?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%2F294%2F&rft.title=Stability+of+Stationary+Velocity+Profiles+in+Fiber+Spinning&rft.creator=%3D%2C+%3D&rft.subject=Materials&rft.description=We+consider+a+process+of+fiber+spinning%2C+where+a+viscous+(but+not+necessarily+Newtonian)+fluid+is+being+pushed+through+a+narrow+%22spinning+hole%22+and%2C+upon+exit%2C+is+being+stretched%2C+the+latter+step+in+order+to+obtain+an+acceptable+alignment+of+the+(polymeric)+molecules+in+the+fluid.+This+alignment+is+necessary+for+the+final+mechanical+properties+of+the+fiber.+After+leaving+the+spinning+hole%2C+the+fluid+passes+through+a+layer+of+air+(the+%22air+gap%22)+and+enters+a+bath%2C+in+which+it+solidifies+almost+instantaneously.+Somewhere+inside+this+bath%2C+the+fiber+is+being+drawn+by+a+wheel%2C+which+delivers+the+force%2C+necessary+for+the+stretching+process.%0D%0A%0D%0AWhen+the+speed+of+the+drawing+wheel+is+set+to+high%2C+it+is+impossible+to+obtain+a+uniform+fiber%3A+one+clearly+observes+variations+in+the+fiber+diameter.+This+phenomenon+is+called+draw+resonance.+Experimental+evidence+suggests+that+the+draw+ratio%2C+that+is%2C+the+ratio+between+the+speeds+at+the+wheel+and+at+the+exit+of+the+spinning+hole%2C+is+the+unique+parameter+to+steer+the+onset+of+draw+resonance%2C+and+for+Newtonian+fluids+this+is+known+to+be+true.+In+the+Newtonian+case%2C+the+onset+of+draw+resonance+can+be+shown+to+be+a+Hopf+bifurcation.%0D%0A%0D%0AThe+question%2C+asked+to+the+Study+Group%2C+was+to+extend+the+results+on+Newtonian+fluids+to+fluids+with+more+general+rheologies%2C+with+power+law+fluids+as+a+first+choice.+What+came+out+of+the+Study+Group+was+not+yet+a+final+solution+to+this+problem%2C+but+rather+an+attempt+to+come+to+an+easier+formulation+of+the+model+equations.+At+the+workshop%2C+we+thought+that+we+had+succeeded%2C+but+afterwards+we+found+that+there+was+a+hidden+mistake%2C+which+we+could+not+easily+correct.+This+mistake+in+itself+is+worth+mentioning%2C+because+the+approach+we+tried+may+be+successful+in+other+cases%2C+and+this+mistake+may+easily+slip+into+the+considerations+there.+In+this+note%2C+we+restrict+ourselves+to+the+Newtonian+case%2C+because+it+is+easy+to+describe+the+mistake+in+this+setting%2C+and+the+power+law+setting+would+not+add+anything.%0D%0A%0D%0AAs+a+final+remark%2C+we+note+that+the+%22power+law+case%22+has+been+solved+now%2C+by+using+similar+methods+as+we+did+in+the+Newtonian+case.+(A+publication+is+in+preparation.)&rft.date=1998&rft.type=Study+Group+Report&rft.type=NonPeerReviewed&rft.format=application%2Fpostscript&rft.language=en&rft.identifier=http%3A%2F%2Fmiis.maths.ox.ac.uk%2Fmiis%2F294%2F1%2Fhout.ps&rft.identifier=++%3D%2C+%3D++(1998)+Stability+of+Stationary+Velocity+Profiles+in+Fiber+Spinning.++%5BStudy+Group+Report%5D+++++