ELSEVIER I)t~,~ dcr ['ct iuulhlT) lit ~ I I)tl~'; I q l -q,i Particle dynamics simulation: a hybrid technique applied to granular mixing J.J. McCarthy, J.M. Oltino :: Received 2"7 .%l,r, llill,: l¢'~P, ctl Ill N,,~cmt,cr Itl'i" A h.,ilrat'l Slll'i-~l~licrt ' particle tk II:iillit~ ~llniilaiiiql~ lia~ t" Il,ulld ~, itl¢ ti~c in rec¢ill ~ear~. (tilt" appllc,iiltql h,I ~ hlt'h ihi~ ict'htlitlU¢ i,, parlit'tilarl) ~ ell ~,Ullc'd P, Ihat ill ~l:illlll;.ll nii tin7 liar lit'k • propcrti¢~ i~;.lll I,~2t :il-it'ti ~11 ~i parliclc-b) -pallid¢ t~.t,,i,, and dr'tailed Illited ,,irtlClUren ;ire caulk captured and ~i~uali/eti. %Vhilc illi, int'ihlld lia~ plOV~.'n Io hi, tlUii¢ ~t'i~CllllC. il i~ t'~,llil~llialiOliall ) illll2rl~i~12. ('urrc'nl particle d)nairlic~ ~inililliliOll~ in Ih¢ IiIt'ralllrC g¢llerall) h,ultllt' 31)till. 51illli palii¢lc~. ~,tllclea~ ;t i)pical itidu~irial itli~,ei" nia) CaUlk t'onlaiii a~ niail) ~1~ IIf' pariiclc~ - ~i\ llldt'l ~, ill +111:.l,~2niilldt ' lilOrL', floxxexer, ill ~t'll,tlll filt'illnsi;.lllCt',, ~tlth ,i~ in a Itllllbk'l +nlix¢i. XXllt'rt" ihc bulk of iitc" pailicle nllliilin t+llli,,i,,i ,, tit li ~lllitl hotk I'tll,ili,lii .... ii is nill llt't'e,,kdr) lit e\pliciil) t'alt'tihiit, lilt" lltoiion o[ all of the p-itlit'le~ l-I) cllnlbillin,_' particle d) llanlic,, alitl ~t'Olilt'lric;il ili',i~211i, ill e,,~t'liCt', b) I'ocunitl7 the parllVIt" tl~,ilatliit., ,,initilalitql olil), x~It#re ii i~ liu'¢ded, a iit'x~ h)brid glellltM ,,f ,,initllaliliii. x~liic h i,, lliiit'll l'a,,It'r Ihall ;i oilily, t, iliiOllal panicle tl\ nalilii.',, liit, lhtld, can be achicvcd. 1"hi,, it, t'hnittll¢ t'Cili ) icld inore ih;.lll all ,+rdcr o[ ill{lTlilllldC ill¢l¢ake in l.'onlliUlaliOllal +peetl. alloxvin 7 ,,illitllalit+il,, o1 the Older el II1' palllclt'~, l~,hilc nlaililaliling the x cr~aillil~ o!~1 parli¢le tk li~illlit'~ nitiitilalitlll "l'x~tl al+plit-alion,, tlf ihi,, lt't'hllittu¢ ,ill" pi¢~eiiled: ~,. iUilihlt'r ,,iwialcd iu Itlc a~al,ulchili.,2 rt':_'itliC and ;i coniilitli~ti,d) Ihlt~lllg itllnblt'r. < It)tl~ lil~u'~ icr Science S...\. All i17111,,re,¢rxcd. hi ~ li +,1+/'+: ( ;l;illill,il Iliedla: lb. li¢1¢ ,l~ ii,itilit',,: '%li,~+nQ. ~iillui,ill~qi !. Introdu¢ihin The sttitk of parliculale svslenls ha,, oiil) recently {2ailled ~ ide,prGtd inlerdi~ciplinar) interest tlespile tin impact llll a nuillher of intluMries -.- pharrnaceulical, agrictlliural, cer;.illl- ic~. etc. Wiiil¢ ~2ranllhir nlixinl2 and Ilo~v has h..:eli all area of illiefiiliileill research Ior ) ears [ 1-4 I. illierest in lhi~ li¢ld has redoubled hil¢l)' in bolh the physics mid engineering coin- nlunilies. Much of Iht" recent ~.ork in thi~ area has been ~ell i-cvi¢~,ed b) Ilehi'iilger 151. Jaeger lind Nil,~121 I i'>l, Jaeger t'i al. [ 7 I, and Bridgwaler [ 8 I. ()lie useful iechnitlUe ~vllk'h has bl2en developed for the stud)' of ~ianular material is Ihai ill particle d)iianiics 19. II) I. While particle dynallli¢.~ has priniaril)' h¢en li~,cd 1o slud) Ilo~. it is oflen diflicult Io i.ist'erlairl lhe ac't'urzit'v of ihe~e resulls due Io the expcrinlelllal diflicullies inherent in mean- tiring particle positions, velocities and bed void frat'lion. On Ihe olher hand. illixing experimenls are olicn draluaiic -- the kinematics of iriixing flows, over long lirne.~, {,.enerai¢.~ large- scale palterns and slruciures which arc easily vinualizcd. :': t'orrc.,q~onding autht,r. Tel.: ÷ 11447 4~II 3558" Fa~.: + I :'147 4t,~ 372S: I--ntail: ottino@" ehem-en~.nwu.cdu 0032-5910/'1,~/519.1x) ~:; 199,'i Elsevier Science S.A. All |igttl~ rc~.crx cd. PIIS(1032-59 Ill( 97 11)33t) 1-3 Therefore, ~rantllar mixing provid¢~ a rich tenl-bed for shn- ulationn, and prelimmar~ results with particle d',,lami¢s ha~¢ ,,ll,~tl con,,iderahle promi.,,e I ! I ]. Ne~e~l.hele.,,s. o~ving to cotnpulatiomd complexity, t}pical particle dynamics simu- lation.,, rarek handle parliculate ,,ystems larger than a few Ihoil~,and particle',, pon,,ibl) nla.~km.~ ~onic of lh¢ ph).,,ics oh,,er~cd in larger s,,,,tem,,, l-Ill~ve~er, in ~,ome applications. ,,uch a~, in a lumhler mixer ~here the bulk of the particle illolion c~n',i~l~ of a ~,olid hod~ rotation, lhere are re, ions of ,,imple Ilo~v. i.e. regions ~ ilhin the IIo~ which exhibit Irk ial d~nalnic~,. For Ihe,,e ~,~,,teln>,, conlbinhlg particle dynamicn and geometrical insight -- in e,,~ence, Ibctt~,ing the particle dynanfics simulation only ~shere it i,, needed -- provides a new b} brid method o| ,dmulation. xs hich is much far,ter than and )ct ;,,, accurate as a conxenlional particle dynamics method. Thin paper outline,, a hybrid technique of particle d} namic~, simulation. The ,~r~anization of the material is as tbllo~vs. Scclion 2 describe,, the inaplementalion of a conventional particle dynanfic-, sinmlai:o.t, from the algorithm to the lbrce schemes. The section close,~ v, ith a discussion of the limita- tions of particle dynamics simulation>,, including the ._'ffccl.,, of varying the time ~,tep. simulation size. and the issue of