Spreadingundervariableviscosityandtime-dependentboundaryconditions:estimateofviscosityfromspreadingexperimentsOriginalResearchArticle

Oneofthecoolingconceptsofthehigh-temperaturecoriummeltwhichmayforminacoremeltdownaccidentreliesonsufficientlyhomogeneousspreading.Theconditionsunderwhichcompletespreadingcanbeexpectedaretheobjectsofcurrenttheoreticalandexperimentalstudies. ThelubricationapproximationforlowReynoldsnumberflowsleadstoanequationforwhichself-similarsolutionsforvariousconditionshavebeenfoundbymanyauthors.Thispaperoffersself-similarsolutionsforthespreadingofavolumeofliquidwhichincreasesasapowerlawoftime.Theeffectofcoolingontheviscosityisrepresentedbythetime-dependentviscosity.Avarietyofspreadingexperimentshavebeenperformedwithinmanyinternationalprograms.Theinitialconditionsandboundaryconditionsusedaremorecomplexthanthoseforwhichself-similarsolutionsareknownexplicitly.Basedontheasymptoticbehavior,ast→∞,ofsolutionsoftheCauchyproblemforaquitegeneralclassofinitialdata,approximatesolutionsaregivendescribingthespreadingoffinitevolumewithatimedependentfluxrelease,andsomeofthehigh-temperatureexperimentsareanalyzed.Theeffectofbubblesonrheologyinspreadingexperimentswithwaterandshear-thinningfluidsisinvestigated.