?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=http%3A%2F%2Fmiis.maths.ox.ac.uk%2Fmiis%2F273%2F&rft.title=Evolution+of+an+elliptical+bubble+in+an+accelerating+extensional+flow&rft.creator=Breward%2C+C.&rft.creator=Cumberbatch%2C+E.&rft.creator=Cummings%2C+L.+J.&rft.creator=Please%2C+C.&rft.creator=Richardson%2C+G.&rft.creator=Schwendeman%2C+D.+W.&rft.creator=Tilley%2C+B.+S.&rft.creator=Ahmed%2C+S.&rft.creator=Fosse%2C+E.&rft.creator=Gewecke%2C+N.&rft.creator=Guevara%2C+A.&rft.creator=Xu%2C+K.&rft.subject=Materials&rft.description=Mathematical+models+that+describe+the+dynamical+behavior+of+a+thin+gas+bubble+embedded+in+a+glass+fiber+during+a+fiber+drawing+process+have+been+discussed+and+analyzed.+%0D%0A%0D%0AThe+starting+point+for+the+mathematical+modeling+was+the+equations+presented+in+%5B1%5D+for+a+glass+fiber+with+a+hole+undergoing+extensional+flow.+These+equations+were+reconsidered+here+with+the+additional+reduction+that+the+hole%2C+i.e.+the+gas+bubble%2C+was+thin+as+compared+to+the+radius+of+the+fiber+and+of+finite+extent.+The+primary+model+considered+was+one+in+which+the+mass+of+the+gas+inside+the+bubble+was+fixed.+This+fixed-mass+model+involved+equations+for+the+axial+velocity+and+fiber+radius%2C+and+equations+for+the+radius+of+the+bubble+and+the+gas+pressure+inside+the+bubble.+The+model+equations+assumed+that+the+temperature+of+the+furnace+of+the+drawing+tower+was+known.%0D%0A%0D%0AThe+governing+equations+of+the+bubble+are+hyperbolic+and+predict+that+the+bubble+cannot+extend+beyond+the+limiting+characteristics+specified+by+the+ends+of+the+initial+bubble+shape.+An+analysis+of+pinch-off+was+performed%2C+and+it+was+found+that+pinch-off+can+occur%2C+depending+on+the+parameters+of+the+model%2C+due+to+surface+tension+when+the+bubble+radius+is+small.%0D%0A%0D%0AIn+order+to+determine+the+evolution+of+a+bubble%2C+a+numerical+method+of+solution+was+presented.+The+method+was+used+to+study+the+evolution+of+two+different+initial+bubble+shapes%2C+one+convex+and+the+other+non-convex.+Both+initial+bubble+shapes+had+fore-aft+symmetry%2C+and+it+was+found+that+the+bubbles+stretched+and+elongated+severely+during+the+drawing+process.+For+the+convex+shape%2C+fore-aft+symmetry+was+lost+in+the+middle+of+the+drawing+process%2C+but+the+symmetry+was+re-gained+by+the+end+of+the+drawing+tower.+A+small+amount+of+pinch-off+was+observed+at+each+end+for+this+case%2C+so+that+the+final+bubble+length+was+slightly+shorter+than+its+theoretical+maximum+length.+For+the+non-convex+initial+shape%2C+pinch-off+occurred+in+the+middle+of+the+bubble+resulting+in+two+bubbles+by+the+end+of+the+fiber+draw.%0D%0AThe+two+bubbles+had+different+final+pressures+and+did+not+have+fore-aft+symmetry.%0D%0A%0D%0AAn+extension+of+the+fixed-mass+model+was+considered+in+which+the+gas+in+the+bubble+was+allowed+to+diffuse+into+the+surrounding+glass.+The+governing+equations+for+this+leaky-mass+model+were+developed+and+manipulated+into+a+form+suitable+for+a+numerical+treatment.&rft.date=2008&rft.type=Study+Group+Report&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.language=en&rft.identifier=http%3A%2F%2Fmiis.maths.ox.ac.uk%2Fmiis%2F273%2F1%2FcorningMPI2008.pdf&rft.identifier=++Breward%2C+C.+and+Cumberbatch%2C+E.+and+Cummings%2C+L.+J.+and+Please%2C+C.+and+Richardson%2C+G.+and+Schwendeman%2C+D.+W.+and+Tilley%2C+B.+S.+and+Ahmed%2C+S.+and+Fosse%2C+E.+and+Gewecke%2C+N.+and+Guevara%2C+A.+and+Xu%2C+K.++(2008)+Evolution+of+an+elliptical+bubble+in+an+accelerating+extensional+flow.++%5BStudy+Group+Report%5D+++++