DEVELOPMENT OF A NEW PROCEDURE FOR THE APPLICATION OF MICROWAVE ENERGY DURING MARBLE SLAB PRODUCTION
Jesus Romera-Fernndez1, Juan Monz-Cabrera2, Maria Eugenia Requena-Prez2, Maria Pilar Vila-Marn1, and Antonio Martnez-Gonzlez2
Centro Tecnolgico del Mrmol, Cehegn, E-30430, Spain. Departamento de Tecnologas de la Informacin y las Comunicaciones, Universidad Politcnica de Cartagena, Cartagena, E-30202 Spain.
In this work a new microwave-heating procedure is presented as a viable alternative for both the conventional and ultraviolet (UV) curing systems used in the natural stone industry. Both thermal simulations and experimental tests demonstrate that microwave energy highly reduces curing and storing times while maintaining the products final quality. Several polymer mixtures have been obtained from commercial products and fillers for maximum microwave absorption and their complex permittivity has been properly measured. A continuous industrial microwave oven has been built specifically for this purpose and tested on Crema-Sierra Puerta marble samples and commercial epoxy and polyester resins. Submission Date: 20 July 2006 Acceptance Date: 13 April 2007 Publication Date: 18 May 2007 INTRODUCTION The natural stone industry transforms large stone blocks into smaller regular-sized slabs by using high-precision cutting methods. After cutting and drying the slabs, the manufacturing process uses several kinds of polymers on the slab surfaces in order to both improve flexural strength and to avoid slab cracking or breaking during further production stages and during transportation. In addition, these resins are used to improve the surface appearance of the material by covering holes and veins, and providing the final shine after polishing. This surface
Keywords: microwave heating, natural stone industry, resin curing, dielectric properties, industrial applicator, marble manufacture.
appearance is very important for stone products, as they must look attractive for the purchasers. Additionally, natural stone deterioration when exposed to outdoor conditions is mainly due to chemical corrosion of aggressive pollutants, freezing cycles and crystallization of salt solutions absorbed from the environment [Toniolo , et al., 2002]. Therefore, resin coatings also play a very important role in preserving the surface appearance of stone materials, such as marble, because they reduce water and chemical absorption. The most commonly used polymers are, at the moment, epoxy and polyester. Both resins are traditionally cured in thermo-set gas ovens with conventional curing agents such as preaccelerated polyester with amine or cobalt and

Vol. 40, No. 4, 2007

Journal of Microwave Power & Electromagnetic Energy
FIGURE 1. Simulation scheme for marble slab and epoxy coating during microwave irradiation. benzoyl peroxide (PBO) or methyl-ethyl ketone peroxide (MEKP) catalysts. The time required for traditional curing of such thermo-set resins has become the bottleneck of the production process due to the fact, for instance, that epoxy needs, approximately, 2 hours to cure on marble. UV-light heating ovens are also used for polyester curing. In this case, the polyester is mixed with light sensitive catalysts and curing times are reduced to several minutes. Nevertheless, this method does not offer satisfactory curing results in the case of deep holes on the marbles surface because UV-light penetration depth is limited to a few m (micrometers) of the resin surface layer. The increasing economic requirements in the natural stone industries have led to the need for curing acceleration, production-line usage and automation. Recently, microwave-assisted curing has been shown to be a viable alternative to traditional techniques during rubber curing [Monz-Cabrera, et al., 2002], provided that uniform temperature profiles are achieved within the material. In fact, microwave-assisted polymerization has shown many advantages over conventional curing such as energy savings, more uniform curing, reduced processing times, structural changes, etc.[Nightingale, et al., 2002;

International Microwave Power Institute
Wiesbrock, et al., 2004; Zhang, et al., 2004]. However, no application has been found in the literature for the particular case of microwaveassisted curing of marble resin coatings. In this work, microwave radiation has been employed to cut down resin curing times during the marble manufacturing process. Thermal simulations and experimental tests carried out with epoxy and polyester resins show that it is possible to greatly reduce curing times without reducing the quality of the final products. Furthermore, an industrial prototype has been specifically designed and tested over CremaSierra Puerta marble samples (a special type of Spanish natural marble) and commercial epoxy mixtures. METHODS Theoretical Study In order to understand the physical phenomena involved in this industrial process several simulations have been carried out. Figure 1 shows a 2-D view of the marble slab and resin coating configuration that has been used for the simulation of the temperature evolution both in the marble slabs and in the epoxy coating during
microwave polymerization. Due to the slab geometry, a 2-D study has been considered adequate enough to obtain the numerical results for temperature distributions. The temperature evolution within the resins when they are irradiated with microwave energy can be described by the so-called heat equation [P. Plaza-Gonzlez, et al., 2004] with internal heat generation,
surfaces since no convective fluxes were considered during polymerization tests: kT T n =0 (4)

T = ( kT T ) + Qgen t

with (kg/m3) being the density of the body, cp (J/kgC) its specific heat, k T (W/mC), its thermal conductivity, T (C) its temperature, and t the elapsed time (seconds). Qgen (W/m3) takes into account the conversion of microwave energy into heat due to dielectric losses(Qgen_diel) and the exothermic heat (Qexo) generated by the epoxy or polyester resin during the curing process: Qgen = Qexo + Qgen_diel (2)
where n represents the normal direction to the considered surface. Complex permittivity of both marble and epoxy resins (*) is composed by two terms, namely the dielectric constant () and the socalled loss factor () as expressed in (5). Both the dielectric constant and the loss factor are responsible for the electric field spatial distribution within the dielectric material and thus its influence on the dielectric heating process [P. Plaza-Gonzlez, et al., 2004]: * = j (5)

In the case of the marble slab the same equation can be considered but, in this case, Qgen considers only the heat generated by dielectric losses. Usually, the dielectric volumetric heating is expressed in terms of the electric field intensity magnitude and the so-called loss factor [P. PlazaGonzlez, et al., 2004]: Qgen _ diel = 2 fE ''
However, in this work the electric field distribution is assumed to be constant both in the epoxy resin and in the marble sample for the sake of simplicity and due to the uniformity effect of sample movement within both materials. Additionally, the attenuation of the electric field is considered negligible in this case since resin coatings are very thin and the marble sample has low dielectric losses. Numerical procedure Since 2-D approach is proposed to study and optimize the temperature-driven polymerization process, the Pdetool function included in MATLAB has been used in order to mesh the domain and to determine the temperature distribution inside the sample through equations (1-4). The Partial Differential Equation (PDE) Toolbox provides an environment for the study and solution of PDEs in two space dimensions and time. In this way, the PDE Toolbox supplies several tools so that the user can define a PDE problem (definition of 2-D regions, boundary conditions, and PDE coefficients), numerically
with E being the electric field intensity magnitude; , the so-called loss factor; 0, the vacuum permittivity; and f 0, the operating frequency (around 2.45 GHz, in this case). This dielectric heating term is considered both in the case of the marble sample and the resin coatings during simulations. An adiabatic condition has been considered for both the epoxy resin and marble external
FIGURE 2. Exothermic heat generation measurement set-up. discretize and solve the PDE equations, produce an approximation to the solution and, finally, visualize the results [Mathworks, 1996]. The numerical technique implemented by Pdetool is the Finite Element Method (FEM) with an adaptive meshing algorithm and in this case it has been applied to the resolution of equations (1-4). Experimental Set-up Dielectric measurements The HP 85070 dielectric probe kit [Agilent Technologies, 2004] has been used to measure the complex permittivity of Crema-Sierra Puerta marble samples and some commercially available epoxy and polyester resins. The epoxy resins and mixtures were obtained from the EPOMAR product range. In addition, a polyester resin doped with calcium carbonate was also measured. The dielectric properties were determined at room temperature before polymerization took place by using the HP 8720 ES Network analyzer and the HP85070 C1.00 commercial software. For a complete description of measured resins please see Table 2. Exothermic heat calculation of polyester and epoxy resins Figure 2 shows the experimental set-up used to measure both the epoxy and polyester exothermic heat generation during polymerization. In this case both resins were poured into a 65 mm diameter glass tube. The UV-light curing proved to be an exothermic polymerization process hence the resins incremented their temperatures. Unfortunately, the temperature distribution within the glass was not uniform since at the glass-resin interface there were heat losses due to conduction and convection. In order to compute both the heat generated by the exothermic reactions and the heat lost at the interface, the procedure described in [MonzCabrera, et al., 2000] was applied. Therefore the temperature across the cylindrical resin sample was assumed to follow a linear form as shown in (6) T (r ) = Ts +

( R r ) (Tc Ts )

where Ts and Tc are sample surface and center temperature, respectively, R is sample radium and r represents the distance to the sample center. Both Ts and Tc were measured by means
FIGURE 3. Schematic of the industrial microwave-assisted prototype. of two fiber optic probes and the FISO fourchannel UMI signal conditioner in order to be able to estimate the temperature distribution described by (6). Two contributions are taken into account for calculating the exothermic heat generation (Q ) as shown in equation (7): one computed by exo the use of the temperature increment (Qexo_1) at the sample center and one lost at the sample edge (Qexo_2) [Monz-Cabrera et al., 2000]. Both Q exo_1 and Q exo_2 have been computed by following (8) and (9), respectively: Qexo= Qexo_1+ Qexo_2 Qexo _ 1 = c p Qexo _ 2 = kT Tc t (7) (8) of this oven are: microwave power control, a rotating crystal dish and an 800 W output power magnetron. For all tests, 552 cm3 Crema-Sierra Puerta marble samples, whose weight was around 131 grams, were employed. The samples were covered with 1 gram of a uniformly distributed epoxy mixture coating on their upper side, as described in Figure 1, which was manually applied. This epoxy mixture consisted of 100 grams of EPOMAR A resin and 25 grams of EPOMAR B resin. Additional tests also used a polyester resin doped with calcium carbonate. The initial temperature of marble samples was varied in order to find the optimal initial condition of the microwave-assisted polymerization process. Industrial Microwave-Assisted Oven A microwave-assisted prototype has been specifically designed and built to test the viability of the microwave-assisted polymerization over marble slabs coated with commercial resins under the same working conditions used by the natural stone industry. A schematic diagram of the industrial prototype is shown in Figure 3. The prototype consisted of a 0.84x0.6x4.05 m3 rectangular metallic box fed by 12 magnetrons, although only 9 magnetrons
T S /V r = kT (Tc Ts ) S / (V R)
where S is the sample surface and V its volume. Laboratory tests in a microwave oven In order to carry out polymerization tests on marble coated with epoxy resin, a SAMSUNG TDS M1711N [Samsung] commercial microwave oven was used. The main features
Table 1. Permittivity for the employed marble and several commercial resins and mixtures
Material Epomar 2003-A Epomar 2003-B 100 grams Epomar A : 25 grams Epomar B 100 grams Epomar A : 25 grams Epomar B + 5 Acelerator 960-grams Epomar A/1 : 25 grams Epomar B Polyester Resin Doped With Calcium Carbontate Crema-Sierra Marble Complex permittivity (*) 4,6052-j1,6354 5,5129-j2.8279 5,0393-j1,8526 4,3373-j1,2438 4,5488-j1,4986 4,3825-j0,4984 7,4590-j0,1509

were active during the irradiation process. All the magnetrons had an output power around 1.2 kW and were attached to the prototype by conventional waveguide launchers [Metaxas et al., 1983]. Two microwave filters with absorbing ferrites were used at the entrance and at the exit of the marble slabs to keep external radiation within the established European electromagnetic compatibility limits. The carrying system is composed of four parallel metallic chains used to support the heavy marble samples. The Crema-Sierra Puerta marble samples had a 30x30x2 cm3 volume and were uniformly covered by 100 grams of a 100 EPOMAR A : 25 EPOMAR B epoxy mixture. The irradiation time within the prototype was set to 80 seconds in order to accomplish the production speed requirements. RESULTS Dielectric Measurements Several commercial polyester and epoxy resins and mixtures generally used in the conventional polymerization processes were measured in order to decide which one was more appropriate for microwave curing. All the measurements were made at 2.45 GHz and at a room temperature around 23C. Table 1 shows
the measured complex permittivity values for several epoxy and polyester products and their mixtures. Crema-Sierra Puerta marble permittivity is also provided in this table. For mixtures, weight relationships for the main components are provided. From this data, it can be concluded that all the commercial epoxy products strongly absorb microwave radiation due to their high loss factor. However, in order to enhance microwave absorption while maintaining low costs, the 100 EPOMAR A : 25 EPOMAR B epoxy mixture was chosen for all the following experimental tests. One can also deduce from this table that the calcium-carbonate doped polyester resin has a loss factor at least three times lower than epoxy resins and their mixtures. Additionally, it is also clear from this data that the employed marble samples show a loss factor much lower than the epoxy and polyester polymers. Thus, their microwave absorption and heating rates were also expected to be lower than those of epoxy and polyester according to equations (1-3). Exothermic Volumetric Heat Generation Terms Polyester Resin Figure 4 shows the temperature evolution at the sample center and surface of polyester resin when measuring as described in Figure 2. In this
FIGURE 4. Temperature distribution evolution for polyester resin during the light-driven polymerization process. case no microwaves were applied and thus the temperature increase was due only to the exothermic curing. From this data it can be concluded that heat generation during polymerization is almost constant, since the temperature behaviors are straight lines during the main heating period. By applying equations (7-9) to the temperature data in Figure 4 the obtained average exothermic volumetric heat generation was Qexo_poliester= Qexo_1 + Qexo_2 = 40285 (W/m3). Epoxy Resin In this case, the temperature evolution during the polymerization process is depicted in Figure 5, where it can be observed that the exothermic volumetric heat depends on the temperature. Again, no microwaves were applied and the temperature increase was due entirely to the exothermic reaction. An expression of the total exothermic volumetric heat for the epoxy resin versus the temperature has been obtained by

applying equations (7-9) to the temperatures in Figure 5 and interpolating a fourth order polynomial. Figure 6 shows Qexo_epoxy versus the temperature and the interpolated data, while equation (10) shows the interpolated expression of Qexo_epoxy. Qexo_epoxi=Qexo_1+ Qexo_2 = -0.03575T4 + 13.3154T3 -1498.71T2 + 0.08124T -1.2923e6 (10) Temperature Simulations Several temperature simulations were carried out by using equations (1-4), Matlab Pdetool function and the simulation scheme in Figure 1. Table 2 shows the thermal features and volumetric heating terms used in all simulations for 100 EPOMAR A : 25 EPOMAR B epoxy mixture, for the polyester resin with calcium carbonate and for Crema-Sierra Puerta marble samples. Due to the fact that epoxy resins show
FIGURE 5. Temperature distribution evolution for epoxy resin during the light-driven polymerization process. Table 2. Thermal features and volumetric heating terms used in simulations for resins and marble
Material Thermal features = 1500 (kg/m3) 100 EPOMAR A : 25 EPOMAR B Epoxy Mixture cp = 1000 (J/kg K) kT = 1.5 (W/m C) = 1300 (kg/m3) Polyester Resin Doped With Calcium Carbonate cp = 1500 (J/kg K) kT = 0.4 (W/m C) = 2700 (kg/m3) Crema-Sierra Puerta Marble cp = 880 (J/kg K) kT = 2.5 (W/m C) Qgen = 523757 (W/m3) Qgen = 1571272 (W/m3)

Qgen = 178571 (W/m3)

FIGURE 6. Exothermic volumetric heat generation for the epoxy resin versus the temperature. an exothermic heat generation that depends on its internal temperature, an average volumetric heat term that takes into account both exothermic and microwave heat generation has been used in simulations as described in Table 2. Figure 7 shows the temperature distribution for both the epoxy coating and the marble slab at 80 seconds for an initial temperature (Tini) of both materials equal to 24 C. Additionally, Figure 8 shows the same temperature pattern for a different initial temperature: 45 C. It can be concluded from both figures that, despite the high loss factor shown by the epoxy mixture, the maximum temperature value in the resin coating only increases by 9C with respect to the initial temperature value. The reason for this behavior can be explained by the different loss factor values for the epoxy mixtures and the marble sample (see Table 1). From this data, it can be concluded that, according to equation (1) and (3), epoxy heats up almost 10 times faster than the marble sample given a constant electric
field intensity at both materials. Due to this effect and to the thermal migration phenomenon, marble absorbs a great part of the curing heat. Additionally, the mass ratio for marble and epoxy coating is very high, indicating that marble rules the temperature increase of the whole system due to its lower heating rate and its higher mass proportion. In this way, the initial temperature of the marble sample is of the utmost importance in achieving a final temperature suitable to ensure a proper polymerization process. Simulation results showed that an initial temperature of around 45-50 C was sufficient to achieve a final epoxy temperature around 55-60 C. This temperature range guarantees a good polymerization process without degrading the epoxy chemical or physical features for the employed products. Similar conclusions were obtained from simulations for polyester resins. However in this case, the temperature increase was slightly

FIGURE 7. 2-D temperature distribution at marble sample and epoxy coating for t=80 seconds. Tini = 24 C. Table 3. Quality description of laboratory tests versus initial temperature and microwave power Resin Tinitial (C) 24 Epoxy Polyester Power (W) 100 Tfinal (C) (resin/marble) 25.2 / 25 41.1 / / / / 70 27/25 43/41 Quality / Comment Bad / no polymerization Bad / incomplete polymerization Good / complete polymerization Good / some hot spots Bad / too many hot spots Bad / no polymerization
Good / polymerization but matt look initial temperatures and microwave power values. Table 3 shows the quality of the surface appearance and the coatings consistency versus different initial temperatures as well as microwave power values for an irradiation time of 80 seconds. Results indicate that it is possible to find a relationship between sample initial temperature and microwave power that provides a cured
lower, hence higher initial temperature for marble samples was required in order to obtain the same final curing temperature. Laboratory Tests Several microwave-assisted polymerization tests were carried out in a commercial microwave oven (Samsung, TDS M1711N) for several
FIGURE 8. 2-D temperature distribution at marble sample and epoxy coating for t=80 seconds. Tini = 45 C.
(b) FIGURE 9. Final 100 EPOMAR A: 25 EPOMAR B epoxy mixture resin curing quality for two different initial temperatures and microwave power values. (a) Tinitial =55 C, Power = 130 W; (b) Tinitial =60 C, Power = 800 W. epoxy coating with a surface appearance similar to that obtained with the conventional process. In fact, from Table 3 it can be concluded that low initial temperature values led to incomplete polymerization epoxy coatings, while high microwave power values caused epoxy uneven curing and the appearance of hot spots due to the thermal runaway [Metaxas et al., 1983] or
overheating. The proper combination for these initial temperature values and microwave irradiation power, 55 C and 130 watts respectively, provided high quality epoxy coatings. Figure 9 shows the polymerization quality of epoxy coatings for two different initial temperatures shown in Table 3. Figure 9(a) shows the final appearance of a marble sample
and epoxy coating for an initial temperature equal to 55 C and a microwave power value around 130 W, while in Figure 9(b) initial values were fixed to 60 C and 800 W respectively. From Figure 9(b), the uneven epoxy growth and the appearance of air bubbles due to local overheating can be appreciated, while the surface quality shown in Figure 9 (a) is good. Thus, the need for a very precise initial condition control both at the marble sample temperature and microwave power values was demonstrated. In the case of polyester coatings, the optimum initial temperature was found to be around 40C, while the microwave power was set to 100 watts as described in Table 3. However, for this resin an adverse chemical effect was detected: the cured resin had a matt finish in all tests. A possible explanation is that waxes did not migrate to the resin surface because of the inverse temperature gradient when compared to the conventional heating process. Wax is employed in the polyester resin with calcium carbonate in order to obtain a glossy surface appearance after curing. Additionally, laboratory tests also show that the final temperature values through epoxy coating should be between 55 and 66C in order to obtain good quality epoxy coatings and to avoid bubble development. Different chemical composition alternatives are now under study in order to avoid this matt look. Industrial Microwave Oven Prototype Trials Several trials were carried out in the industrial prototype described in Figure 2 with epoxy coatings. Two different initial temperatures were used for the marble slabs and epoxy coatings: 24 C and 50 C and the microwave power was fixed to 10.8 kW. The results obtained were very similar to that obtained during laboratory tests. Therefore, good quality epoxycoated marble slabs were obtained provided that an initial temperature of 50 C was used during

the process. CONCLUSIONS In this work, a novel microwave-assisted polymerization process for the films used in the natural stone industry has been simulated and tested. Results show that it is possible to drastically reduce curing times from 2 hours, in the conventional process, to 80 seconds while maintaining the final quality, mainly for epoxy coatings. The numerical simulations of temperature distributions for marble and resin coatings during microwave-assisted curing, dielectric properties and heating tests show that CremaSierra Puerta marble samples heat at a much lower rate than the epoxy resin so that the thermal gradient favors heat migration from epoxy coating to marble sample. Thus, the initial temperature of the marble slab is of the utmost importance for the epoxy resin to reach the final temperature around 60C and to avoid overheating during exothermal curing. Fortunately, all the marble processing stages performed before microwave curing can be readily altered to obtain this requirement without significant additional investment and, consequently, this novel production technique is shown as a promising improvement in the natural stone industry that can lead to important savings in terms of storage spaces and production times. The proposed method for microwaveassisted curing of marble coatings has been patented [Romera-Fernandez, et al., 2005] and the prototype presented here is intended to be in the market in the near future. The first detected advantages of its use under real working conditions are: continuous fabrication, increment of line production velocity, pile-up time reduction and decrease of storage space.
ACKNOWLEDGEMENTS The authors wish to thank Qumicas del Mrmol, S.L., located at Cehegn (Murcia) for the provision of epoxy and polyester resins and Crema-Sierra Puerta, S.L.(Cehegn, Spain), for the provision of marble slabs. REFERENCES
Agilent Technologies (2004). 85070E Dielectric Probe Kit, 200 MHz to 50 GHz, Technical Overview. http: //cp.literature.agilent.com/litweb/pdf/59890222EN.pdf. Mathworks (1996). Partial Differential Equation Toolbox For Use with MATLAB. Users Guide. http:// www.mathworks.com. Metaxas, A. C. and Meredith, R.J.(1983). Industrial Microwave Heating, first ed., Peter Peregrinus, London. Monz-Cabrera, J., Daz-Morcillo, A., Catal-Civera, J.M. and De los Reyes, E. (2000). Heat Flux and Heat Generation Characterisation in a Wet-Laminar Body in Microwave-Assisted Drying: an Application to Microwave Drying Of Leather. Int. Comm. Heat Mass Transfer. 27(8), pp.1101-1110. Monz-Cabrera, J., Cans, A. J., Catal-Civera, J.M., and De los Reyes, E. (2002). Simulation of Temperature Distributions in Pressure-Aided Microwave Rubber Vulcanization Processes.J. Microwave Power E. E. 37, pp.73-88. Nightingale, C. and Day, R. J.(2002). Flexural and interlaminar share strength properties of carbon fibre/epoxy compositescured thermally and with microwave radiation. Compos. Part A-Appl. S. 33, pp.1021-1030. Plaza-Gonzlez, P., Monz-Cabrera, J., Catal-Civera, J. M. and, Snchez-Hernndez, D.(2004). A New Approach for the Prediction of the Electric Field Distribution in Multimode Microwave-Heating Applicators with Mode Stirrers. IEEE Trans. Magnetics. 40, pp.1672-1678. Samsung, Microwave oven, owners instructions, M1711N http://www.samsung.com. Romera-Fernandez, J., Vila-Marin, M.P., Snchez Hernndez, D., Diaz-Morcillo, A., MartinezGonzalez, A.M. and Monz-Cabrera, J.(2005). Method for microwave-aided polymerization of resins that are applied to marble. Asoc. Empresarial Investigacion Cent Tech (ASEM-Non-standard), Patent Numbers:WO2005121046-A1;ES2245880210

A1. Toniolo, L., Poli, T., Castelvetro, V., Manariti, A., Chiantore, O. and Lazzari, M. (2002). Tailoring new fluorinated acrylic copolymers as protective coatings for marble. J. Cultural Heritage. 3, pp.309316. Wiesbrock, F., Hoogenboom, R. and Schubert, U. S. (2004). Microwave-Assisted Polymer Synthesis: State-of-the-Art and Future Perspectives. Macromol. Rapid Commun. 25, pp.1739-1764. Zhang, D., Crivello, J.V. and Stoffer, J.O.(2004). Polymerizations of Epoxides With Microwave Energy. J. Polym. Sci. Pol. Phys. 42, pp.42304246.

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