Still wat St water dead zone & collimat dead zone & col mated ej ed eject ecta in g in granula lar jet im jet impact ct Wendy W. We W. Zh Zhang Ni Nicholas G Guttenberg, He Herve T Turlier, Jake E Jake Ellowitz, Si Sidney R R. Nagel Physics De Ph Department & James Fr Franck Institute Un University of Chi Chicago cago No Nonequilibrium Dy Dynamics in A in Astrophysics and M strophysics and Material Science aterial Science Kyoto, Japan 2011 Ky
Introdu oduction on De Dense granular flow w is complex heterogeneous heterogeneous fl flow avalanches avalanches heterogeneous s heterogeneous stress fi field fo forc rce n netw twork rks Jaeger, Nagel imposed mustard seeds shear Zhang, Majmudar & Behringer photoelastic discs
Introdu oduction on im impact pact sc scattering st structure Rutherford’s goldfoil scattering experiment wikipedia light scattering from light scattering from infrared to x-ray infrared to x-ray dense dense molecular olecular beam beams s in in ultracold ultracold chem chemistry istry relativistic particle beam relativistic particle beams in collider physics ... s in collider physics ...
Preview Preview Im Impact pact of of dense dense granul granular ar je jet • C Collim llimated ted (liq (liquid id-lik -like) e) ej ejecta & interior dead zone • D Differ ifferen ent in t inter terio ior s str tructu cture e sa same ejecta e pe • L Liq iquid id-lik -like r e res esponse perfect fluid flow dissipationless flow di dissipation = fr frictional fl fluid jet continuum flow remains no co non-Newtonian in in limit to lim it towards d dis issip ipatio tionle less p perfe fect flu t fluid id flo flow jet
Outline Outline 1. 1. Introduction Introduction 2. 2. Ba Background 3. 3. Ex Experiments & simulation 4. 4. Mo Model 5. 5. Discussion iscussion & Conclusion onclusion jet jet
Bac Backgr kgrou ound: gr d: gran anular ar j jet i impac pact col ollimat ated (l d (liqu quid-l d-like ke) e ) ejecta non-cohesive particles non-cohesive glass beads Cheng et al. PRL 07 target jet jet target holder loosely packed jet dense jet dense jet ej ejecta co collimated shower of recoils hollow conical hollow conical sheet sheet
Ej Ejecta s a sheet an angl gle c chan ange ges wi with D Tar ar /D /D Je Jet redu ducing g D Ta Tar /D /D Je Jet w wate ter Gran anular ar e ejecta an a angl gle ψ 0 g gla lass beads b agr agree n numerical ally wi with val alues for or wat water j jet liqu quid-l d-like ke e ejecta
Did i d impac pact c creat ate a l a liqu quid ph d phas ase? dimensionless reaction force Mome Mo mentum m balance " 0 = 1 # A ( D Tar / D Jet ) 2 1 # B ( D Tar / D Jet ) 2 w wate ter g gla lass dimensionless drag force beads b When D Ta Wh Tar < << D Je Jet jet ) ( D Tar / D Jet ) 2 ( " 0 # 1 $ A $ B jet Sam ame ψ 0 sam ame A-B -B Bu But i indi dividu dual al v val alues of A an of A and B m d B may ay di diffe ffer
Con Context xt • E Ellip lliptic flo tic flow: co : collim llimated ted ejecta ejecta fr from co collis llisio ion o of gol gold d io ions at relativistic speeds Liq iquid quark- gl gluon uon phase phase with h New ewtoni onian an vi viscosi scosity? y? • F Formatio tion o of p f pla lanetis etismals ls fr from d dust a t aggreg egates tes via col vi a collisi sion ons Pozkanser, Voloshin, Ritter... 2008 APS Bonner prize talk Romatschke & Romatschke PRL 2007 Teiser & Wurm, Mon. Not. R. Astron. Soc. 2009
Outline Outline 1. 1. Introduction Introduction 2. 2. Ba Background 3. 3. Ex Experiments & simulation jet jet
Experiment jet i Expe interior or i is n not ot l liqu quid-l d-like ke Look at ook at i impac pact of h of hal alf a j f a jet | u |/U 0 pressed agai pr d against gl glas ass 1 0.5 d e a 0 target side de-v -view of j w of jet i interior or d z o n e
Experiment dead z Expe ad zon one i is c col old tran anspar parent t tar arge get (b) 1 θ eff = T eff / max(T eff ) 0.4 0.5 <u r (z=0)> m/s 0 0.2 0.25 0 0.25 r /D Jet 0 0.25 0.25 0 r /D Jet
liqu quid-l d-like ke ejecta ejecta ? jet interior or structure structure target jet ) ( D Tar / D Jet ) 2 ( " 0 # 1 $ A $ B reac action on drag dr ag force for for force
Simulat ation on jet rigid grains rigid grains inelastic collisions inelastic collisions fric frictio tion b betw tween g gra rain ins sticky target sticky target grains immobile after gr co colliding with target red = d = h high gh s spe peed d blue = bl = z zero s o spe peed
Simulat ation on r repr produ oduces e expe xperiment collimated ejecta jet dead zone norm normalized alized velocity velocity red = d = h high gh s spe peed d contours contours bl blue = = z zero s o spe peed agree agree quantitatively quantitatively
No de o dead z ad zon one at at fr friction onless t tar arge get jet coeff. of restitution and/or friction between grains weak variation Guttenberg (2011)
or Sam Diffe fferent i interior ame e ejecta 0.01 no 0.008 dead P( ψ−ψ 0 ) zone dead 0.004 zone 0 ψ−ψ 0 -10 -5 5 10 0 ejecta angle ejecta angle changes changes from rom ejecta ejecta r remains collimated 45 45 ° (w (with dead zone) 40 40 ° (w (without deadzone)
Outline Outline 1. 1. Introduction Introduction 2. 2. Ba Background ) ( D Tar / D Jet ) 2 ( " 0 # 1 $ A $ B 3. Ex 3. Experiments & simulation reac action on drag dr ag force for for force Same ψ 0 Sa 0 i in granular & water jet impact li liquid phase in granular jet? No No Ejecta ≠ sc Ej scattering pattern (dilute regime) jet De Dense jet impact is different T To see relevant limit, model as continuum insted of simulating as hard spheres jet
Fr Friction onless t tar arge get s simulat ation on r results con ontinuum m mode odel of gr of gran anular ar j jet i impac pact 1. 1. Ma Mass conservation 2. 2. En Energy conservation 3. 3. Mo Mome mentum m conservation No Not assuming hydrodynamic limit obtains Ph Phenomenological
Fr Friction onless t tar arge get s simulat ation on r results con ontinuum m mode odel of gr of gran anular ar j jet i impac pact 1. 1. Ma Mass conservation velocity field density incom ompr pressibl ble fl flow ow
Fr Friction onless t tar arge get s simulat ation on r results con ontinuum m mode odel of gr of gran anular ar j jet i impac pact 2. 2. Energy nergy conservation conservation granular granular tem temperature perature T G = = 0 flow
Fr Friction onless t tar arge get s simulat ation on r results con ontinuum m mode odel of gr of gran anular ar j jet i impac pact 3. 3. Mo Mome mentum m conservation density × acceleration = - pressure gradient + dissipation (shear stress tensor) shear stress = µ pressure e local shear direction phenomenological friction coefficient µ
Fr Friction onless t tar arge get s simulat ation on r results con ontinuum m mode odel of gr of gran anular ar j jet i impac pact 1. 1. Ma Mass conservation 2. 2. En Energy conservation T G = 0 3. Mo 3. Mome mentum m conservation µ Incom ompr pressibl ble fr friction onal al fl fluid Bo Boundary conditions: At At un unknown j jet surface, normal stress and tangential stress both 0 stress both 0 At At target, tangential and normal velocity both 0
Fr Friction onless t tar arge get s simulat ation on r results con ontinuum m mode odel of gr of gran anular ar j jet i impac pact 1. 1. Ma Mass conservation 2. En 2. Energy conservation T G = 0 3. 3. Mo Mome mentum m conservation µ Incom ompr pressibl ble fr friction onal al fl fluid hard sphere Choose µ to fit simulation simulated ψ 0 quantitatively reproduces u(x) & p(x) in hard sphere simulation
Fr Friction onless t tar arge get s simulat ation on r results con ontinuum m mode odel of gr of gran anular ar j jet i impac pact 1. 1. Ma Mass conservation 2. 2. En Energy conservation T G = 0 3. 3. Mo Mome mentum m conservation µ Dissipat pation onless pe perfe fect fl fluid fl d flow e ow emerge ges wh when we we t take ake t the l limit µ 0 Con Continuou ous appr approac oach i instead of abr ad of abrupt pt c chan ange ge
o 0 as µ 0 Deadz adzon one s shrinks ks c con ontinuou ously t to 0 as H DZ H DZ D Tar ✖ µ
Ejecta an Ej a angl gle dom dominat ated by d by con ontribu bution on fr from om reac action on for force A as as µ 0 ) ( D Tar / D Jet ) 2 ( " 0 # 1 $ A $ B reac action on drag dr ag force for force for µ
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