Electric Field and Voltage Distribution On a glass Insulating Surface Covered With Pollution and different shapes of electrodes by Using a Finite Element Method

Electric Field and Voltage Distribution On a glass Insulating Surface Covered With Pollution and different shapes of electrodes by Using a Finite Element Method | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Electric Field and Voltage Distribution On a glass Insulating Surface Covered With Pollution and different shapes of electrodes by Using a Finite Element Method samia SATTA, Fatiha Aouabed, Meriem Messaoudi, a.hafid Bayadi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8192487/v1 This work is licensed under a CC BY 4.0 License Status: Under Revision Version 1 posted 12 You are reading this latest preprint version Abstract This research paper aims to simulate on 3D the potential distribution and electric field on insulating surfaces of different sizes uniformly polluted for a comparison between them, moreover, it is aimed to find equivalence between multiple rods-rods and plane-plane configurations. This work is devoted to study the effects of many parameters on the electric strength of the considered air gap system configurations are presented; these parameters are the length of the flashover distance; the pollution degree and the contaminated surface. Glass rectangular surfaces are used for the tests. Finally, the obtained results show that there is a width limit approximately equal to 8 cm between two critical points, parallel, consecutive and independent can develop. This limit represents the minimal electrical performance of the insulation and we did not observe any effect of the volume conductivity on it. A numerical method is developed for analyzing the influence of the system configurations on the electric field, the electric discharge activities of the insulation. To evaluate the distribution of the electric field along the insulator's flashover distance and to identify the main regions of the critical field, the COMSOL Multiphysics software has been exploited. A numerical method via a COMSOL Multiphysics 6.0 has proven to be one of the best solutions. For this purpose, the finite element method was better adapted to the constraints imposed by the operating conditions of the insulators. Physical sciences/Engineering Physical sciences/Materials science Physical sciences/Physics Pollution Electric Field Simulation COMSOL Multiphysics 6.0 Glass surface High voltage Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Full Text Additional Declarations No competing interests reported. Table 1 is available in the Supplementary Files section Supplementary Files S.SATTATABLES.docx Cite Share Download PDF Status: Under Revision Version 1 posted Editorial decision: Revision requested 02 Jan, 2026 Reviews received at journal 31 Dec, 2025 Reviews received at journal 23 Dec, 2025 Reviews received at journal 22 Dec, 2025 Reviewers agreed at journal 11 Dec, 2025 Reviewers agreed at journal 10 Dec, 2025 Reviewers agreed at journal 10 Dec, 2025 Reviewers invited by journal 10 Dec, 2025 Editor assigned by journal 10 Dec, 2025 Editor invited by journal 09 Dec, 2025 Submission checks completed at journal 03 Dec, 2025 First submitted to journal 03 Dec, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8192487","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":558706561,"identity":"ad814762-ef0b-4636-9057-7541c2ec8112","order_by":0,"name":"samia SATTA","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4ElEQVRIiWNgGAWjYDADNgbmAwyMDUAWkCYAmMHqgFrYEiBagDRxWhgYeAyI0yLffv74gx9/7KL52M98k/i5w0aOgY33AV4tBmeSGRt725Jz23hyt0n2nkkzZmBjN8CvhSGZsYG3gTm3jSF3mwRv2+HEBvk2Ag7rf8zY+OdPfW4b/5tnkn9BWtjY8GthuJHM2MzDdji3TSKHTZqXGC0GNx4bzpZtOw7U8szYWrYtzZiNkBb5/sQHH9/8qc6d35/88ObbNhs5foIOQwIsEiCSBA3ASP1AiupRMApGwSgYOQAA8mlDcEdyWxIAAAAASUVORK5CYII=","orcid":"","institution":"","correspondingAuthor":true,"prefix":"","firstName":"samia","middleName":"","lastName":"SATTA","suffix":""},{"id":558706563,"identity":"daa6dcdf-579c-4fb4-98d9-71ff2ebff666","order_by":1,"name":"Fatiha Aouabed","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Fatiha","middleName":"","lastName":"Aouabed","suffix":""},{"id":558706570,"identity":"807a3061-03a2-4370-9b07-471cc91fb708","order_by":2,"name":"Meriem Messaoudi","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Meriem","middleName":"","lastName":"Messaoudi","suffix":""},{"id":558706572,"identity":"223503cc-bec5-4095-9e44-b53dc7c67cb7","order_by":3,"name":"a.hafid Bayadi","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"a.hafid","middleName":"","lastName":"Bayadi","suffix":""}],"badges":[],"createdAt":"2025-11-24 10:53:25","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8192487/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8192487/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":98349885,"identity":"da8c9972-ca69-4ab4-8bd4-d65aad8655da","added_by":"auto","created_at":"2025-12-16 20:17:28","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":42886,"visible":true,"origin":"","legend":"","description":"","filename":"s.sattaart4.docx","url":"https://assets-eu.researchsquare.com/files/rs-8192487/v1/de8e6c07aca1dc2f15f98e5b.docx"},{"id":98349891,"identity":"08cff179-e7f7-4d1f-92c9-ed591461c0ea","added_by":"auto","created_at":"2025-12-16 20:17:28","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":1411546,"visible":true,"origin":"","legend":"","description":"","filename":"S.SATTAFIGURES.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8192487/v1/3573f0f68e93ca1634cad8c6.pdf"},{"id":98438635,"identity":"8bca6a9b-1876-4d86-acfd-d16a6508742c","added_by":"auto","created_at":"2025-12-17 16:59:42","extension":"json","order_by":3,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":6151,"visible":true,"origin":"","legend":"","description":"","filename":"52db3653bfb24750a700693d00d1117f.json","url":"https://assets-eu.researchsquare.com/files/rs-8192487/v1/5569da59b2afd357da45897a.json"},{"id":98438133,"identity":"927ad183-247f-4bd8-9a29-ceaa31348e7b","added_by":"auto","created_at":"2025-12-17 16:58:41","extension":"xml","order_by":4,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":71935,"visible":true,"origin":"","legend":"","description":"","filename":"52db3653bfb24750a700693d00d1117f1enriched.xml","url":"https://assets-eu.researchsquare.com/files/rs-8192487/v1/987e865c3526912f2321cbef.xml"},{"id":98439375,"identity":"a14588cb-41d9-4df7-a99e-64d859432d7c","added_by":"auto","created_at":"2025-12-17 17:01:43","extension":"pdf","order_by":5,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":1411546,"visible":true,"origin":"","legend":"","description":"","filename":"S.SATTAFIGURES.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8192487/v1/b0d9c793a4f75b77f8b09fce.pdf"},{"id":98349903,"identity":"5e20ea00-525e-401a-ba37-ddef845666bf","added_by":"auto","created_at":"2025-12-16 20:17:28","extension":"wmf","order_by":6,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":424,"visible":true,"origin":"","legend":"","description":"","filename":"image1.wmf","url":"https://assets-eu.researchsquare.com/files/rs-8192487/v1/9e917f9a81a950278ce5ec37.wmf"},{"id":98439296,"identity":"4c2f00c9-32c2-4b89-96fd-446368211fd5","added_by":"auto","created_at":"2025-12-17 17:01:34","extension":"png","order_by":7,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":273,"visible":true,"origin":"","legend":"","description":"","filename":"Onlineimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-8192487/v1/30c25d3f64ad766270147671.png"},{"id":98349908,"identity":"c1f75403-d386-410a-ae66-4ccfda229684","added_by":"auto","created_at":"2025-12-16 20:17:28","extension":"xml","order_by":8,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":68770,"visible":true,"origin":"","legend":"","description":"","filename":"52db3653bfb24750a700693d00d1117f1structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-8192487/v1/89df908e86e8afa75d919324.xml"},{"id":98439082,"identity":"ada51f34-56a3-4d85-b252-c6a79854c2b6","added_by":"auto","created_at":"2025-12-17 17:01:00","extension":"html","order_by":9,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":81369,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-8192487/v1/99f93d725c23313d2f6f636f.html"},{"id":98439339,"identity":"936407d0-ec6a-48b3-95fe-db7f9d5ac514","added_by":"auto","created_at":"2025-12-17 17:01:39","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":131593,"visible":true,"origin":"","legend":"\u003cp\u003eView of the studied configurations [14, \u0026nbsp;\u0026nbsp;16].\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-8192487/v1/96435f4e531763c7c0d534ea.png"},{"id":98349889,"identity":"f22d18d6-a907-45d7-9f3d-08bd6d29f3c5","added_by":"auto","created_at":"2025-12-16 20:17:28","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":37187,"visible":true,"origin":"","legend":"\u003cp\u003eProfile of the model used\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-8192487/v1/466f333d247692d07065a965.png"},{"id":98438605,"identity":"d98b9ed1-bb32-41a9-84c4-54a8cfc908d1","added_by":"auto","created_at":"2025-12-17 16:59:38","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":150183,"visible":true,"origin":"","legend":"\u003cp\u003eMesh obtained\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-8192487/v1/d24db957a975c8a2c9be81f5.png"},{"id":98439695,"identity":"39812136-0f9b-4e40-902b-8ee63bfb0cbd","added_by":"auto","created_at":"2025-12-17 17:02:44","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":380361,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of electrical voltage (clean case)\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-8192487/v1/126712f3441dcc74201a7147.png"},{"id":98439208,"identity":"58bf5a83-dd46-495a-b353-e02c8db6be98","added_by":"auto","created_at":"2025-12-17 17:01:28","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":129785,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of electrical voltage L= 320 mm (polluted case)\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-8192487/v1/4812cb2e7acdf957b7bc0804.png"},{"id":98349895,"identity":"e7e6d8e8-96c3-4f70-926c-8f94f8c4c94b","added_by":"auto","created_at":"2025-12-16 20:17:28","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":6413,"visible":true,"origin":"","legend":"\u003cp\u003eElectric potential along insulator surface (L= 320 mm)\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-8192487/v1/e1c44a9e443dd3b980ffc3a2.png"},{"id":98439673,"identity":"3a1d7125-9e28-4c99-bc03-e6385f216bdd","added_by":"auto","created_at":"2025-12-17 17:02:37","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":436202,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of the electric field (clean case)\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-8192487/v1/734f67acad43006b5699e279.png"},{"id":98439395,"identity":"d80a1daa-bccf-4a5a-9328-0228c19c8a99","added_by":"auto","created_at":"2025-12-17 17:01:46","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":142464,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of the electric field L= 320 mm (polluted case)\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-8192487/v1/bdc477a83e2d22251be140a8.png"},{"id":98438971,"identity":"01bb81ce-8eef-47b9-a4e9-877fbcd6d8af","added_by":"auto","created_at":"2025-12-17 17:00:36","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":8285,"visible":true,"origin":"","legend":"\u003cp\u003eDistribution of the electric field along insulator surface (L= 320 mm)\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-8192487/v1/1ca55b6bb253060d9b395046.png"},{"id":98349910,"identity":"14a1bd21-a49d-41b6-af5d-8c78c66b030c","added_by":"auto","created_at":"2025-12-16 20:17:29","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":290354,"visible":true,"origin":"","legend":"\u003cp\u003eElectrical Potentiel Distribution (L= 320 mm)\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-8192487/v1/9fcbf97e55cfa9d52f935331.png"},{"id":98439935,"identity":"94e80dff-ebfa-4616-921d-e664c094fb8c","added_by":"auto","created_at":"2025-12-17 17:03:06","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":370510,"visible":true,"origin":"","legend":"\u003cp\u003eEquipotential Lines Distribution (L= 320 mm)\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-8192487/v1/ed41a0689c381de0cc3378e5.png"},{"id":98349897,"identity":"d2b5582e-05c5-4fa0-b110-e3d3cbd41c89","added_by":"auto","created_at":"2025-12-16 20:17:28","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":91710,"visible":true,"origin":"","legend":"\u003cp\u003eElectric Field Distribution (L= 320 mm)\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-8192487/v1/ee1a2a16e7c1179444b39f29.png"},{"id":98349907,"identity":"e03b6ce0-5213-4bb9-8faa-08f2d78104da","added_by":"auto","created_at":"2025-12-16 20:17:28","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":186667,"visible":true,"origin":"","legend":"\u003cp\u003eField Lines Distribution (L= 320 mm)\u003c/p\u003e","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-8192487/v1/85a078a0b73684db79d642bb.png"},{"id":98438405,"identity":"7834cbd9-94c2-4bee-9ce5-1f7a0a347c4a","added_by":"auto","created_at":"2025-12-17 16:59:11","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":17260,"visible":true,"origin":"","legend":"\u003cp\u003ePotential and Field Electric distribution (Plane-plane; 2 rods – 2rods case, L= 160 mm)\u003c/p\u003e","description":"","filename":"14.png","url":"https://assets-eu.researchsquare.com/files/rs-8192487/v1/0fab8c1733aaa7204ef397ea.png"},{"id":98438300,"identity":"9108b79f-63c0-478b-97b0-b5541d536e31","added_by":"auto","created_at":"2025-12-17 16:58:59","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":10863,"visible":true,"origin":"","legend":"\u003cp\u003eElectric potential Distribution for Different Electrode Systems (L= 320 mm)\u003c/p\u003e","description":"","filename":"15.png","url":"https://assets-eu.researchsquare.com/files/rs-8192487/v1/2aa52677f757f34beecef2d8.png"},{"id":98439337,"identity":"a9297aae-0f0c-4c3e-b6a0-a3486ac7833b","added_by":"auto","created_at":"2025-12-17 17:01:39","extension":"png","order_by":16,"title":"Figure 16","display":"","copyAsset":false,"role":"figure","size":10179,"visible":true,"origin":"","legend":"\u003cp\u003eElectric Field Distribution for Different Electrode Systems\u003c/p\u003e","description":"","filename":"16.png","url":"https://assets-eu.researchsquare.com/files/rs-8192487/v1/912b1ce4c7f74c7cc2ea2981.png"},{"id":98623223,"identity":"43f8b220-a136-4e60-ac45-2d10e264bdbb","added_by":"auto","created_at":"2025-12-19 17:05:21","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1031265,"visible":true,"origin":"","legend":"","description":"","filename":"s.sattaart4.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8192487/v1_covered_6b3c6bf1-07f8-4ed7-bd79-e7e92366a133.pdf"},{"id":98349886,"identity":"d5594716-a428-4470-a911-d7114ba7a2a2","added_by":"auto","created_at":"2025-12-16 20:17:28","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":14824,"visible":true,"origin":"","legend":"","description":"","filename":"S.SATTATABLES.docx","url":"https://assets-eu.researchsquare.com/files/rs-8192487/v1/09ed4183deb68f8d57445aca.docx"}],"financialInterests":"\u003cp\u003eNo competing interests reported.\u003c/p\u003e\n\u003cp\u003eTable 1 is available in the Supplementary Files section\u003c/p\u003e","formattedTitle":"Electric Field and Voltage Distribution On a glass Insulating Surface Covered With Pollution and different shapes of electrodes by Using a Finite Element Method","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Pollution, Electric Field, Simulation, COMSOL Multiphysics 6.0, Glass surface, High voltage ","lastPublishedDoi":"10.21203/rs.3.rs-8192487/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8192487/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis research paper aims to simulate on 3D the potential distribution and electric field on insulating surfaces of different sizes uniformly polluted for a comparison between them, moreover, it is aimed to find equivalence between multiple rods-rods and plane-plane configurations. This work is devoted to study the effects of many parameters on the electric strength of the considered air gap system configurations are presented; these parameters are the length of the flashover distance; the pollution degree and the contaminated surface. Glass rectangular surfaces are used for the tests. Finally, the obtained results show that there is a width limit approximately equal to 8 cm between two critical points, parallel, consecutive and independent can develop. This limit represents the minimal electrical performance of the insulation and we did not observe any effect of the volume conductivity on it.\u003c/p\u003e \u003cp\u003eA numerical method is developed for analyzing the influence of the system configurations on the electric field, the electric discharge activities of the insulation. To evaluate the distribution of the electric field along the insulator's flashover distance and to identify the main regions of the critical field, the COMSOL Multiphysics software has been exploited. A numerical method via a COMSOL Multiphysics 6.0 has proven to be one of the best solutions. For this purpose, the finite element method was better adapted to the constraints imposed by the operating conditions of the insulators.\u003c/p\u003e","manuscriptTitle":"Electric Field and Voltage Distribution On a glass Insulating Surface Covered With Pollution and different shapes of electrodes by Using a Finite Element Method","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-12-16 20:17:23","doi":"10.21203/rs.3.rs-8192487/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-01-02T07:34:42+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-31T12:41:15+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-24T01:04:56+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-22T16:21:36+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"251971497129167841753225615116145496028","date":"2025-12-11T05:45:36+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"85551114843978381306831540021059985690","date":"2025-12-11T01:59:29+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"77950811915715388119927287699244316987","date":"2025-12-11T01:13:59+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-12-11T01:06:06+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-12-11T00:58:10+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-12-09T14:40:04+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-12-03T10:23:35+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-12-03T10:06:57+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"270a9e5c-1d9a-4b37-bd1a-f2c8ded53324","owner":[],"postedDate":"December 16th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"in-revision","subjectAreas":[{"id":59474853,"name":"Physical sciences/Engineering"},{"id":59474854,"name":"Physical sciences/Materials science"},{"id":59474855,"name":"Physical sciences/Physics"}],"tags":[],"updatedAt":"2026-01-02T07:39:17+00:00","versionOfRecord":[],"versionCreatedAt":"2025-12-16 20:17:23","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8192487","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8192487","identity":"rs-8192487","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}