?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%2F751%2F&rft.title=Mathematical+Modelling+of+the+Impact+of+Liquid+Properties+on+Droplet+Size+from+Flat+Fan+Nozzles&rft.creator=Al-Izzi%2C+Sami&rft.creator=Broggi%2C+Francesco&rft.creator=Cimpeanu%2C+R.&rft.creator=Connellan%2C+Lloyd&rft.creator=Gowers%2C+Robert&rft.creator=Hunt%2C+Mat&rft.creator=Lunz%2C+Davin&rft.creator=Moore%2C+Matthew&rft.creator=Ockendon%2C+John&rft.creator=Pereira%2C+Victoria&rft.creator=Sprittles%2C+James&rft.creator=Warrington%2C+Rachael&rft.subject=Fluids&rft.description=Flat+fan+nozzles+atomize+crop+protection+products%2C+breaking+them+into+droplets.+Droplet+size+matters+-+smaller+droplets+give+better+perfor-+mance%2C+but+very+small+droplets+drift.+We+want+to+use+mathematical+models+to+better+understand+how+liquid+properties+affect+droplet+size.%0D%0AThere+are+three+types+of+breakup%3A+wavy+sheet%2C+perforation%2C+and+rim.+In+wavy+sheet+breakup%2C+increasing+viscosity+or+surface+tension+increases+droplet+size.+To+investigate+further%2C+we+carry+out+direct+numerical+simulations+of+jet+breakup%2C+which+show+that+suface+tension+has+little+effect%2C+but+increasing+viscosity+leads+to+fewer+droplets.+Decreasing+the+jet+velocity+also+results+in+fewer+droplets%2C+with+a+wider+size+distribution.%0D%0AEach+type+of+breakup+involves+primary+breakup+into+cylinders+of+fluid%2C+then+secondary+breakup+into+droplets.+We+thus+consider+the+breakup+of+a+cylinder+of+fluid.+Direct+numerical+simulations+suggest+that+within+the+tested+parameter+range+viscosity+has+little+impact+on+droplet+size%2C+however+it+does+influence+the+timescale+on+which+the+instability+evolves+considerably.+Linear+stability+analysis+suggests+that+increasing+viscosity+increases+the+wavelength+of+the+most+unstable+mode%2C+which+we+expect+leads+to+larger+droplets%2C+and+that+it+reduces+the+rate+of+breakup.%0D%0APerforations+-+holes+in+the+sheet+-+also+lead+to+breakup.+We+find+how+the+length+fraction+of+the+sheet+that+is+void+changes+with+time.%0D%0AAfter+breakup%2C+the+droplets+continue+to+evolve.+We+develop+a+model%2C+based+on+a+transport+equation%2C+for+this+process.+A+key+parameter+is+the+breakup+rate+constant+-+larger+values+lead+to+more+breakup%2C+fewer+large+droplets%2C+and+a+narrower+size+distribution.%0D%0ATogether%2C+these+mathematical+approaches+improve+our+understanding+of+how+droplets+form%2C+and+can+be+used+to+guide+experimental+work.&rft.date=2017&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%2F751%2F1%2Fsyngenta_study_group_report.pdf&rft.identifier=++Al-Izzi%2C+Sami+and+Broggi%2C+Francesco+and+Cimpeanu%2C+R.+and+Connellan%2C+Lloyd+and+Gowers%2C+Robert+and+Hunt%2C+Mat+and+Lunz%2C+Davin+and+Moore%2C+Matthew+and+Ockendon%2C+John+and+Pereira%2C+Victoria+and+Sprittles%2C+James+and+Warrington%2C+Rachael++(2017)+Mathematical+Modelling+of+the+Impact+of+Liquid+Properties+on+Droplet+Size+from+Flat+Fan+Nozzles.++%5BStudy+Group+Report%5D+++++