References
- Siebert, T.; Zuber, M.; Hamann, E.; Baumbach, T.; Karbstein, H. P.; Gaukel, V. Micro-CT Visualization of Structure Development during Freeze-Drying Processes. Drying Technol. 2020, 38, 376–384. DOI: https://doi.org/10.1080/07373937.2019.1572619.
- Nakagawa, K.; Tamiya, S.; Sakamoto, S.; Do, G.; Kono, S. Observation of Microstructure Formation during Freeze-Drying of Dextrin Solution by In-Situ X-Ray Computed Tomography. Front. Chem. 2018, 6, 418. DOI: https://doi.org/10.3389/fchem.2018.00418.
- Mujumdar, A. S. Handbook of Industrial Drying, 2nd ed.; CRC Press: New York, 1995. DOI: https://doi.org/10.1201/9780429289774.
- Prat, M. Percolation Model of Drying under Isothermal Conditions in Porous Media. Int. J. Multiphase Flow 1993, 19, 691–704. DOI: https://doi.org/10.1016/0301-9322(93)90096-D.
- Metzger, T.; Irawan, A.; Tsotsas, E. Influence of Pore Structure on Drying Kinetics: A Pore Network Study. AIChE J. 2007, 53, 3029–3041. DOI: https://doi.org/10.1002/aic.11307.
- Yiotis, A. G.; Boudouvis, A. G.; Stubos, A. K.; Tsimpanogiannis, I. N.; Yortsos, Y. C. Effect of Liquid Films on the Isothermal Drying of Porous Media. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 2003, 68, 037303. DOI: https://doi.org/10.1103/PhysRevE.68.037303.
- Segura, L. A.; Toledo, P. G. Pore-Level Modeling of Isothermal Drying of Pore Networks Accounting for Evaporation, Viscous Flow, and Shrinking. Drying Technol. 2005, 23, 2007–2019. DOI: https://doi.org/10.1080/07373930500210457.
- Prat, M. On the Influence of Pore Shape, Contact Angle and Film Flows on Drying of Capillary Porous Media. Int. J. Heat Mass Transf. 2007, 50, 1455–1468. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2006.09.001.
- 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: https://doi.org/10.1007/s11242-009-9372-7.
- Yiotis, A. G.; Tsimpanogiannis, I. N.; Stubos, A. K.; Yortsos, Y. C. Pore-network study of the characteristic periods in the drying of porous materials. J. Colloid Interface Sci. 2006, 297, 738–748. DOI: https://doi.org/10.1016/j.jcis.2005.11.043.
- Metzger, T.; Tsotsas, E. Viscous Stabilization of Drying Front: Three-Dimensional Pore Network Simulations. Chem. Eng. Res. Des. 2008, 86, 739–744. DOI: https://doi.org/10.1016/j.cherd.2008.03.003.
- Wang, Y.; Kharaghani, A.; Metzger, T.; Tsotsas, E. Pore Network Drying Model for Particle Aggregates: Assessment by X-Ray Microtomography. Drying Technol. 2012, 30, 1800–1809. DOI: https://doi.org/10.1080/07373937.2012.713422.
- Sun, Y.; Kharaghani, A.; Metzger, T.; Müller, J.; Tsotsas, E. Lotion Distribution in Wet Wipes Investigated by Pore Network Simulation and X-Ray Micro Tomography. Transp. Porous Med. 2015, 107, 449–468. DOI: https://doi.org/10.1007/s11242-014-0448-7.
- Gostick, J. Versatile and Efficient Pore Network Extraction Method Using Marker-Based Watershed Segmentation. Phys. Rev. E 2017, 96, 023307. DOI: https://doi.org/10.1103/PhysRevE.96.023307.
- Lee, J. K.; Bazylak, A. Optimizing Porous Transport Layer Design Parameters via Stochastic Pore Network Modelling: Reactant Transport and Interfacial Contact Considerations. J. Electrochem. Soc. 2020, 167, 013541. DOI: https://doi.org/10.1149/1945-7111/ab6557.
- Foroughi, S.; Bijeljic, B.; Lin, Q.; Raeini, A.; Blunt, M. J. Pore-by-pore modeling, analysis, and prediction of two-phase flow in mixed-wet rocks. Phys. Rev. E 2020, 102, 023302. DOI: https://doi.org/10.1103/PhysRevE.102.023302.
- Gao, Y.; Lin, Q.; Bijeljic, B.; Blunt, M. J. Pore-Scale Dynamics and the Multiphase Darcy Law. Phys. Rev. Fluids 2020, 5, 013801, 1–12. DOI: https://doi.org/10.1103/PhysRevFluids.5.013801.
- Haide, R.; Fest-Santini, S.; Santini, M. Use of X-Ray Micro-Computed Tomography for the Investigation of Drying Processes in Porous Media: A Review. Drying Technol. 2021, 9, 1–14. DOI: https://doi.org/10.1080/07373937.2021.1876723.
- Pisano, R.; Barresi, A. A.; Capozzi, L. C.; Novajra, G.; Oddone, I.; Vitale-Brovarone, C. Characterization of the Mass Transfer of Lyophilized Products Based on X-Ray Micro-Computed Tomography Images. Drying Technol. 2017, 35, 933–938. DOI: https://doi.org/10.1080/07373937.2016.1222540.
- Defraeye, T.; Nicolaï, B.; Mannes, D.; Aregawi, W.; Verboven, P.; Derome, D. Probing inside Fruit Slices during Convective Drying by Quantitative Neutron Imaging. J. Food Eng. 2016, 178, 198–202. DOI: https://doi.org/10.1016/j.jfoodeng.2016.01.023.
- Foerst, P.; Gruber, S.; Schulz, M.; Vorhauer, N.; Tsotsas, E. Characterization of Lyophilization of Frozen Bulky Solids. Chem. Eng. Technol. 2020, 43, 789–796. DOI: https://doi.org/10.1002/ceat.201900500.
- Vorhauer-Huget, N.; Mannes, D.; Hilmer, M.; Gruber, S.; Strobl, M.; Tsotsas, E.; Foerst, P. Freeze-Drying with Structured Sublimation Fronts: Visualization with Neutron Imaging. Processes 2020, 8, 1091. DOI: https://doi.org/10.3390/pr8091091.
- van der Walt, S.; Schönberger, J. L.; Nunez-Iglesias, J.; Boulogne, F.; Warner, J. D.; Yager, N.; Gouillart, E.; Yu, T, Scikit-Image Contributors. Scikit-Image: Image Processing in Python. PeerJ 2014, 2, e453. DOI: https://doi.org/10.7717/peerj.453.
- Virtanen, P.; Gommers, R.; Oliphant, T. E.; Haberland, M.; Reddy, T.; Cournapeau, D.; Burovski, E.; Peterson, P.; Weckesser, W.; Bright, J.; et al. SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nat. Methods 2020, 17, 261–272. DOI: https://doi.org/10.1038/s41592-019-0686-2.
- Gostick, J.; Khan, Z.; Tranter, T.; Kok, M.; Agnaou, M.; Sadeghi, M.; Jervis, R. PoreSpy: A Python Toolkit for Quantitative Analysis of Porous Media Images. JOSS. 2019, 4, 1296. DOI: https://doi.org/10.21105/joss.01296.
- Geistlinger, H.; Ding, Y.; Apelt, B.; Schlüter, S.; Küchler, M.; Reuter, D.; Vorhauer, N.; Vogel, H.‐J. Evaporation Study Based on Micromodel Experiments: Comparison of Theory and Experiment. Water Resour. Res. 2019, 55, 6653–6672. DOI: https://doi.org/10.1029/2018WR024647.
- Panda, D.; Bhaskaran, S.; Paliwal, S.; Kharaghani, A.; Tsotsas, E.; Surasani, V. K. Pore-Scale Physics of Drying Porous Media Revealed by Lattice Boltzmann Simulations. Drying Technol. 2020, 1–16. DOI: https://doi.org/10.1080/07373937.2020.1850469.
- Zhao, J.; Qin, F.; Derome, D.; Kang, Q.; Carmeliet, J. Improved Pore Network Models to Simulate Single-Phase Flow in Porous Media by Coupling with Lattice Boltzmann Method. Adv. Water Resour. 2020, 145, 103738. DOI: https://doi.org/10.1016/j.advwatres.2020.103738.
- Vorhauer, N.; Först, P.; Schuchmann, H.; Tsotsas, E. Pore Network Model of Primary Freeze Drying. Proceedings of the International Drying Symposium, Valencia, Spain, Sept 11–14, 2018.
- Gruber, S.; Vorhauer, N.; Schulz, M.; Hilmer, M.; Peters, J.; Tsotsas, E.; Foerst, P. Estimation of the Local Sublimation Front Velocities from Neutron Radiography and Tomography of Particulate Matter. Chem. Eng. Sci. 2020, 211, 115268. DOI: https://doi.org/10.1016/j.ces.2019.115268.
- Nakagawa, K.; Tamiya, S.; Ochiai, T. Evaluation of Degree of Collapse and Its Relationship with Retention of Organic Volatiles in Freeze-Dried Dextrin Matrices. Ind. Eng. Chem. Res. 2020, 59, 18298–18306. DOI: https://doi.org/10.1021/acs.iecr.0c03394.
- Liapis, A. I.; Bruttini, R. A Mathematical Model for the Spray Freeze Drying Process: The Drying of Frozen Particles in Trays and in Vials on Trays. Int. J. Heat Mass Transf. 2009, 52, 100–111. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2008.06.026.
- Rasetto, V.; Marchisio, D. L.; Fissore, D.; Barresi, A. A. On the Use of a Dual-Scale Model to Improve Understanding of a Pharmaceutical Freeze-Drying Process. J. Pharm. Sci. 2010, 99, 4337–4350. DOI: https://doi.org/10.1002/jps.22127.
- Foerst, P.; Melo de Carvalho, T.; Lechner, M.; Kovacevic, T.; Kim, S.; Kirse, C.; Briesen, H. Estimation of Mass Transfer Rate and Primary Drying Times during Freeze-Drying of Frozen Maltodextrin Solutions Based on X-Ray μ-Computed Tomography Measurements of Pore Size Distributions. J. Food Eng. 2019, 260, 50–57. DOI: https://doi.org/10.1016/j.jfoodeng.2019.05.002.
- Kaestner, A.; Lehmann, E.; Stampanoni, M. Imaging and Image Processing in Porous Media Research. Adv. Water Resour. 2008, 31, 1174–1187. DOI: https://doi.org/10.1016/j.advwatres.2008.01.022.
- Wildenschild, D.; Sheppard, A. P. X-Ray Imaging and Analysis Techniques for Quantifying Pore-Scale Structure and Processes in Subsurface Porous Medium Systems. Adv. Water Resour. 2013, 51, 217–246. DOI: https://doi.org/10.1016/j.advwatres.2012.07.018.
- Al-Raoush, R. I.; Willson, C. S. Extraction of Physically Realistic Pore Network Properties from Three-Dimensional Synchrotron X-Ray Microtomography Images of Unconsolidated Porous Media Systems. J. Hydrol. 2005, 300, 44–64. DOI: https://doi.org/10.1016/j.jhydrol.2004.05.005.
- Pashminehazar, R.; Ahmed, S. J.; Kharaghani, A.; Tsotsas, E. Spatial Morphology of Maltodextrin Agglomerates from X-Ray Microtomographic Data: Real Structure Evaluation vs. spherical Primary Particle Model. Powder Technol. 2018, 331, 204–217. DOI: https://doi.org/10.1016/j.powtec.2018.03.008.
- Garfi, G.; John, C. M.; Berg, S.; Krevor, S. The Sensitivity of Estimates of Multiphase Fluid and Solid Properties of Porous Rocks to Image Processing. Transp. Porous Med. 2020, 131, 985–1005. DOI: https://doi.org/10.1007/s11242-019-01374-z.
- Patmonoaji, A.; Tsuji, K.; Suekane, T. Pore-Throat Characterization of Unconsolidated Porous Media Using Watershed-Segmentation Algorithm. Powder Technol. 2020, 362, 635–644. DOI: https://doi.org/10.1016/j.powtec.2019.12.026.
- Dong, H.; Blunt, M. J. Pore-Network Extraction from Micro-Computerized-Tomography Images. Phys. Rev. E Stat. Nonlin. Soft. Matter Phys. 2009, 80, 036307. DOI: https://doi.org/10.1103/PhysRevE.80.036307.
- Jähne, B. Digital Image Processing,6th ed.; Springer-Verlag: Berlin/Heidelberg, 2005. DOI: https://doi.org/10.1007/3-540-27563-0
- Perona, P.; Malik, J. Scale-Space and Edge Detection Using Anisotropic Diffusion. IEEE Trans. Pattern Anal. Machine Intell. 1990, 12, 629–639. DOI: https://doi.org/10.1109/34.56205.
- Otsu, N. A Threshold Selection Method from Gray-Level Histograms. IEEE Trans. Syst. Man Cybern. 1979, 9, 62–66. DOI: https://doi.org/10.1109/TSMC.1979.4310076.
- Bradley, D.; Roth, G. Adaptive Thresholding Using the Integral Image. J. Graph. Tools 2007, 12, 13–21. DOI: https://doi.org/10.1080/2151237X.2007.10129236.
- Rabbani, A.; Babaei, M.; Javadpour, F. A Triple Pore Network Model (T-PNM) for Gas Flow Simulation in Fractured, Micro-Porous and Meso-Porous Media. Transp. Porous Med. 2020, 132, 707–740. DOI: https://doi.org/10.1007/s11242-020-01409-w.
- Youssef, S.; Rosenberg, E.; Gland, N.; Bekri, S.; Vizika, O. Quantitative 3D Characterization of the Pore Space of Real Rocks: Improved μ-Ct Resolution and Pore Extraction Methodology. International Symposium of the Society of Core Analysts, Calgary, Canada, 2007, SCA2007–17.
- Rabbani, A.; Jamshidi, S.; Salehi, S. An Automated Simple Algorithm for Realistic Pore Network Extraction from Micro-Tomography Images. J. Pet. Sci. Eng. 2014, 123, 164–171. DOI: https://doi.org/10.1016/j.petrol.2014.08.020.
- Gruber, S.; Vorhauer-Huget, N.; Foerst, P. In Situ µ-CT Measurements during Freeze-Drying Offers Detailed Information on Microstructure and Sublimation Front. Food Struct. 2021, 29, 100213. DOI: https://doi.org/10.1016/j.foostr.2021.100213.
- Chantler, C. T. Detailed Tabulation of Atomic Form Factors, Photoelectric Absorption and Scattering Cross Section, and Mass Attenuation Coefficients in the Vicinity of Absorption Edges in the Soft X-Ray (Z = 30–36, Z = 60–89, E = 0.1 keV–10 keV), Addressing Convergence Issues of Earlier Work. J. Phys. Chem. Ref. Data 2000, 29, 597–1056. DOI: https://doi.org/10.1063/1.1321055.
- Metzger, T.; Tsotsas, E.; Prat, M. Pore-Network Models: A Powerful Tool to Study Drying at the Pore Level and Understand the Influence of Structure on Drying Kinetics. Mod. Dry. Technol. 2011, 1, 57–102. DOI: https://doi.org/10.1002/9783527631629.ch2.
- Huang, X.; Zhou, W.; Deng, D. Effective Diffusion in Fibrous Porous Media: A Comparison Study between Lattice Boltzmann and Pore Network Modeling Methods. Materials (Basel) 2021, 14, 756. DOI: https://doi.org/10.3390/ma14040756.
- Zarekar, S.; Bück, A.; Jacob, M.; Tsotsas, E. Reconsideration of the Hydrodynamic Behavior of Fluidized Beds Operated under Reduced Pressure. Powder Technol. 2016, 287, 169–176. DOI: https://doi.org/10.1016/j.powtec.2015.09.027.