiation inferior to 20 kW m2 are performed. The thermal and hydric behaviors of the product are analyzed in term of drying time and heating rate. Then, several experiments with modulated infrared radiation are carried out. The impact of drying conditions on curing rate of varnish is then discussed. Ó 2014 Elsevier Masson SAS. All rights reserved.
Keywords: Experiment Nanoindentation Calorimetric analysis Numerical model Inverse method Crosslinking
1. Introduction In industry, rubber profiles designed for the automotive sector are produced on extrusion lines. During its manufacturing, the extruded product successively undergoes many thermal operations. One of them consists in drying and reticulating a thin film of varnish applied on the profile surface. The reticulated varnish protects the profile of its environment (light, humidity), increases its water tightness, accentuates the product brilliance or increases the abrasion protection. The topical environmental challenges encourage industries to use water based varnishes instead of organic based varnish [1,2]. Thus, the drying step needs a larger amount of energy. A classical solution is to add in the industrial process a superficial radiative heat source, such as infrared technologies [3,4]. Previous works [5,6] have shown the difficulty to dry aqueous polymer solution or dispersion without forming an impermeable skin at the surface of the solution. The use of superficial heating, in case of thin polymer film drying such as varnishes, needs a good control of energy inputs to avoid material deterioration. This work deals with the infrared heating of a water based varnish containing polyurethane, coated on an elastomer substrate. Due to several physical phenomena involved in the drying (evaporation, shrinkage, crystallization, crosslinking.) [7,8], the product * Corresponding author. Tel.: þ33 (0) 2 28 09 20 26; fax: þ33 (0) 2 28 09 20 17. E-mail address: [email protected] (N. Allanic). 1290-0729/$ e see front matter Ó 2014 Elsevier Masson SAS. All rights reserved. http://dx.doi.org/10.1016/j.ijthermalsci.2014.01.013
is very sensitive to energy inputs. Thus, to understand well the product’s behavior, an experimental laboratory setup, enabling to obtain the drying kinetics of thin coat during drying under infrared radiation, is involved. First, the influence of level of infrared radiation on the heat and mass transfers during the drying is studied. In parallel, a comparison of drying with short-wave and mediumwave infrared radiations is performed. After examining the results, an experimental investigation which consists in modulating the infrared irradiation to dry the product at a constant level of temperature is presented. The final state of crosslinking is linked with the mechanical properties of the varnish by a nanoindentation method, which confirms the possibility to improve the quality of the final product by the control of the infrared inputs. 2. Material and techniques 2.1. Experimental dryer and procedure The experimental dryer enables to perform experiments with infrared heating combined with natural convection (Fig. 1). The infrared emitters are placed at the upper side of the chamber. Experiments were performed separately with short-wave and medium-wave infrared emitters having a low thermal inertia. The nominal powers of the lamps are respectively of 2 kW for shortwave infrared lamp and 1.5 kW for medium-wave infrared lamp. Each lamp is fitted out with a parabolic reflector to obtain a homogenous radiation on the product surface. A power controller unit
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N. Allanic et al. / International Journal of Thermal Sciences 79 (2014) 103e110
Fig. 1. Experimental setup.
operating in syncopated wave train controls the electrical power supplied to the emitter [9]. This unit is controlled by an input voltage (0e10 V). The infrared radiation received by the product is measured using a sensor developed at the laboratory for both kinds of emitters [10]. The laboratory dryer was designed in order to measure the evolutions of mass and temperatures. Thus, the substrate is placed on a weighting system, located in the chamber. Several precautions are necessary to limit disturbances of mass measurements during the drying stage. Two glass plates are located between the emitters and the sample to avoid convection phenomena involved by emitters’ fan inside the chamber. It is also important to avoid the increase of air temperature around the sample during drying. Thus, the chamber is a closed enclosure, whose walls are cooled down with a water circulation. The sample is surrounded with a plate cooled down with the same water circulation. The sample, schematized in Fig. 1, is constituted of an elastomer plate of dimensions 100 50 4 mm. A spray gun is used to apply a thin film of varnish, corresponding to a thickness of 80 mm, at the upper surface of the substrate. In order to record the temperature evolutions of the substrate, three K-type thermocouples of diameter 200 mm are placed inside the elastomer: at the surface (T1), 2 mm-deep (T2) and 4 mm-deep (T3). An optical pyrometer measures the surface temperature (Tsurf) of the varnish. The emissivity is assumed to be constant and equal to 0.93. The measurement of air temperature is also performed by a K-type thermocouple inserted in a cylindrical radiative shield. All sensors are connected to an acquisition system. Despite the significant precautions taken to avoid it, a drift of the weighting caused by the increase of the air temperature inside the chamber is observed. Thus, before each experiment, a no-load test (substrate without varnish and without thermocouples) is performed to correct it. Then, at each level of infrared radiation, an experiment is performed with a first instrumented coated substrate to measure the temperature evolutions. A second experiment is performed using a coated substrate without thermocouples to
avoid disturbances on the mass measurement. Using this configuration, the precision on mass measurement is estimated to 30 mg.
2.2. Material description A water-based black varnish containing polyurethane is studied. A thermogravimetric analysis (TGA), performed at 2 C/min, showed that water is not the only volatile constituent of the varnish [11]. Several weight losses were observed before 100 C, corresponding to an evaporation of solvent. The density of its dried and reticulated base, measured with a pycnometer, is rvd ¼ 1120 kg m3. The varnish density is expressed by Ref. [12]:
rv ¼ rvd
1þW 1 þ jW
(1)
with W the moisture content in dry basis.
Fig. 2. Calorimetric analysis of dried varnish from 20 C to 240 C at heating rate of 20 K/min.
N. Allanic et al. / International Journal of Thermal Sciences 79 (2014) 103e110
To characterize the curing phenomena, a differential scanning calorimetry analysis (DSC) was investigated on samples of varnish dried three hours at 80 C. Two thermal cycles were carried out in a temperature range of 20 Ce240 C at a heating rate of 20 C/min. Product can be assumed to be not cured during the first temperature cycle and cured during the second one. Fig. 2 presents the obtained heat flows. Below 120 C, the observed peaks correspond to evaporation of residual solvent. The comparison of the first and second increases of temperature shows several exothermic peaks after 120 C, corresponding to curing. Moreover, the peak centered around 115 C is present at the first and second temperature cycle, which is characteristic of the crystallization of one of the constituents of the varnish. Therefore, the crosslinking reaction was studied by means of a second calorimetric analysis, performed on varnish with its initial moisture content. The varnish was heated from the ambient temperature to 180 C according to a temperature increase of 10 C/min. Then, the temperature remains constant during 10 min. Two temperature cycles were performed. During the first cycle, the varnish is dried and reticulated. Fig. 3 presents a zoom of this analysis after the evaporation stage of water and solvents. The difference of heat flow levels between both temperature cycles is mainly due to the reticulation reaction. After 10 min with a constant temperature of 180 C, the heat flows become equivalent. The varnish is thus totally reticulated. This analysis shows that the kinetic of the reticulation may be deduced from the temperature evolution of the product during drying. The isotherm desorption (water activity of a product) of the product was measured at a temperature of 60 C. Varnish was introduced in a dish of 30 mm and placed into a climatic room, which humidity and temperature were regulated [4]. Fig. 4 shows that the evolution of water activity decreases for low moisture content. Indeed, the critical moisture content is located between WC ¼ 0.1e0.15 kg kg1. The isotherm desorption was expressed using a GAB model [13e15]:
W ¼
Wm CKaw ð1 Kaw Þð1 Kaw þ CKaw Þ
(2)
with the fitted parameters Wm ¼ 0.0152, C ¼ 0.6139 and K ¼ 0.9887. The studied elastomer contains about 28 wt% EPDM gum, 39 wt % reinforcing agent (carbon black, chalk.) and about 33 wt% of other components (oil, sulfur, activators, accelerators, antioxidant.). Its properties were previously determined [9] and are given in Table 1.
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Fig. 4. Isotherm desorption (water activity) of varnish measured at 60 C.
2.3. Nanoindentation measurements Nanoindentation tests were investigated, involving the contact of an indenter on the samples surface and its penetration to a specified load or depth. Using the load versus penetration depth responses, effective elastic modulus and hardness were calculated [16,17]. Indentation tests were performed with a commercial nanoindentation system (Nanoindenter XP, MTS Nano Instruments) at room temperature (23 1 C) with a continuous stiffness measurement (CSM) technique. In this technique, an oscillating force at controlled frequency (70 Hz) and amplitude (3 nm) was superimposed onto a nominal applied force. After the indenter made contact with the surface, it was driven into the material with a constant strain rate, 0.05 s1 to a depth of 5000 nm; the load was held at its maximum value for 60 s; finally, the indenter was withdrawn from the surface with the same rate as loading until 10% of the maximum load was reached. The modulus values have been obtained from the unloading segment according to the work of Oliver and Pharr. [18]. 2.4. Mathematical modeling Model is briefly presented here since it was previously described [4,23]. Mass transfers are unidirectional and varnish temperature is homogenous. Inside the product, only liquid diffusion is considered. The evaporation (Fm) is located at the product’s surface and involves a linear shrinkage (j). By assuming a local thermodynamical equilibrium [19,20], the drying rate Fm is usually given by Refs. [21,22]:
Fm ¼ km
Pt Mv Pt Pv ðTÞ ln Pt aw Pvsat ðTÞ RT
(3)
Governing equations are expressed in a dimensionless form and in a fixed base linked to the dried product (0 < x < ed) to ease numerical resolution. Thus, the mass balance is written [4]:
vW * v ¼ * vt * vx
D* ðW; TÞ
vW *
! (4)
2 * vx 1 þ jW0 W *
with D* ¼ D/D0, W* ¼ W/W0, t* ¼ tD0/e2d, and x* ¼ x/ed. Table 1 Thermophysical properties of elastomer substrate.
Fig. 3. Calorimetric analysis of varnish.
l (W m1 K1)
r (kg m3)
Cp (J kg1 K1)
0.32
0.73 T þ 1215
2.73 T þ 1420
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N. Allanic et al. / International Journal of Thermal Sciences 79 (2014) 103e110
The mass diffusion coefficient is expressed as follows [23,24]: ERTa
DðW; TÞ ¼ D1 þ D2 e
eW b
(5)
with D1, D2, Ea and b constant values. The parameter D1 was introduced in the expression in order to avoid the divergence of numerical solving when the moisture content tends to zero (end of the drying). The mass transfer boundary condition at the varnish surface is expressed by:
x* ¼ 1 Fm ð1 þ JWÞ2 ¼ r0v D* D0
W0 vW
(6)
*
ed vx
The assumption of impermeable substrate results in the following boundary condition:
vW *
x* ¼ 0
*
vx
¼ 0
(7)
The heat balance for the varnish is given by:
D0 vT *
rv cp;v e
e2d vt *
*4 ¼ hc Ta* T * þ εs Tw T *4 þ
1 ðf Tl T0 s
þ av EIR Fm Lv Þ (8) with T* ¼ T T0/Tl T0, Ta* ¼ Ta T0 =Tl T0 and * ¼ T T =T T . Tw w 0 l 0 Tl corresponds to a limit temperature and ɸs is the conductive heat transfer at the substrate/varnish interface. T0 is the initial temperature of the varnish. An efficient heat capacity of dried varnish cp,vd is deduced from calorimetric analysis and introduced into the model (Fig. 2). Thus, the heat capacity of varnish cp,v is expressed by:
cpv ¼ cp;vd
1 W þ cp;w 1þW 1þW
(9)
Due to its radiative properties [11], the infrared radiation av EIR is assumed absorbed at the varnish surface. Thus, the transfer of energy inside the substrate is mainly due to conductive transfer. The experimental temperature (T3) is introduced as a boundary condition inside the model for the bottom face. However, numerical studies conducted in parallel have shown that this temperature can be numerically determined by assuming that the substrate is a semi-infinite medium. The initial conditions are:
t* ¼ 0
W* ¼ 1
T* ¼ 0
3.1. Preliminary drying experiments In this experimental investigation, samples were exposed to infrared radiation until their temperature reached the limit temperature Tl ¼ 180 C. Considering the calorimetric analysis (Figs. 2 and 3), the varnish is partially cured at this temperature. Fig. 5 presents the experimental drying kinetics obtained with a short infrared irradiation of Esw1 ¼ 10.2 kW m2. In order to analyze the impact of varnish presence on the thermal response, the measured temperature of the substrate without varnish (noted “no varnish” on Fig. 5) for the same solicitation (Esw1) is also reported. Moreover, the evolution of air temperature inside the chamber, which progressively increases to reach 36 C at the end of experiment, is also given. During the first 20 s, the temperature of product remains constant, which corresponds to the period before starting the emitters. Ten seconds after, the gradient of temperature inside the product, varnished or not, reaches 25 C. For the substrate without varnish, the elastomer surface temperature, measured with thermocouple T1 and optical pyrometer (Tsurf), are similar. The temperature difference stays lower than 1 K. In the case of varnished substrate, due to the energy used for water evaporation, the surface temperature remains relatively constant while mean moisture content begins to considerably decrease. This step corresponds to a water activity product close to 1 (Fig. 4). During this step, both temperatures Tsurf and T1 are similar. Then, one observes a difference less than 1 K which progressively increases and reaches 10 K at 250 s. This result shows that the surface temperature is certainly underestimated. Indeed, in this work, the emissivity of the product is assumed to be constant. In fact, it decreases all along the drying due to water evaporation which has a consequence on measured temperature by optical pyrometer. In another way, it is possible that the thermocouple T1 receives a part of infrared irradiation and thus gives an overestimated temperature. In the elastomer, the product temperature at the middle position (T2) and on the bottom face (T3) is progressively lower for the varnished substrate compared to not varnished substrate. At the end of the experiment, the gaps are respectively of 5 C for T2 and 7 C for T3. After 70 s, the mean moisture content of varnish begins to slowly decrease, which corresponds to the third stage of drying, when activity is lower. Thus, the surface temperature increases to reach a value close to the case of substrate heated without varnish. Thus, the experimental curves are used to determine the global absorptivity of varnish towards emitters infrared radiation. At the beginning of heating, the substrate can be considered as a semi-
(10)
A control volume method is used to spatially integrate the differential equations. All the equations were simultaneously solved by means of a predictorecorrector method with a high order. The coupling and the nonlinearity of equations were solved by a Newton method. Forty control volumes were considered in the varnish (only for mass balance) and twenty control volumes in the elastomer substrate. The time step was variable to ensure the convergence of calculations. 3. Results and discussion Several configurations of drying have been tested and are now discussed. A mass of 415 35 mg is applied on substrate, which corresponds to a thickness of 80 7 mm.
Fig. 5. Evolution of temperature obtained for substrate with and without varnish for short-wave infrared with Esw1 ¼ 10 kW m2.
N. Allanic et al. / International Journal of Thermal Sciences 79 (2014) 103e110
107
infinite medium, with constant thermophysical properties. We assume that convective and long wave radiative exchanges are negligible comparable to incident infrared radiation. Knowing substrate absorptivity (as ¼ 0.57) [9], varnish absorptivity is estimated using the temperature evolutions of substrate with and without varnish thanks to the following relation:
av ¼ as
v =dt dTsurf s =dt dTsurf
(11)
Mean absorptivity av calculated during the period t ¼ 5 s and t ¼ 20 s is av ¼ 0.64. A similar analysis carried out on dried product gives an identical value. 3.2. Curing with short-wave and medium-wave infrared radiation The influence of the spectral domain of the emitters (short-wave and medium-wave) is now studied. Indeed, it avoids moving the emission spectrum to medium-wave infrared wavelengths. Experiments were performed with infrared irradiation of Esw1 ¼ 10.2 kW m2 and Esw2 ¼ 15.4 kW m2 corresponding respectively to 40% and 60% of control voltage. For medium-wave infrared lamps, the infrared radiations tested are Emw1 ¼ 10 kW m2 and Emw2 ¼ 13 kW m2, corresponding respectively of 70% and 100% of control voltage. Fig. 6 presents the evolutions of product temperature (6a and 6b), mean moisture content and drying rate (6c), obtained for the four tests previously described. Experiments were stopped when the product temperature reached 180 C to avoid its deterioration. First, the comparison of evolution of short-wave infrared radiation (6a) and medium-wave infrared irradiation (6b) shows a quicker setting period for short-waves emitters. For each test, the three steps in heating previously described are also observed. For the same infrared irradiation, even if the varnish temperature increases slightly quicker with short-wave infrared than with medium-wave infrared, the behavior of varnish is globally the same. When the drying rate decreases, differences begin to appear between the two drying kinetics. At 350 s, when the drying can be considered as over, the moisture content is W ¼ 0.78 kg kg1 for Esw1 and W ¼ 0.98 kg kg1 for Emw1. Esw1 ¼ 10.2 kW m2 is slightly higher than Emw1 ¼ 10 kW m2. Thus, the surface temperature increases slightly higher in the first case. At the end of drying, Tsurf is equals to 180 C with Esw1 and only 175 C with Emw1. The consequence of this temperature increase could be a lower final moisture content. However, the precision on mass measurements was estimated to Dm ¼ 30 mg, which involves an uncertainty on moisture content lower than DX ¼ 0.25 kg kg1. Thus, it is difficult to interpret further the difference observed between both mass evolutions at the end of drying. Considering the drying rate, it clearly appears that the level of radiation is the essential element in short-wave and mediumwave infrared. Indeed, the higher drying rate is obtained with the infrared irradiation Esw2. 3.3. Drying experiments with a temperature set point Drying experiments are performed by regulating the surface temperature at different set points. The maximum of infrared irradiation is limited at 10.2 kW m2 and is controlled using a proportional corrector. The aim is to obtain samples with different final moisture content to be analyzed by nanoindentation method. Table 2 gives the condition of experiments performed for three levels of bound temperature (130 C, 150 C and 180 C). Fig. 7a shows the incident irradiation variations during the heating step and the corresponding evolutions of surface temperature. We notice the thermal responses are similar during the first 150 s (i.e.
Fig. 6. Evolutions of product temperatures and infrared irradiation in the case of shortwave infrared emitters (a), evolutions of product temperatures and infrared irradiation in the case of medium-wave infrared emitters (b), evolution of moisture content and drying rate obtained with short-wave and medium-wave infrared emitters (c).
the infrared irradiation set point equals to 10.2 kW m2). Mainly due to the initial varnish mass, which is not exactly the same (Table 2), the mean moisture content evolutions differed during this first stage (Fig. 7b). Finally, the samples have a final moisture content varying from 0.4 kg kg1 to 0.75 kg kg1. During the varnish crosslinking, the mechanical properties, like elastic modulus or hardness, are supposed to be increasing. In order Table 2 Results of drying experiments with a temperature set point. Test Tsp Initial varnish ( C) mass (mg)
Final moisture content (kg kg1)
Mean modulus from unload (MPa)
RMS (MPa)
1 2 3
0.75 0.6 0.4
39.4 32.7 24.6
3.5 2.8 2.6
180 451 150 425 130 435
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N. Allanic et al. / International Journal of Thermal Sciences 79 (2014) 103e110 Table 3 Simulated results of diffusion coefficients estimated parameters. D1 (m2 s1)
D2 (m2 s1)
Ea (kJ mol1) b
Research intervals 1017e1013 5 107e5 105 20e40 Estimated values 1014 105 25.065
0.05e6 4.65
From these measurements, we could conclude that the crosslinking is incomplete for the tests performed at 130 C and 150 C. Indeed, the corresponding moduli are inferior to those obtained with the full crosslinking (180 C). 3.4. Comparison of simulated and experimental results An equivalent Cp taking into account crystallization peak is deduced of calorimetric analysis (Fig. 2) and introduced into the
Fig. 7. Drying results for three bound temperature (130 C, 150 C and 180 C) e surface temperature and infrared irradiation (a), moisture content and drying rate (b).
to characterize its state of curing after the drying and reticulation tests, we measured the elastic modulus of thin varnish film. The load-penetration curves are presented in Fig. 8 and Table 3 presents the different modulus values and their root mean squares. The measured stiffnesses are included between 24.6 and 39.4 MPa. A good agreement is found between our Young’s modulus values and literature. For example, Ferencz et al. [25] evidenced an EPDM Young’s modulus from 30 to 48 MPa by using AFM nanoindentation. In another study, Yusoh and Song [26] studied the mechanical behavior of polyurethane elastomer/organoclay composites; they evidenced some stiffness values closed to 14 MPa for the virgin elastomer. As expected, our values could present an overestimate due to the varnish presence.
Fig. 8. Load-penetration curves resulting of nanoindentation tests.
Fig. 9. Confrontation of experimental and simulated results for three infrared irradiations (a) Esw1 ¼ 10.2 kW m2, (b) Esw2 ¼ 15.4 kW m2, (c) Esw3 ¼ 20.3 kW m2.
N. Allanic et al. / International Journal of Thermal Sciences 79 (2014) 103e110
model. For the simulations; the limit temperature Tl ¼ 180 C is considered. In this study, the values of D1 and D2 are fixed. At the opposite, the parameters Ea and a are estimated by inverse method. The minimization is performed on mass and surface temperature evolutions, obtained for low infrared irradiation [23]. Thus, an experiment with short-wave infrared irradiation Esw1 ¼ 10.2 kW m2 is used for the estimation procedure. Tests are performed for several values of D1 and D2 and boundary values of parameters. The retained set of parameters is given in Table 3. Fig. 9 compares experimental results (noted exp) and simulated results (noted sim) for three short-wave infrared irradiations Esw1 ¼ 10.2 kW m2, Esw2 ¼ 15.4 kW m2 and Esw3 ¼ 20.3 kW m2. For each case, the gap between simulated and experimental moisture content remains lower than 0.25 kg kg1. This value corresponds to the uncertainty on mass measurement. In parallel, we can note that the mean squares between experimental and simulated surface temperature of varnish are respectively 2.6 C for Esw1, 8 C for Esw2 and 14 C for Esw3. These gaps are mainly due to an overestimation of simulated temperature during the second stage of drying, when the drying rate is highest and activity close to one. These results show the necessity to improve the determination of water activity. Moreover, it can be interesting to introduce reticulation energy before estimating mass diffusion coefficient. Despite of this fact, the final substrate temperatures are well described in the three cases: this denotes a good description of thermal and radiative properties of materials. 4. Conclusion In this work, the behavior of water based varnish exposed to infrared radiation was analyzed with an adapted instrumentation of temperature sensors inside the substrate and the measurement of weight loss in continuous. The experimental investigation showed the influence of infrared irradiation on drying rate and heating rate. The analysis performed on varnish showed the necessity to control the infrared irradiation and to perform experiments with low infrared irradiation with well-known mechanisms to improve numerical parameters determination. The study has also enabled to determine the methodology to link the state of reticulation with the varnish mechanical properties. In the following steps, the experimental and numerical tools could be used to define quality criteria and determine optimal temperature and moisture content evolutions to obtain a fixed final reticulated stage. References [1] R. Dhib, Infrared drying: from process modelling to advanced process control, Dry. Technol. 25 (2007) 97e105. [2] Z. Ul-Islam, R. Dhib, Y. Dahman, Modeling of infrared drying of polymer solutions, Chem. Prod. Process Model. 5 (2010) 1. Article 21. [3] P. Dufour, Control engineering in drying technology: review and trends, Dry. Technol. 24 (2006) 889e904. [4] N. Allanic, P. Salagnac, P. Glouannec, Convective and radiant drying of a polymer aqueous solution, Heat Mass Transfer 43 (10) (2007) 1087e1095. [5] A. Overbeek, Polymer heterogeneity in waterborne coatings, J. Coat. Technol. Res. 7 (1) (2010) 1e21. [6] I. Ludwig, W. Schabel, P. Ferlin, J.C. Castaing, M. Kind, Drying, film formation and open time of aqueous polymer dispersions, Eur. Phys. J. Spec. Top. 166 (2009) 39e43. [7] J.Z. Lai, Y.C. Chang, J.T. Yeh, K.N. Chen, Single component self-curable aqueousbased PU system with new aziridinyl curing agent, J. Appl. Polym. Sci. 91 (2004) 1997e2007. [8] J.Z. Lai, P.J. Chen, J.T. Yeh, K.N. Chen, A cross self-curing system for an aqueousbased PU hybrid, J. Appl. Polym. Sci. 97 (2005) 550e558. [9] P. Le Bideau, J.P. Ploteau, P. Dutournie, P. Glouannec, Experimental and modelling study of superficial elastomer vulcanization by short wave infrared radiation, Int. J. Therm. Sci. 48 (2009) 573e582.
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[10] J.P. Ploteau, P. Glouannec, H. Noël, Thermoelectric flux-meters for infrared radiation measurements, Appl. Therm. Eng. 27 (2e3) (2007) 674e681. [11] N. Allanic, P. Salagnac, P. Glouannec, J.P. Ploteau, Experimental study of the drying and curing of water based varnishes by infrared radiation, in: A.S. Mujumdar (Ed.), 16th International Drying Symposium, Hyderabad, India, 9e12 November 2008, 2008, pp. 1219e1224. [12] S. Khalloufi, C. Almeida-Rivera, P. Bongers, A fundamental approach and its experimental validation to simulate density as a function of moisture content during drying processes, J. Food Eng. (2010) 177e187. [13] J. Frias, J.C. Olivieira, K. Schittkowski, Modelling and parameter identification of a maltodextrin DE 12 drying process in a convection oven, Appl. Math. Model. 25 (2001) 449e462. [14] S. Basu, U.S. Shivhare, A.S. Mujumdar, Models for sorption isotherms for foods: a review, Dry. Technol. 24 (2006) 917e930. [15] A. Belghit, A. Bennis, Experimental analysis of the drying kinetics of cork, Energy Convers. Manage. 50 (2008) 618e625. [16] X. Li, B. Bhushan, A review of nanoindentation continuous stiffness measurement technique and its applications, Mater. Charact. 48 (1) (2002) 11e36. [17] I.B. Topcu, T. Bilir, Experimental investigation of drying shrinkage cracking of composite mortars incorporating crushed tile fine aggregate, Mater. Des. 31 (9) (2010) 4088e4097. [18] W.C. Oliver, G.M. Pharr, An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments, J. Mater. Res. 7 (1992) 1564e1583. [19] A. Erriguible, P. Bernada, F. Couture, M.A. Roques, Simulation of vaccum drying by coupling models, Chem. Eng. Process. (2007) 1274e1285. [20] A.S. Mujumdar, Handbook of Industrial Drying, third ed., Taylor & Francis, Philadelphia, 2007. [21] F.P. Incropera, D.P. De Witt, Fundamentals of Heat and Mass Transfer, fourth ed., John Wiley & Sons Inc., 1996. [22] R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, second ed., John Wiley & Sons, Inc., 2002. [23] N. Allanic, P. Salagnac, P. Glouannec, B. Guerrier, Estimation of an effective water diffusion coefficient during infrared-convective drying of a polymer solution, AIChE J. 55 (9) (2009) 2345e2355. [24] P. Navarri, J. Andrieu, High-intensity infrared drying study. II. Case of thin coated films, Chem. Eng. Process. 32 (1993) 319e325. [25] R. Ferencz, J. Sanchez, B. Blümich, W. Herrmann, AFM nanoindentation to determine Young’s modulus for different EPDM elastomers, Polym. Test. 31 (3) (2012) 425e432. [26] K. Yusoh, J. Jin, M. Song, Subsurface mechanical properties of polyurethane/ organoclay nanocomposite thin films studied by nanoindentation, Prog. Org. Coatings 67 (2) (2010) 220e224.
Nomenclature
Symbols aw: water activity b: water diffusion coefficient parameters C: water activity parameter Cp: specific heat capacity, J kg1 K1 D: water diffusion coefficient, m2 s1 D1, D2: water diffusion coefficient parameters, m2 s1 hc: heat convective exchange coefficient, W m2 K1 e: thickness, m E: infrared radiation, W m2 Ea: activation energy, J mol1 Fm: evaporation rate, kg m2 s1 K: water activity parameter km: mass transfer coefficient, m s1 Lv: latent heat of vaporization, J kg1 Mv: molecular weight, kg mol1 Pt: atmospheric pressure, Pa Pv: water vapor pressure, Pa R: gas constant, J mol1 K1 T: temperature, K T1, T2, T3: thermocouple measures, K t: time, s W: moisture content in dried basis, kg1 kg1 Wm: water activity parameter Greek letters
a: infrared absorptivity ε: product emissivity x: spatial coordinate, m ɸ: heat flow, W m2 l: thermal conductivity, W m1 K1 r: density, kg m3
110
j: linear shrinkage coefficient s: StefaneBoltzmann constant, W m2 K4 Subscripts a: ambient d: dried product IR: infrared l: limit
N. Allanic et al. / International Journal of Thermal Sciences 79 (2014) 103e110 s: substrate sat: saturated sp: set point surf: surface sw: short waves mw: medium waves 0: initial value *: dimensionless v: varnish