State-of-the-art in the mechanistic modeling of the drying of solids: A review of 40 years of progress and perspectives

References

• Krischer, O.; Kröll, K. Die wissenschaftlichen Grundlagen der Trocknungstechnik. Springer, Berlin, 1956.
   Google Scholar
• Luikov, A. V. Heat and Mass Transfer in Capillary-Porous Bodies. Advances in Heat Transfer; volume 1; Elsevier, 1964; pp 123–184. DOI: 10.1137/1.9780898718003
   Google Scholar
• Philip, J. R.; De Vries, D. A. Moisture Movement in Porous Materials under Temperature Gradients. Trans. AGU 1957, 38, 222–232. DOI: 10.1029/TR038i002p00222.
   Google Scholar
• Gray, W. G. A Derivation of the Equations for Multiphase Transport. Chemiv. Eng. Sci. 1975, 30, 229–233. DOI: 10.1016/0009-2509(75)80010-8.
   Web of Science ®Google Scholar
• Slattery, J. C. Momentum, Energy and Mass Transfer in Continua. McGraw-Hill: New York, 1972. [Database][Mismatch
   Google Scholar
• Whitaker, S. Simultaneous Heat, Mass and Momentum Transfer in Porous Media: A Theory of Drying. In Advances in Heat Transfer; J. P. Hartnett and T. F. Irvine, Eds.; volume 13; Elsevier, 1977; pp 119–203.
   Google Scholar
• Whitaker, S. Coupled Transport in Multiphase Systems: A Theory of Drying. In Advances in Heat Transfer; Y. I. Cho J. P. Hartnett, T. F. Irvine and G. A. Greene, Eds; volume 31; Elsevier, 1998; pp 1–104
   Google Scholar
• Bear, J.; Corapcioglu, M. Y. Advances in Transport Phenomena in Porous Media. Martinus Nijhoff Publishers: Lancaster, 1987.
   Google Scholar
• Perré, P.; Turner, I. W. A 3D Version of Transpore: A Comprehensive Heat and Mass Transfer Computational Model for Simulating the Drying of Porous Media. Inter. J. Heat Mass Trans. 1999a, 42, 4501–4521. DOI: 10.1016/S0017-9310(99)00098-8.
   Web of Science ®Google Scholar
• Perré, P.; Remond, R.; Turner, I. W. Comprehensive Drying Models Based on Volume Averaging: Background, Application and Perspective. In Modern Drying Technology; E. Tsotsas and A. S. Mujumdar, Eds.; volume 1. Wiley-VCH, 2007.
   Google Scholar
• Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. Transport Phenomena. John Wiley & Sons: New York, 1960.
   Google Scholar
• Bouali, A.; Rémond, R.; Almeida, G.; Perré, P. Thermo-Diffusion in Wood: X-Ray mc Profiles Analysed Using a 2-D Computational Model. In Proceedings of the 18th International Drying Symposium, 2012; p 5.
   Google Scholar
• Martin, B. Dynamique des transferts d’humidité au sein de l’épicéa commun (Picea abies (L.) Karst.): mesures par imagerie X et simulations numériques,. PhD Thesis, Université de Lorraine, 2022.
   Google Scholar
• Siau, J. F.; Jin, Z. Nonisothermal Moisture Diffusion Experiments Analyzed by Four Alternative Equations. Wood Sci. Technol. 1985, 19, 151–157. DOI: 10.1007/BF00353075.
   Web of Science ®Google Scholar
• Arballo, J. R.; Campañone, L. A.; Mascheroni, R. H. Modeling of Microwave Drying of Fruits. Drying Technol. 2010, 28, 1178–1184. DOI: 10.1080/07373937.2010.493253.
   Web of Science ®Google Scholar
• Constant, T.; Moyne, C.; Perre, P. Drying with Internal Heat Generation: Theoretical Aspects and Application to Microwave Heating. AIChE J. 1996, 42, 359–368. DOI: 10.1002/aic.690420206.
   Web of Science ®Google Scholar
• Perré, P.; Turner, I. W. The Use of Numerical Simulation as a Cognitive Tool for Studying the Microwave Drying of Softwood in an over-Sized Waveguide. Wood Sci. Technol. 1999b, 33, 445–464. DOI: 10.1007/s002260050129.
   Web of Science ®Google Scholar
• Turner, I. W.; Jolly, P. C. Combined Microwave and Convective Drying of a Porous Material. Drying Technol. 1991, 9, 1209–1269. DOI: 10.1080/07373939108916749.
   Web of Science ®Google Scholar
• Zhu, H.; Gulati, T.; Datta, A. K. Huang, K. Microwave Drying of Spheres: Coupled Electromagnetics-Multiphase Transport Modeling with Experimentation. part i: Model Development and Experimental Methodology. Food Bioprod. Process. 2015, 96, 314–325. DOI: 10.1016/j.fbp.2015.08.003.
   Web of Science ®Google Scholar
• Bucki, M.; Perré, P. Physical Formulation and Numerical Modeling of High Frequency Heating of Wood. Drying Technol. 2003, 21, 1151–1172. DOI: 10.1081/DRT-120023173.
   Web of Science ®Google Scholar
• Rémond, R.; Perré, P. High-Frequency Heating Controlled by Convective Hot Air: Toward a Solution for on-Line Drying of Softwoods. Drying Technol. 2008, 26, 530–536. DOI: 10.1080/07373930801944614.
   Web of Science ®Google Scholar
• Sharp, J. R. A Review of Low Temperature Drying Simulation Models. J. Agric. Eng. Res. 1982, 27, 169–190. DOI: 10.1016/0021-8634(82)90060-9.
   Web of Science ®Google Scholar
• Bramhall, G.; et al. Mathematical Model for Lumber Drying. I: Principles Involved. 1979, 5.
   Google Scholar
• Peishi, C.; Pei, D. C. A Mathematical Model of Drying Processes. Int. J. Heat Mass Transf. 1989, 32, 297–310. DOI: 10.1016/0017-9310(89)90177-4.
   Web of Science ®Google Scholar
• Stanish, M. A.; Schajer, G. S.; Kayihan, F. A Mathematical Model of Drying for Hygroscopic Porous Media. AIChE J. 1986, 32, 1301–1311. DOI: 10.1002/aic.690320808.
   Web of Science ®Google Scholar
• Ilic, M.; Turner, I. W. Convective Drying of a Consolidated Slab of Wet Porous Material. Int. J. Heat Mass Transf. 1989, 32, 2351–2362. DOI: 10.1016/0017-9310(89)90196-8.
   Web of Science ®Google Scholar
• Nasrallah, S. B.; Perre, P. Detailed Study of a Model of Heat and Mass Transfer during Convective Drying of Porous Media. Int. J. Heat Mass Transf. 1988, 31, 957–967. DOI: 10.1016/0017-9310(88)90084-1.
   Web of Science ®Google Scholar
• Puiggali, J. R.; Quintard, M.; Whitaker, S. Drying Granular Porous Media: gravitational Effects in the Isenthalpic Regime and the Role of Diffusion Models. Drying Technol. 1988, 6, 601–629. DOI: 10.1080/07373938808916401.
   Web of Science ®Google Scholar
• Quintard, M.; Puiggali, J. R. Numerical Modelling of Transport Processes during the Drying of a Granular Porous Medium. Heat Technol. 1986, 4, 37–57.
   Google Scholar
• Carr, E. J.; Turner, I. W.; Perré, P. A Dual-Scale Modelling Approach for Drying Hygroscopic Porous Media. Multiscale Model. Simul. 2013a, 11, 362–384. DOI: 10.1137/120873005.
   Web of Science ®Google Scholar
• Carr, E. J.; Perré, P.; Turner, I. W. The Extended Distributed Microstructure Model for Gradient-Driven Transport: A Two-Scale Model for Bypassing Effective Parameters. Comput. Phys. 2016, 327, 810–829. DOI: 10.1016/j.jcp.2016.10.004.
   Google Scholar
• Thompson, N. C.; Ge, S.; Manso, G. F. The Importance of (Exponentially More) Computing Power. 2022. arXiv preprint arXiv:2206.14007
   Google Scholar
• Patankar, S. Numerical Heat Transfer and Fluid Flow. CRC press, 1980.
   Google Scholar
• Turner, I.; Perré, P. A Synopsis of the Strategies and Efficient Resolution Techniques Used for Modelling and Numerically Simulating the Drying Process. Mathematical Modeling and Numerical Techniques in Drying Technology; CRC Press, 1996, pp 1–82.
   Google Scholar
• Ypma, T. J. Historical Development of the Newton–Raphson Method. SIAM Rev. 1995, 37, 531–551. DOI: 10.1137/1037125.
   Web of Science ®Google Scholar
• Iyota, H.; Nishimura, N.; Yoshida, M.; Nomura, T. Simulation of Superheated Steam Drying considering Initial Steam Condensation. Drying Technol. 2001, 19, 1425–1440. DOI: 10.1081/DRT-100105298.
   Web of Science ®Google Scholar
• Jia, C.-C.; Sun, D.-W.; Cao, C.-W. Mathematical Simulation of Temperature and Moisture Fields within a Grain Kernel during Drying. Drying Technol. 2000, 18, 1305–1325. DOI: 10.1080/07373930008917778.
   Web of Science ®Google Scholar
• Perré, P.; Degiovanni, A. Simulation par volumes finis des transferts couplés en milieux poreux anisotropes: séchage du bois à basse et à haute température. Int. J. Heat Mass Transf. 1990, 33, 2463–2478. DOI: 10.1016/0017-9310(90)90004-E.
   Web of Science ®Google Scholar
• Torres, S. s.; Jomaa, W.; Puiggali, J.-R.; Avramidis, S. Multiphysics Modeling of Vacuum Drying of Wood. Appl. Math. Model. 2011, 35, 5006–5016. DOI: 10.1016/j.apm.2011.04.011.
   Web of Science ®Google Scholar
• Turner, I. W. A Two-Dimensional Orthotropic Model for Simulating Wood Drying Processes. Appl. Math. Model. 1996, 20, 60–81. DOI: 10.1016/0307-904X(95)00106-T.
   Web of Science ®Google Scholar
• Perre, P.; Turner, I. W. Microwave Drying of Softwood in an Oversized Waveguide: Theory and Experiment. AIChE J. 1997, 43, 2579–2595. DOI: 10.1002/aic.690431019.
   Web of Science ®Google Scholar
• Turner, I. W.; Puiggali, J. R.; Jomaa, W. A Numerical Investigation of Combined Microwave and Convective Drying of a Hygroscopic Porous Material: A Study Based on Pine Wood. Chem. Eng. Res. Des. 1998, 76, 193–209. DOI: 10.1205/026387698524622.
   Web of Science ®Google Scholar
• Carr, E. J.; Turner, I. W.; Perré, P. A Variable-Stepsize Jacobian-Free Exponential Integrator for Simulating Transport in Heterogeneous Porous Media: Application to Wood Drying. Comput. Phys. 2013b, 233, 66–82. DOI: 10.1016/j.jcp.2012.07.024.
   Google Scholar
• Carr, E. J.; Moroney, T. J.; Turner, I. W. Efficient Simulation of Unsaturated Flow Using Exponential Time Integration. Appl. Math. Comput. 2011, 217, 6587–6596. DOI: 10.1016/j.amc.2011.01.041.
   Web of Science ®Google Scholar
• Saad, Y. Iterative Methods for Sparse Linear Systems. SIAM, 2003.
   Google Scholar
• Couture, F.; Jomaa, W.; Puiggali, J.-R. Relative Permeability Relations: A Key Factor for a Drying Model. Transp Porous Med 1996, 23, 303–335. DOI: 10.1007/BF00167101.
   Web of Science ®Google Scholar
• Perré, P.; Pierre, F.; Casalinho, J.; Ayouz, M. Determination of the Mass Diffusion Coefficient Based on the Relative Humidity Measured at the Back Face of the Sample during Unsteady Regimes. Drying Technol. 2015, 33, 1068–1075. DOI: 10.1080/07373937.2014.982253.
   Web of Science ®Google Scholar
• Rémond, R.; Baettig, R.; Perré, P. Identification of Relative Permeability Curves for Softwood Using a Computational Model and Moisture Content Profiles Determined by x-Ray Absorptiometry. In 15th International Drying Symposium, Drying’2006, Budapest, Hungary, volume C, pp 1793–1797, 2006.
   Google Scholar
• Marle, C. On Macroscopic Equations Governing Multiphase Flow with Diffusion and Chemical Reactions in Porous Media. Int. J. Eng. Sci. 1982, 20, 643–662. DOI: 10.1016/0020-7225(82)90118-5.
   Web of Science ®Google Scholar
• Allaire, G. Homogenization and Two-Scale Convergence. SIAM J. Math. Anal. 1992, 23, 1482–1518. DOI: 10.1137/0523084.
   Web of Science ®Google Scholar
• Bourgat, J.-F. Numerical Experiments of the Homogenization Method. Computing Methods in Applied Sciences and Engineering, 1977, I; Springer, 1979; pp 330–356.
   Google Scholar
• Sanchez-Palencia, E. Homogenization Method for the Study of Composite Media. Asymptotic Analysis II; Springer, 1983; pp 192–214.
   Google Scholar
• Hammouda, I.; Mihoubi, D. Modelling of Drying Induced Stress of Clay: elastic and Viscoelastic Behaviours. Mech. Time-Depend Mater. 2014, 18, 97–111. DOI: 10.1007/s11043-013-9216-2.
   Web of Science ®Google Scholar
• Nguyen, D. M.; Almeida, G.; Nguyen, T. M. L.; Zhang, J.; Lu, P.; Colin, J.; Perré, P. A Critical Review of Current Imaging Techniques to Investigate Water Transfers in Wood and Biosourced Materials. Transp. Porous Med. 2021, 137, 21–61. DOI: 10.1007/s11242-020-01538-2.
   Web of Science ®Google Scholar
• Perré, P. A Review of Modern Computational and Experimental Tools Relevant to the Field of Drying. Drying Technol. 2011, 29, 1529–1541. DOI: 10.1080/07373937.2011.580872.
   Web of Science ®Google Scholar
• Louërat, M.; Ayouz, M.; Perré, P. Heat and Moisture Diffusion in Spruce and Wood Panels Computed from 3-D Morphologies Using the Lattice Boltzmann Method. Int. J. Therm. Sci. 2018, 130, 471–483. DOI: 10.1016/j.ijthermalsci.2018.05.009.
   Web of Science ®Google Scholar
• Ali, M. A.; Umer, R.; Khan, K. A.; Cantwell, W. J. Application of x-Ray Computed Tomography for the Virtual Permeability Prediction of Fiber Reinforcements for Liquid Composite Molding Processes: A Review. Compos. Sci. Technol. 2019, 184, 107828. DOI: 10.1016/j.compscitech.2019.107828.
   Web of Science ®Google Scholar
• Gao, Y.; Zhang, X.; Rama, P.; Liu, Y.; Chen, R.; Ostadi, H.; Jiang, K. Calculating the Anisotropic Permeability of Porous Media Using the Lattice Boltzmann Method and x-Ray Computed Tomography. Transp. Porous Med. 2012, 92, 457–472. DOI: 10.1007/s11242-011-9914-7.
   Web of Science ®Google Scholar
• Piller, M.; Schena, G.; Nolich, M.; Favretto, S.; Radaelli, F.; Rossi, E. Analysis of Hydraulic Permeability in Porous Media: From High Resolution X-Ray Tomography to Direct Numerical Simulation. Transp. Porous Med. 2009, 80, 57–78. DOI: 10.1007/s11242-009-9338-9.
   Web of Science ®Google Scholar
• García-Salaberri, P. A.; Zenyuk, I. V.; Shum, A. D.; Hwang, G.; Vera, M.; Weber, A. Z.; Gostick, J. T. Analysis of Representative Elementary Volume and through-Plane Regional Characteristics of Carbon-Fiber Papers: Diffusivity, Permeability and Electrical/Thermal Conductivity. Int. J. Heat Mass Transf. 2018, 127, 687–703. DOI: 10.1016/j.ijheatmasstransfer.2018.07.030.
   Web of Science ®Google Scholar
• Quenjel, E.-H.; Perré, P. Computation of the Effective Thermal Conductivity from 3d Real Morphologies of Wood. Heat Mass Transfer 2022, 58, 2195–2206. DOI: 10.1007/s00231-022-03246-7.
   Web of Science ®Google Scholar
• Assad-Bustillos, M.; Guessasma, S.; Réguerre, A. L.; Della Valle, G. Impact of Protein Reinforcement on the Deformation of Soft Cereal Foods under Chewing Conditions Studied by x-Ray Tomography and Finite Element Modelling. J. Food Eng. 2020, 286, 110108. DOI: 10.1016/j.jfoodeng.2020.110108.
   Web of Science ®Google Scholar
• Laurent, C. P.; Latil, P.; Durville, D.; Rahouadj, R.; Geindreau, C.; Orgéas, L.; Ganghoffer, J.-F. Mechanical Behaviour of a Fibrous Scaffold for Ligament Tissue Engineering: Finite Elements Analysis vs. X-Ray Tomography Imaging. J. Mech. Behav. Biomed. Mater. 2014, 40, 222–233. DOI: 10.1016/j.jmbbm.2014.09.003.
   PubMed Web of Science ®Google Scholar
• Liu, Y.; Straumit, I.; Vasiukov, D.; Lomov, S. V.; Panier, S. Prediction of Linear and Non-Linear Behavior of 3d Woven Composite Using Mesoscopic Voxel Models Reconstructed from x-Ray Micro-Tomography. Compos. Struct. 2017, 179, 568–579. DOI: 10.1016/j.compstruct.2017.07.066.
   Web of Science ®Google Scholar
• Zhang, L.; Ferreira, J. M.; Olhero, S.; Courtois, L.; Zhang, T.; Maire, E.; Rauhe, J. C. Modeling the Mechanical Properties of Optimally Processed Cordierite–Mullite–Alumina Ceramic Foams by X-Ray Computed Tomography and Finite Element Analysis. Acta Mater. 2012, 60, 4235–4246. DOI: 10.1016/j.actamat.2012.04.025.
   Web of Science ®Google Scholar
• Štěpánek, F.; Šoóš, M.; Rajniak, P. Characterisation of Porous Media by the Virtual Capillary Condensation Method. Colloids Surf., A 2007, 300, 11–20. DOI: 10.1016/j.colsurfa.2006.10.018.
   Google Scholar
• Perré, P.; May, B. K. The Existence of a First Drying Stage for Potato Proved by Two Independent Methods. J. Food Eng. 2007, 78, 1134–1140. DOI: 10.1016/j.jfoodeng.2005.12.025.
   Web of Science ®Google Scholar
• Rémond, R.; De La Cruz, M.; Aléon, D.; Perré, P. Investigation of Oscillating Climates for Wood Drying Using the Flying Wood Test and Loaded Beams: need for a New Mechano-Sorptive Model. Maderas. Ciencia y tecnología 2013, 15, 269–280.
   Web of Science ®Google Scholar
• Salem, T.; Perré, P.; Bouali, A.; Mougel, E.; Rémond, R. Experimental and Numerical Investigation of Intermittent Drying of Timber. Drying Technol. 2017, 35, 593–605. DOI: 10.1080/07373937.2016.1195842.
   Web of Science ®Google Scholar
• Bažant, Z. P. Mathematical Model for Creep and Thermal Shrinkage of Concrete at High Temperature. Nucl. Eng. Des. 1983, 76, 183–191. DOI: 10.1016/0029-5493(83)90133-4.
   Web of Science ®Google Scholar
• Kofi Mensah, J.; Nelson, G. L.; Hamdy, M. Y.; Richard, T. G. A Mathematical Model for Predicting Soybean Seedcoat Cracking during Drying. Transactions of the ASAE 1985, 28, 580–587.
   Google Scholar
• Thomas, H. R. A Finite Element Analysis of Shrinkage Stresses in Building Materials. PhD Thesis, University College of Swansea, UK, 1981.
   Google Scholar
• Chen, G.; Keey, R. B.; Walker, J. C. F. The Drying Stress and Check Development on High-Temperature Kiln Seasoning of Sapwoodpinus Radiata Boards. Holz Als Roh-Und Werkstoff 1997, 55, 59–64. DOI: 10.1007/BF02990517.
   Google Scholar
• Kowalski, S. J.; Rajewska, K. Drying-Induced Stresses in Elastic and Viscoelastic Saturated Materials. Chem. Eng. Sci. 2002, 57, 3883–3892. DOI: 10.1016/S0009-2509(02)00307-X.
   Web of Science ®Google Scholar
• Ponsart, G.; Vasseur, J.; Frias, J. M.; Duquenoy, A.; Méot, J. M. Modelling of Stress Due to Shrinkage during Drying of Spaghetti. J. Food Eng. 2003, 57, 277–285. DOI: 10.1016/S0260-8774(02)00308-4.
   Web of Science ®Google Scholar
• Remond, R.; Passard, J.; Perré, P. The Effect of Temperature and Moisture Content on the Mechanical Behaviour of Wood: A Comprehensive Model Applied to Drying and Bending. European Journal of Mechanics-A/Solids 2007, 26, 558–572. DOI: 10.1016/j.euromechsol.2006.09.008.
   Web of Science ®Google Scholar
• Salin, J.-G. Numerical Prediction of Checking during Timber Drying and a New Mechano-Sorptive Creep Model. Holz als Roh-und Werkstoff 1992, 50, 195–200. DOI: 10.1007/BF02663286.
   Google Scholar
• Perré, P.; Turner, I. Determination of the Material Property Variations across the Growth Ring of Softwood for Use in a Heterogeneous Drying Model. Part 2. Use of Homogenisation to Predict Bound Liquid Diffusivity and Thermal Conductivity. Holzforschung. 2001, 55, 417–425.
   Google Scholar
• Haque, M. N.; Langrish, T. A. G.; Keep, L.-B.; Keey, R. B. Model Fitting for Visco-Elastic Creep of Pinus Radiata during Kiln Drying. Wood Sci. Technol. 2000, 34, 447–457. DOI: 10.1007/s002260000058.
   Web of Science ®Google Scholar
• Perré, P.; Passard, J. A Physical and Mechanical Model Able to Predict the Stress Field in Wood over a Wide Range of Drying Conditions. Drying Technol. 2004, 22, 27–44. DOI: 10.1081/DRT-120028202.
   Web of Science ®Google Scholar
• Florisson, S.; Vessby, J.; Ormarsson, S. A Three-Dimensional Numerical Analysis of Moisture Flow in Wood and of the Wood’s Hygro-Mechanical and Visco-Elastic Behaviour. Wood Sci. Technol. 2021, 55, 1269–1304. DOI: 10.1007/s00226-021-01291-9.
   Web of Science ®Google Scholar
• Heydari, M.; Khalili, K.; Ahmadi-Brooghani, S. Y. More Comprehensive 3d Modeling of Clay-like Material Drying. AIChE J. 2018, 64, 1469–1478. DOI: 10.1002/aic.16027.
   Web of Science ®Google Scholar
• Mihoubi, D.; Zagrouba, F.; Vaxelaire, J.; Bellagi, A.; Roques, M. Transfer Phenomena during the Drying of a Shrinkable Product: Modeling and Simulation. Drying Technol. 2004, 22, 91–109. DOI: 10.1081/DRT-120028216.
   Web of Science ®Google Scholar
• Perré, P.; May, B. K. A Numerical Drying Model That Accounts for the Coupling between Transfers and Solid Mechanics. Case of Highly Deformable Products. Drying Technol. 2001, 19, 1629–1643. DOI: 10.1081/DRT-100107263.
   Web of Science ®Google Scholar
• Vinjamur, M.; Cairncross, R. A. Non-Fickian Nonisothermal Model for Drying of Polymer Coatings. AIChE J. 2002, 48, 2444–2458. DOI: 10.1002/aic.690481104.
   Web of Science ®Google Scholar
• Lelievre, D.; Colinart, T.; Glouannec, P. Hygrothermal Behavior of Bio-Based Building Materials Including Hysteresis Effects: Experimental and Numerical Analyses. Energy Build. 2014, 84, 617–627. DOI: 10.1016/j.enbuild.2014.09.013.
   Web of Science ®Google Scholar
• Perré, P.; Rémond, R.; Almeida, G. Multiscale Analysis of Water Vapor Diffusion in Low Density Fiberboard: Implications as a Building Material. Constr. Build. Mater. 2022b, 329, 127047. DOI: 10.1016/j.conbuildmat.2022.127047.
   Web of Science ®Google Scholar
• Rémond, R.; Almeida, G. Mass Diffusivity of Low-Density Fibreboard Determined under Steady- and Unsteady-State Conditions: Evidence of Dual-Scale Mechanisms in the Diffusion. Wood Mater. Sci. Eng. 2011, 6, 23–33. DOI: 10.1080/17480272.2010.515035.
   Google Scholar
• Rojas, M. L.; Augusto, P. E. D. Microstructure Elements Affect the Mass Transfer in Foods: The Case of Convective Drying and Rehydration of Pumpkin. LWT 2018, 93, 102–108.
   Web of Science ®Google Scholar
• Krabbenhoft, K.; Damkilde, L. Double Porosity Models for the Description of Water Infiltration in Wood. Wood Sci. Technol. 2004, 38, 641–659. DOI: 10.1007/s00226-004-0253-5.
   Web of Science ®Google Scholar
• Nyman, U.; Gustafsson, P. J.; Johannesson, B.; Hägglund, R. A Numerical Method for the Evaluation of Non-Linear Transient Moisture Flow in Cellulosic Materials. Int. J. Numer. Meth. Eng. 2006, 66, 1859–1883. DOI: 10.1002/nme.1597.
   Web of Science ®Google Scholar
• Perré, P. Multiscale Aspects of Heat and Mass Transfer during Drying. Transp. Porous Media 2007, 33, 2463–2478.
   Google Scholar
• Perré, P. Multiscale Modelling of Drying as a Powerful Extension of the Macroscopic Approach: application to Solid Wood and Biomass Processing. Drying Technology 2010, 28, 944–959. DOI: 10.1080/07373937.2010.497079.
   Web of Science ®Google Scholar
• Perré, P.; Remond, R. A Dual–Scale Computational Model of Kiln Wood Drying Including Single Board and Stack Level Simulation. Drying Technol. 2006, 24, 1069–1074. DOI: 10.1080/07373930600778106.
   Web of Science ®Google Scholar
• Crank, J. A Theoretical Investigation of the Influence of Molecular Relaxation and Internal Stress on Diffusion in Polymers. J. Polym. Sci 1953, 11, 151–168. DOI: 10.1002/pol.1953.120110206.
   Web of Science ®Google Scholar
• Christensen, G. N. Sorption and Swelling within Wood Cell Walls. Nature 1967, 213, 782–784. DOI: 10.1038/213782a0.
   Web of Science ®Google Scholar
• Wadsö, L. Describing non-Fickian Water-Vapour Sorption in Wood. J. Mater. Sci. 1994, 29, 2367–2372. DOI: 10.1007/BF00363428.
   Web of Science ®Google Scholar
• Perré, P. Coupled Heat and Mass Transfer in Biosourced Porous Media without Local Equilibrium: A Macroscopic Formulation Tailored to Computational Simulation. Int. J. Heat Mass Transfer 2019, 140, 717–730. DOI: 10.1016/j.ijheatmasstransfer.2019.06.043.
   Web of Science ®Google Scholar
• Almeida, G.; Domenek, S.; Perre, P. Transpoly: A Theoretical Model to Quantify the Dynamics of Water Transfer through Nanostructured Polymer Films. Polymer 2020, 191, 122256. DOI: 10.1016/j.polymer.2020.122256.
   Web of Science ®Google Scholar
• Waananen, K. M.; Litchfield, J. B.; Okos, M. R. Classification of Drying Models for Porous Solids. Drying Technol. 1993, 11, 1–40. DOI: 10.1080/07373939308916801.
   Web of Science ®Google Scholar
• Van Meel, D. A. Adiabatic Convection Batch Drying with Recirculation of Air. Chem. Eng. Sci. 1958, 9, 36–44. DOI: 10.1016/0009-2509(58)87005-0.
   Web of Science ®Google Scholar
• Le Bray, Y.; Prat, M. Three-Dimensional Pore Network Simulation of Drying in Capillary Porous Media. Int. J. Heat Mass Transf. 1999, 42, 4207–4224. DOI: 10.1016/S0017-9310(99)00006-X.
   Web of Science ®Google Scholar
• Surasani, V. K.; Metzger, T.; Tsotsas, E. A Non-Isothermal Pore Network Drying Model with Gravity Effect. Transp. Porous. Med. 2009, 80, 431–439. DOI: 10.1007/s11242-009-9372-7.
   Web of Science ®Google Scholar
• Perré, P. The Proper Use of Mass Diffusion Equations in Drying Modeling: Introducing the Drying Intensity Number. Drying Technol. 2015, 33, 1949–1962. DOI: 10.1080/07373937.2015.1076836.
   Web of Science ®Google Scholar
• Valocchi, A. J. Validity of the Local Equilibrium Assumption for Modeling Sorbing Solute Transport through Homogeneous Soils. Water Resour. Res. 1985, 21, 808–820. DOI: 10.1029/WR021i006p00808.
   Web of Science ®Google Scholar
• U. Hornung, editor. Homogenization and Porous Media. Springer–Verlag: New York, 1997.
   Google Scholar
• Peter, M. A.; Showalter, R. E. Homogenization of Secondary-Flux Models of Partially Fissured Media. Int. J. Numer. Anal. Model. 2008, 5, 150–156.
   Web of Science ®Google Scholar
• Rahman, M. M.; Joardder, M. U. H.; Khan, M. I. H.; Pham, N. D.; Karim, M. A. Multi-Scale Model of Food Drying: Current Status and Challenges. Crit. Rev. Food Sci. Nutr. 2018, 58, 858–876.
   PubMed Web of Science ®Google Scholar
• Showalter, R. E. Distributed Microstructured Models of Porous Media. Inter. Series Num. Math. 1993, 114, 155–163.
   Google Scholar
• Defraeye, T. Advanced Computational Modelling for Drying Processes–a Review. Appl. Energy 2014, 131, 323–344. DOI: 10.1016/j.apenergy.2014.06.027.
   Web of Science ®Google Scholar
• Nouri, M.; Perré, P. Direct Numerical Simulation of Coupled Heat and Mass Transfer in Hygroscopic Porous Media. Paper 534, 8 Pages, IDS’2022,, 2022. DOI: 10.55900/lavrknht.
   Google Scholar
• Mujumdar, A. S. Handbook of Industrial Drying. CRC Press, 2014.
   Google Scholar
• Kudra, T. Energy Aspects in Drying. Drying Technol. 2004, 22, 917–932. DOI: 10.1081/DRT-120038572.
   Web of Science ®Google Scholar
• Mujumdar, A. S. Research and Development in Drying: Recent Trends and Future Prospects. Drying Technol. 2004, 22, 1–26. DOI: 10.1081/DRT-120028201.
   Web of Science ®Google Scholar
• Wang, W.; Chen, G.; Mujumdar, A. S. Physical Interpretation of Solids Drying: An Overview on Mathematical Modeling Research. Drying Technol. 2007, 25, 659–668. DOI: 10.1080/07373930701285936.
   Web of Science ®Google Scholar
• Perré, P.; Turner, I. W. A Heterogeneous Wood Drying Computational Model That Accounts for Material Property Variation across Growth Rings. Chem. Eng. J. 2002, 86, 117–131. DOI: 10.1016/S1385-8947(01)00270-4.
   Web of Science ®Google Scholar
• Perré, P.; Nguyen, D. M.; Almeida, G. A Macroscopic Washburn Approach of Liquid Imbibition in Wood Derived from x-Ray Tomography Observations. Sci. Rep. 2022a, 12, 1–14. DOI: 10.1038/s41598-022-05508-0.
   PubMed Web of Science ®Google Scholar
• Marques, B.; Perré, P.; Casalinho, J.; Tadini, C. C.; Plana-Fattori, A.; Almeida, G. Evidence of Iso-Volume Deformation during Convective Drying of Yacón: An Extended Van Meel Model Adapted to Large Volume Reduction. J. Food Eng. 2023, 341, 111311. ISSN 0260-8774. https://www.sciencedirect.com/science/article/pii/S026087742200365X. DOI: 10.1016/j.jfoodeng.2022.111311.
   Web of Science ®Google Scholar
• Trystram, G. Modelling of Food and Food Processes. J. Food Eng. 2012, 110, 269–277. DOI: 10.1016/j.jfoodeng.2011.05.001.
   Web of Science ®Google Scholar
• Madoumier, M.; Trystram, G.; Sébastian, P.; Collignan, A. Towards a Holistic Approach for Multi-Objective Optimization of Food Processes: A Critical Review. Trend. Food Sci. Technol. 2019, 86, 1–15. DOI: 10.1016/j.tifs.2019.02.002.
   Web of Science ®Google Scholar
• Perré, P.; Rémond, R.; Colin, J.; Mougel, E.; Almeida, G. Energy Consumption in the Convective Drying of Timber Analyzed by a Multiscale Computational Model. Drying Technol. 2012, 30, 1136–1146. DOI: 10.1080/07373937.2012.705205.
   Web of Science ®Google Scholar
• Miano, A. C.; Sabadoti, V. D.; Augusto, P. E. D. Combining Ionizing Irradiation and Ultrasound Technologies: effect on Beans Hydration and Germination. J. Food Sci. 2019, 84, 3179–3185. DOI: 10.1111/1750-3841.14819.
   PubMed Web of Science ®Google Scholar
• Khan, M. I. H.; Sablani, S. S.; Joardder, M. U. H.; Karim, M. A. Application of Machine Learning-Based Approach in Food Drying: Opportunities and Challenges. Drying Technol. 2022, 40, 1051–1067. DOI: 10.1080/07373937.2020.1853152.
   Web of Science ®Google Scholar
• Khan, M. I. H.; Sablani, S. S.; Nayak, R.; Gu, Y. Machine Learning-Based Modeling in Food Processing Applications: State of the Art. Compr. Rev. Food Sci. Food Saf. 2022, 21, 1409–1438.
   PubMed Web of Science ®Google Scholar
• Martynenko, A.; Misra, N. N. Machine Learning in Drying. Drying Technol. 2020, 38, 596–609. DOI: 10.1080/07373937.2019.1690502.
   Web of Science ®Google Scholar
• Sun, Q.; Zhang, M.; Mujumdar, A. S. Recent Developments of Artificial Intelligence in Drying of Fresh Food: A Review. Crit. Rev. Food Sci. Nutr. 2019, 59, 2258–2275. DOI: 10.1080/10408398.2018.1446900.
   PubMed Web of Science ®Google Scholar
• Yang, R.; Chen, J. Mechanistic and Machine Learning Modeling of Microwave Heating Process in Domestic Ovens: A Review. Foods 2021, 10, 2029. DOI: 10.3390/foods10092029.
   PubMed Web of Science ®Google Scholar