Dear Daisuke,

thank you for your question. We would propose the following workflow to estimate the shell thickness:
Assume you have core-shell particles of a base material (MaterialID 01) and a shell material (MaterialID 02). Then we propose the following workflow:

• Reassign the base material to a liquid material. The example structure may now look as in the following picture.
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• Use "Analyze -> Grain Find -> Estimate Grain Diamters" to estimate the coating thickness.
  
  • “Estimate Grain Diameters” uses internally the Euclidian Distance Map, a watershed algorithm is used to transfer the values of voxels with small components to neighboring voxels with large components
  • We have a technical paper available that describes the background of the “Estimate Grain Diameters” algorithm: https://www.math2market.de/fileadmin/Showroom/Technical-Reports/M2M-2021-01_TechReport_Math2Market.pdf
  • In the example, I used the options “Chosen Material IDs: 2” (coating’s material ID) and “Remove Grain Fragments at Domain Boundary” (if you leave this checked you will get low coating thickness at the domain boundaries in the result
  • [ IMAGE NOT SHOWN - GUESTS CANNOT VIEW ATTACHED IMAGES ]

Finally, you can interpretate the grain diameters as the shell thickness. It can be visualized by the volume field "Diameter".
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Note: You could use a similar workflow with Analyse -> MatDict -> Material Characterization -> Solid Size Distribution (Granulometry) in the step 2 from above.

• Please note the instruction for Granulometry in the MatDict UserGuide (page 20 and following).
• Especially the bin size must be selected small enough depending on the expected minimum coating thicknesses.
• Different visualization options are described, probably the best for your problem is the volume fraction visualization.

This approach will also fit spheres in the coating material, however corners are a differently treated as in the "Estimate Grain Diameter" approach from above, because smaller spheres are not merged with neighboring large spheres.

I hope my answer helped you.

Best regards, Roman