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Each object is treated as a continuous medium of materials points interacting by the Lennard-Jones 12\u20136 potential. By integrating this potential in a pairwise manner, expressions for the potentials and resultant forces between extended objects are obtained. All the results are validated with numerical integrations. The analytical potentials are implemented in LAMMPS and used to simulate two-dimensional suspension of disks with an explicit solvent modeled as a Lennard-Jones liquid. In monodisperse disk suspensions, a disorder-to-order transition of disk packing is observed as the area fraction of disks is increased or as the solvent evaporates. In bidisperse disk suspensions being rapidly dried, stratification is found with the smaller disks enriched at the evaporation front. Such \u201csmall-on-top\u201d stratification echoes the similar phenomenon occurring in three-dimensional polydisperse colloidal suspensions that undergo fast drying. These potentials can be applied to a wide range of two-dimensional systems involving disk-like objects.<\/jats:p>","DOI":"10.1063\/5.0313885","type":"journal-article","created":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T10:41:52Z","timestamp":1773744112000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Analytical interaction potentials for disks in two dimensions"],"prefix":"10.1063","volume":"164","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-3382-5790","authenticated-orcid":false,"given":"Binghan","family":"Liu","sequence":"first","affiliation":[{"name":"Department of Physics, Virginia Tech 1 , Blacksburg, Virginia 24061,","place":["USA"]},{"name":"Center for Soft Matter and Biological Physics, Virginia Tech 2 , Blacksburg, Virginia 24061,","place":["USA"]},{"name":"Macromolecules Innovation Institute, Virginia Tech 3 , Blacksburg, Virginia 24061,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-7263-1964","authenticated-orcid":false,"given":"Junwen","family":"Wang","sequence":"additional","affiliation":[{"name":"Center for Soft Matter and Biological Physics, Virginia Tech 2 , Blacksburg, Virginia 24061,","place":["USA"]},{"name":"Macromolecules Innovation Institute, Virginia Tech 3 , Blacksburg, Virginia 24061,","place":["USA"]},{"name":"Department of Mechanical Engineering, Virginia Tech 4 , Blacksburg, Virginia 24061,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5260-9788","authenticated-orcid":false,"given":"Gary S.","family":"Grest","sequence":"additional","affiliation":[{"name":"Sandia National Laboratories 5 , Albuquerque, New Mexico 87185,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6066-2968","authenticated-orcid":false,"given":"Shengfeng","family":"Cheng","sequence":"additional","affiliation":[{"name":"Department of Physics, Virginia Tech 1 , Blacksburg, Virginia 24061,","place":["USA"]},{"name":"Center for Soft Matter and Biological Physics, Virginia Tech 2 , Blacksburg, Virginia 24061,","place":["USA"]},{"name":"Macromolecules Innovation Institute, Virginia Tech 3 , Blacksburg, Virginia 24061,","place":["USA"]},{"name":"Department of Mechanical Engineering, Virginia Tech 4 , Blacksburg, Virginia 24061,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"317","published-online":{"date-parts":[[2026,3,17]]},"reference":[{"key":"2026031706414924400_c1","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1039\/tf9322800333","article-title":"Processes of adsorption and diffusion on solid surfaces","volume":"28","year":"1932","journal-title":"Trans. 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