FM 304: BATCHS ETTL I NGOFS OL I DS LURR I ES Objectives:1!e"tic#$C%$i&'e"s:Obtainthebatchsettlingdataforthegivencalciumcarbonate slurry (i.e. the settling rateversusconcentration ofslurry),anddemarcatethe different settling regimes. (free settling and hindered settling)(Ti$te'C%$i&'e"s:Obtainthebatchsettlingdatainthefreesettlingregimefordifferentangles and check its agreement with P! theory.Observetheflow"atternsduring the settling.A))#"#t*s:#erticalsettlingcylinder,inclinedsettlingcylinder,glassrod,sto"watchRe#+e&ts:$ater, %alcium %arbonateT,e-"%:I&t"-'*cti-&:Sett$i&+isthe"rocessbywhich"articulatessettletothebottomofali&uidandformas e d i m e n t .Particlesthate'"erienceaforce,eitherduetogravityorduetoce n t rifu g a lm o ti o nwilltendtomoveinauniformmannerinthedirectione'ertedbythatforce.(orgravity settling,thismeansthatthe"articleswilltendtofalltothebottomofthevessel,forminga s l u rryat the vessel base.Fi+*"e1 F-"ces #cti&+ -& # )#"tic$e '*"i&+ sett$i&+(or settling "articles that are considered individually, i.e. dilute "article solutions, there are two main forcesenacting u"on any "article. )he"rimary force isana""liedforce, suchas gravity,andad ra g forcethatisduetothemotionofthe"articlethroughtheflu i d .)he a""liedforceisusuallynotaffectedbythe"article velocity."article*svelocity,whereasthedragforceisafunctionofthe(ora"articleatrestnodragforcewille'hibited,whichcausesthe"articletoaccelerate due to thea""lied force. $hen the"article accelerates, the drag force actsin thedirection o""ositetothe"article*s motion,retardingfurtheracceleration,intheabsenceofotherforces dragdirectly o""oses the a""lied force. +s the "article increases in velocity eventuallythedragforceandthea""liedforcewill a""ro'imately e&uate,causingno further change in the"article*svelocity.)hisvelocityisknownasthete".i$ve$-cit%,settlingvelocity orfallvelocity ofthe"article.)hisisreadily measurablebye'aminingtherateoffallofindividual"articles.)heterminalvelocity ofthe"articleisaffectedbymany"arameters,i.e.anythingthatwillalter the "article*s drag. ,ence the terminal velocity is most notably de"endent u"on grain si-e,the sha"e(roundnessands"hericity)anddensityofthegrains,aswellastotheviscosityand density of the fluid.)hebehaviourofsettling"articlesinslurrycanbeconvenientlystudiedinsmallbatche'"eriments.)hedataisthenusefulfordesigninglargescalesettlingtankswhichhavea number ofa""lications (e.g.clarification ofwaste water). )hemain information re&uired fordesign is the settling rate of the "articles as a function of the system "arameters such as "articlesi-e and sha"e, concentration, geometry of the system, etc.)heeffectofconcentrationonthesettlingslurrycontinuouslyincreaseswithtime.)heeffectofgeometryofthesystemonthesettlingratecanbesignificant.$henthecylinder istilted, .oycott(/012)foundthatthesettlingrateincreasesduetoshortersedimentation "ath.)his "henomenon is known as the B-%c-tt e//ect, and is used to enhance the rate of settling insome a""lications.(i)VerticalCylinders:3e"endingontheconcentrationoftheslurry,tworegimesofsettlingare"ossible,freesettling and hindered settling. +s the name im"lies, in free settling, each "articleisunaffected by the motion of the neighboring ones and its terminal velocity is givenby4+ll above e&uations are valid only for 5eynolds no. 5e 6 /. $here " and are the densities of the "article and the sus"ending medium res"ectively, 3" is the diameter of the "article, %3 is the drag coefficient+nd "article 5eynolds no. 7 7 7 7 7 7 (a)7 7 7 7 7 7 (b)7 7 7 7 7 7 (c)7 7 7 7 7 (d))he modelassumed for describing (ree 8ettling,has some limitations in "racticala""lication.8uchastheinteractionof"articlesinthefluid,ortheinteractionofthe"articleswiththecontainerwallscanmodifythesettlingbehavior.8ettlingthathasthese forces in a""reciable magnitude is known as hindered settling.9nthe,i&'e"e'sett$i&+regimedueto"article7"articleinteractionsandu"draftofli&uid,the velocity of individual "articlesisconsiderably smaller.)he settling velocity (US) may beestimated by an em"irical e&uation of the form.where,isthe volumefractionof the fluid and n is a constant.7 7 7 7 7 7 7 7 (e))he void fraction can be calculated as : ;/7 %