{"id":"https://openalex.org/W1968560303","doi":"https://doi.org/10.1098/rsta.1971.0031","title":"The profiles of axially symmetric menisci","display_name":"The profiles of axially symmetric menisci","publication_year":1971,"publication_date":"1971-02-05","ids":{"openalex":"https://openalex.org/W1968560303","doi":"https://doi.org/10.1098/rsta.1971.0031","mag":"1968560303"},"language":"en","primary_location":{"id":"doi:10.1098/rsta.1971.0031","doi":"https://doi.org/10.1098/rsta.1971.0031","is_oa":false,"landing_page_url":"https://doi.org/10.1098/rsta.1971.0031","pdf_url":null,"source":{"id":"https://openalex.org/S4210181956","display_name":"Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences","issn_l":"0080-4614","issn":["0080-4614","2054-0272"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310319787","host_organization_name":"Royal Society","host_organization_lineage":["https://openalex.org/P4310319787"],"host_organization_lineage_names":["Royal Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086809939","display_name":"John F. Padday","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"J. F. Padday","raw_affiliation_strings":["Research Laboratories, Kodak Limited, Wealdstone, Harrow, Middlesex"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Research Laboratories, Kodak Limited, Wealdstone, Harrow, Middlesex","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5086809939"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.9627,"has_fulltext":false,"cited_by_count":197,"citation_normalized_percentile":{"value":0.95298707,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":87,"max":99},"biblio":{"volume":"269","issue":"1197","first_page":"265","last_page":"293"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11382","display_name":"Fluid Dynamics and Heat Transfer","score":0.9643999934196472,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11382","display_name":"Fluid Dynamics and Heat Transfer","score":0.9643999934196472,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12141","display_name":"Fluid Dynamics and Thin Films","score":0.010999999940395355,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13951","display_name":"Fluid dynamics and aerodynamics studies","score":0.003100000089034438,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/meniscus-shape","display_name":"meniscus shape","score":0.6579999923706055},{"id":"https://openalex.org/keywords/sessile-drop","display_name":"sessile drop","score":0.7979999780654907},{"id":"https://openalex.org/keywords/pendant-drop","display_name":"pendant drop","score":0.9990000128746033},{"id":"https://openalex.org/keywords/liquid-bridges","display_name":"liquid bridges","score":0.9879999756813049},{"id":"https://openalex.org/keywords/laplace-equation","display_name":"Laplace equation","score":0.7910000085830688},{"id":"https://openalex.org/keywords/shape-factor","display_name":"shape factor","score":0.7250000238418579},{"id":"https://openalex.org/keywords/surface-tension-force","display_name":"surface tension force","score":0.5600000023841858}],"concepts":[{"id":"https://openalex.org/C189178095","wikidata":"https://www.wikidata.org/wiki/Q15834833","display_name":"Meniscus","level":3,"score":0.7132529616355896},{"id":"https://openalex.org/C33026886","wikidata":"https://www.wikidata.org/wiki/Q593950","display_name":"Rotational symmetry","level":2,"score":0.6967068910598755},{"id":"https://openalex.org/C35377427","wikidata":"https://www.wikidata.org/wiki/Q3886264","display_name":"Axial symmetry","level":2,"score":0.6869246959686279},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.5028819441795349},{"id":"https://openalex.org/C77993745","wikidata":"https://www.wikidata.org/wiki/Q3072364","display_name":"Shape factor","level":2,"score":0.4933737814426422},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.4843326807022095},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.43772703409194946},{"id":"https://openalex.org/C196806460","wikidata":"https://www.wikidata.org/wiki/Q188603","display_name":"Capillary action","level":2,"score":0.4217957854270935},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.41976338624954224},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3141993284225464},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28485262393951416},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2578304409980774},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.1287219226360321},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11693918704986572},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.08824673295021057},{"id":"https://openalex.org/C61511704","wikidata":"https://www.wikidata.org/wiki/Q1671857","display_name":"Incidence (geometry)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1098/rsta.1971.0031","doi":"https://doi.org/10.1098/rsta.1971.0031","is_oa":false,"landing_page_url":"https://doi.org/10.1098/rsta.1971.0031","pdf_url":null,"source":{"id":"https://openalex.org/S4210181956","display_name":"Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences","issn_l":"0080-4614","issn":["0080-4614","2054-0272"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/P4310319787","host_organization_name":"Royal Society","host_organization_lineage":["https://openalex.org/P4310319787"],"host_organization_lineage_names":["Royal Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1964941922","https://openalex.org/W2039074753","https://openalex.org/W2040415374","https://openalex.org/W2045858150","https://openalex.org/W2066882854","https://openalex.org/W2074064212","https://openalex.org/W2076067354","https://openalex.org/W2089124630","https://openalex.org/W2093502908","https://openalex.org/W2119138855","https://openalex.org/W4239644063"],"related_works":["https://openalex.org/W1982918776","https://openalex.org/W2317235648","https://openalex.org/W4238125578","https://openalex.org/W176630481","https://openalex.org/W2380296903","https://openalex.org/W651391009","https://openalex.org/W2050594910","https://openalex.org/W2897861065","https://openalex.org/W2172183203","https://openalex.org/W2126168062"],"abstract_inverted_index":{"Abstract":[0],"The":[1,20,170,179,208],"shape":[2,54,113,157,175],"and":[3,16,44,76,196,226],"forces":[4,201],"of":[5,22,41,53,58,92,94,98,107,114,129,145,148,173,181,184,220,231],"axisymmetric":[6],"menisci":[7,100,144,162],"have":[8,26,84],"been":[9,27,86,194],"calculated":[10],"for":[11,78],"sessile":[12],"drops,":[13],"pendant":[14],"drops":[15],"liquid":[17,31,124,137],"bridge":[18,32,138],"profiles.":[19],"tables":[21,110,130,152,209],"Bashforth":[23,149],"&":[24,150],"Adams":[25],"extended":[28,132],"into":[29,45],"the":[30,38,59,89,105,112,133,146,185,200,204,217,229],"region":[33,134],"by":[34,48,64,71,88,118,155,188],"generating":[35],"profiles":[36,93],"beyond":[37],"180\u00b0":[39],"angle":[40],"their":[42,168],"study,":[43],"regions":[46],"covered":[47],"a":[49,66,95,115,119,122],"much":[50],"wider":[51],"range":[52,97],"factor.":[55],"Numerical":[56],"integration":[57],"Laplace":[60],"equation":[61],"was":[62],"performed":[63],"using":[65],"first-order":[67],"method":[68],"originally":[69],"proposed":[70],"Lord":[72],"Kelvin":[73],"but":[74,160,216],"adapted":[75],"modified":[77],"use":[79],"with":[80,228],"high-speed":[81],"computers.":[82],"Tables":[83],"also":[85,193],"generated,":[87],"same":[90],"techniques,":[91],"wide":[96],"asixymmetric":[99],"that":[101],"do":[102],"not":[103,213],"cross":[104],"axis":[106],"symmetry.":[108],"Such":[109],"include":[111],"meniscus":[116,186],"formed":[117],"rod":[120],"at":[121],"free":[123],"surface.":[125],"This":[126],"second":[127],"group":[128],"greatly":[131],"over":[135],"which":[136],"shapes":[139,223],"could":[140],"be":[141],"obtained.":[142],"Closed":[143],"type":[147],"Adams\u2019s":[151],"are":[153,177,212,224],"defined":[154],"one":[156],"factor":[158],"B,":[159],"open":[161],"require":[163],"two":[164,189],"parameters":[165],"to":[166,199],"identify":[167],"shape.":[169],"general":[171],"properties":[172],"these":[174,221],"factors":[176],"discussed.":[178],"volume":[180],"any":[182],"part":[183],"bounded":[187],"horizontal":[190],"planes":[191,205],"has":[192],"derived":[195],"its":[197],"relationship":[198],"acting":[202],"between":[203],"is":[206],"given.":[207],"(400":[210],"pages)":[211],"reproduced":[214],"here":[215],"main":[218],"features":[219],"profile":[222],"summarized":[225],"discussed":[227],"aid":[230],"graphs.":[232]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":6},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":7}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2016-06-24T00:00:00"}