30 Years of pore network modeling in drying

It is now almost 30 years since pore network modeling has for the first time been adopted from hydrology and soil science to drying of porous media by Marc Prat in 1993. Since then, also thanks to the improvement in experimental techniques and computational power, the application of pore network modeling has spread to many novel and diverse topics. Some of them are now more application-oriented and interdisciplinary than the pioneering theoretical works.

A Scopus literature review, executed on July 29, 2021, using the keywords “pore” and “network” and “drying,” yielded 1,202 search results. The majority of these publications is, however, related to topics that are out of the scope of this special issue as they consider, for example, sol-gel-processes or purely experimental characterization methods. Only the post-filtering of these search results, on the basis of the interesting field of pore network modeling and percolation concepts applied to heat and mass transfer problems related to drying of porous media, can provide a more accurate overview. The summary in Figure 1 shows the estimated number of papers published in this research field by year. The number of publications almost annually increased since 1993, especially between 2005 and 2014, but compared to the total number of initial matches of 1,202, the actual number of publications focused on pore network simulation of drying of porous media is small, suggesting potentials for further developments in the future.

Figure 1. Publications related to drying of porous media based on pore networks and percolation theory from Scopus literature search using the keywords “pore,” “network” and “drying.” The result includes journal papers, conference proceedings and book chapters between 1993 and July 29, 2021.

This special issue therefore collects a number of papers that document the current trends of pore network modeling in drying and offers perspectives for future research needs. They show that, while still employing the classical invasion rules and pore network structures, the diversity of problems has become much broader and also more interdisciplinary. Based on an increase in the computational power, more complex problems and larger domains than 30 years ago are now considered. One prominent example is the implementation of particle transport and evaporation-induced salt crystallization.^[1] Another important development is the coupling of pore network modeling with computational fluid dynamics based on the Navier-Stokes equations^[2] or Lattice Boltzmann modeling.^[3,4] Additionally, there is clearly a rising interest in the reconstruction of the pore space using high-resolution imaging, which offers great potentials to improve the model predictions.^[5]

Considering Marc Prat’s significant contributions to the field, it is clear that not only he has been leading the drying community from the first days, but he is still playing a central role in shaping the directions for future studies. Born in September 1956, he obtained his B.Sc. in Civil Engineering from Ecole Nationale des Ponts et Chaussées, Paris, France in 1979 and his M.Sc. from the University of Toulouse, France in 1982. Afterwards, he continued with his doctorate and obtained his Ph.D. in Physical Sciences with the thesis “Modélisation des transferts en milieux poreux: Changement d'échelle et conditions aux limites” in 1989 from the Institut National Polytechnique de Toulouse (INPT) in France. Afterwards, he visited UC Davis, USA as an assistant visiting professor in the period of 1989–1990. Since then and up to now, he has been continuously contributing to the research community as a CNRS researcher at the Institut de Mécanique des Fluides de Toulouse, France.¹

Marc Prat did author and coauthor more than 110 scientific papers in peer-reviewed journals and supervised or co-supervised more than 40 Ph.D. students, receiving scientific awards for his excellent work. An example is the Interpore Award for Porous Media Research, which he received in 2016. The influential contributions of Marc Prat to the drying community is reflected by his extensive list of publications combined with the ever-growing number of citations of his papers on pore network modeling of drying of porous materials.^[6–8] This special issue is therefore dedicated to his lifetime achievements and contribution to the field.

Marc Prat has inspired and supported many of the researchers who have now become active pore networkers. In pore network modeling, the newly developed clusters, which are separated from the mother cluster due to evaporation and invasion of the gas phase, are often named the children. A large number of clusters can develop from the former mother cluster. They typically remain interconnected by liquid films, which enable the liquid communication beyond the cluster boundaries. Taking this idea as an analog, one can be optimistic that the still relatively small community of pore networkers in drying technology, initiated and inspired by the works of Marc Prat, might be further growing in the future and tackle the many open questions that are still existing, even after 30 years.

In this sense, pore network modeling has the potential to contribute toward the efforts to solve some of the current global challenges, such as reducing CO₂ emissions and increasing the energy efficiency of processes. Especially in drying, where the kinetics of heat and mass transfer inside of a porous medium control the overall energy consumption of the process, optimization cannot be obtained without consideration of pore scale mechanisms.^[9] The need for reliable and predictive pore network models might thus be much more urgent than ever before, especially because direct numerical simulation methods are still not competitive in terms of computational time and power. The progress could be directed by the simulation of larger domains, enabled through computational parallelization and upscaling strategies, universal consideration of heat transfer, implementation of realistic structures as well as further development of microfluidic experiments with more realistic 3D structures.^[10] In addition, implementation of mechanical stresses, shrinkage and cracks, which are natural phenomena of drying processes, deserves further attention as they not only dynamically alter the pore structure but also affect the drying kinetics and product properties.

Many more examples might be added to this overview. On that note, this special issue can only serve as an inspiration and impulse for future innovative and interdisciplinary projects.

N. Vorhauer-Huget^a and N. Shokri^b
aOtto-von-Guericke University, Magdeburg, Germany
^bInstitute of Geo-Hydroinformatics, Hamburg University of Technology, Hamburg, Germany
[email protected]

Notes

1 Information taken from the website marcprat.free.fr on September 13, 2021.