Still wat St water dead zone & collimat dead zone & col - - PowerPoint PPT Presentation

We Wendy W.

• W. Zh

Zhang Ph Physics De 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 Ky Kyoto, Japan 2011

St Still wat water dead zone & col dead zone & collimat mated ej ed eject ecta in in g granula lar jet im jet impact ct

Ni Nicholas G Guttenberg, He Herve T Turlier, Jake Jake E Ellowitz, Si Sidney R

• R. Nagel

Introdu

• duction
• n

De Dense granular flow w is complex heterogeneous heterogeneous fl flow avalanches avalanches

Jaeger, Nagel mustard seeds

heterogeneous heterogeneous s stress fi field fo forc rce n netw twork rks

Zhang, Majmudar & Behringer photoelastic discs

imposed shear

Introdu

• duction
• n

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

• lecular beam

beams s in in ultracold ultracold chem chemistry istry relativistic particle beam relativistic particle beams in collider physics ... s in collider physics ...

jet jet

Im Impact pact of

• f 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

• L

Liq iquid id-lik

• like r

e res esponse e  pe perfect fluid flow dissipationless flow di dissipation = fr frictional fl fluid co continuum flow remains no non-Newtonian in in lim limit to it towards d dis issip ipatio tionle less p perfe fect flu t fluid id flo flow

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jet jet

1.

• 1. Introduction

Introduction 2.

• 2. Ba

Background 3.

• 3. Ex

Experiments & simulation 4.

• 4. Mo

Model 5.

• 5. Discussion

iscussion & Conclusion

• nclusion

Outline Outline

jet

loosely packed jet  shower of recoils

dense dense jet jet  ej ejecta co collimated hollow hollow conical conical sheet sheet

Cheng et al. PRL 07

Bac Backgr kgrou

• und: gr

d: gran anular ar j jet i impac pact col

• llimat

ated (l d (liqu quid-l d-like ke) e ) ejecta

non-cohesive particles

jet target target holder

non-cohesive glass beads

Ej Ejecta s a sheet an angl gle c chan ange ges wi with DTar

ar /D

/DJe

Jet redu ducing g DTa

Tar /D

/DJe

Jet

Gran anular ar e ejecta an a angl gle ψ0 agr agree n numerical ally wi with val alues for

• r wat

water j jet  liqu quid-l d-like ke e ejecta

 w wate ter  g gla lass b beads

jet jet

Did i d impac pact c creat ate a l a liqu quid ph d phas ase?

"0 = 1# A(DTar /DJet)2 1# B(DTar /DJet)2

dimensionless reaction force dimensionless drag force Mo Mome mentum m balance Wh When DTa

Tar <

<< DJe

Jet

"0 #1$ A $ B

( )(DTar /DJet)2

 w wate ter  g gla lass b beads

Sam ame ψ0  sam ame A-B

• B

Bu But i indi dividu dual al v val alues of A an

• f A and B m

d B may ay di diffe ffer

Con Context xt

Pozkanser, Voloshin, Ritter... 2008 APS Bonner prize talk Romatschke & Romatschke PRL 2007 Teiser & Wurm, Mon. Not. R. Astron. Soc. 2009

• E

Ellip lliptic flo tic flow: co : collim llimated ted ejecta ejecta fr from co collis llisio ion o

• f

gol gold d io ions at relativistic speeds Liq iquid quark- gl gluon uon phase phase with h New ewtoni

• nian

an vi viscosi scosity? y?

• F

Formatio tion o

• f p

f pla lanetis etismals ls fr from d dust a t aggreg egates tes vi via col a collisi sion

• ns

jet jet

1.

• 1. Introduction

Introduction 2.

• 2. Ba

Background 3.

• 3. Ex

Experiments & simulation

Outline Outline

target 1 0.5 |u|/U0

Expe Experiment  jet i interior

• r i

is n not

• t l

liqu quid-l d-like ke

d e a d z

• n

e Look at

• ok at i

impac pact of h

• f hal

alf a j f a jet pr pressed agai d against gl glas ass side de-v

• view of j

w of jet i interior

• r

(b) 0.2 0.4 <ur(z=0)> m/s θeff = Teff / max(Teff) 0.25 0.25 r /DJet

0.25 0.25 0.5 1

Expe Experiment  dead z ad zon

• ne i

is c col

• ld

tran anspar parent t tar arge get

r /DJet

jet jet

target

"0 #1$ A $ B

( )(DTar /DJet)2

reac action

• n

for force dr drag ag for force

liqu quid-l d-like ke ejecta ejecta interior

• r

structure structure

?

Simulat ation

• n

red = d = h high gh s spe peed d bl blue = = z zero s

• spe

peed

jet rigid grains rigid grains inelastic collisions inelastic collisions fric frictio tion b betw tween g gra rain ins sticky target sticky target gr grains immobile after co colliding with target

Simulat ation

• n r

repr produ

• duces e

expe xperiment

norm normalized alized velocity velocity contours contours agree agree quantitatively quantitatively

red = d = h high gh s spe peed d bl blue = = z zero s

• spe

peed

jet collimated ejecta dead zone

No de

• dead z

ad zon

• ne at

at fr friction

• nless t

tar arge get

jet

• coeff. of restitution and/or friction between grains  weak variation

Guttenberg (2011)

P(ψ−ψ0) ψ−ψ0 0.004 0.01 5

• 5

 no dead zone  dead zone 0.008

• 10

10

Diffe fferent i interior

• r Sam

ame e ejecta

ejecta ejecta angle angle changes changes from rom 45 45° (w (with dead zone)  40 40° (w (without deadzone) ejecta ejecta r remains collimated

jet jet

1.

• 1. Introduction

Introduction 2.

• 2. Ba

Background 3.

• 3. Ex

Experiments & simulation Sa Same ψ0

0 i

in granular & water jet impact  li liquid phase in granular jet? No No Ej Ejecta ≠ sc scattering pattern (dilute regime)

Outline Outline

"0 #1$ A $ B

( )(DTar /DJet)2

reac action

• n

for force dr drag ag for force

De Dense jet impact is different  T To see relevant limit, model as continuum insted of simulating as hard spheres

Fr Friction

• nless t

tar arge get s simulat ation

• n r

results  con

• ntinuum m

mode

• del of gr
• f 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

• nless t

tar arge get s simulat ation

• n r

results  con

• ntinuum m

mode

• del of gr
• f gran

anular ar j jet i impac pact

1.

• 1. Ma

Mass conservation

density velocity field



incom

• mpr

pressibl ble fl flow

• w

Fr Friction

• nless t

tar arge get s simulat ation

• n r

results  con

• ntinuum m

mode

• del of gr
• f gran

anular ar j jet i impac pact

2.

• 2. Energy

nergy conservation conservation granular granular tem temperature perature

TG = = 0 flow

Fr Friction

• nless t

tar arge get s simulat ation

• n r

results  con

• ntinuum m

mode

• del of gr
• f 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 elocal shear direction phenomenological friction coefficient

µ

Fr Friction

• nless t

tar arge get s simulat ation

• n r

results  con

• ntinuum m

mode

• del of gr
• f 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

Incom

• mpr

pressibl ble fr friction

• nal

al fl fluid

TG = 0 µ

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

• nless t

tar arge get s simulat ation

• n r

results  con

• ntinuum m

mode

• del of gr
• f 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

TG = 0 µ

Choose µ to fit simulated ψ0 quantitatively reproduces u(x) & p(x) in hard sphere simulation

Incom

• mpr

pressibl ble fr friction

• nal

al fl fluid

hard sphere simulation

Fr Friction

• nless t

tar arge get s simulat ation

• n r

results  con

• ntinuum m

mode

• del of gr
• f 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

Dissipat pation

• nless pe

perfe fect fl fluid fl d flow e

• w emerge

ges wh when we we t take ake t the l limit µ  0

TG = 0 µ

Con Continuou

• us appr

approac

• ach i

instead of abr ad of abrupt pt c chan ange ge

HDZ

DTar

HDZ

µ

Deadz adzon

• ne s

shrinks ks c con

• ntinuou
• usly t

to 0 as

• 0 as µ  0

✖

µ

"0 #1$ A $ B

( )(DTar /DJet)2

reac action

• n

for force dr drag ag for force

Ej Ejecta an a angl gle dom dominat ated by d by con

• ntribu

bution

• n fr

from

• m

reac action

• n for

force A as as µ  0

jet jet

1.

• 1. Introduction

Introduction 2.

• 2. Ba

Background 3.

• 3. Ex

Experiments & simulation 4.

• 4. Model
• del  al

alternative i interpretation S Same ψ0 b because sm small drag but same reaction force (B (B << A, same A) Di Different di dissipation mechanisms Sa Same limit of perfect fluid flow as dissipation  0 D Dire irect d t demonstra stratio tion th that p t perfe rfect flu t fluid id flo flow is re is rele levant fo for h r hard rd-sp

• sphere

re je jet im t impact? t?

Outline Outline

"0 #1$ A $ B

( )(DTar /DJet)2

reac action

• n

for force dr drag ag for force

Quan antitat ative c check exac xact s sol

• lution
• n

2D perfect fluid flow zero surface tension

gr gran anular ar s simulat ation

• n

2D inelastic / friction non-cohesive

di direct c com

• mpar

parison

• n

Pressure c con

• ntou
• urs

local pressure / pressure at target center

Quan antitat ative agr agreement

solid line = granular simulation dashed line = perfect fluid solution

Discussion

• n
• E

Ellip lliptic flo tic flow a at RHIC Sm Small deviation from perfect fluid flow in inte terprette tted a as v very lo low N Newto tonia ian v vis iscosity ity

• - assumes hydrodynamics

Gr Granular jet imp mpact sm small deviation ≠ l low Newtonian viscosity ap approaches pe perfect fluid flow as frictional flu fluid (alw id (always far-from ays far-from-equ

• equilibriu

ilibrium)

fo form rmatio tion o

• f d

f dead zo zone during during initial initial im impact pact

Discussion

• n

Teiser & Wurm

• Mon. Not. R. Astron. Soc. 2009
• F

Formatio tion o

• f p

f pla lanetis etismals ls fr from d dust a t aggreg egates tes col collisi sion

• ns

ejecta ejecta collim collimated ated wi within 1°

40 m/s

Mo Model as frictional fluid impact?

jet jet

Con Conclusion

• n

Acknowledgements: Xiang Cheng, Eric Brown, Heinrich M. Jaeger Support: NSF-MRSEC, Keck Foundation, NSF-CBET

Than ank y k you

• u

Im Impact pact of

• f 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

• L

Liq iquid id-lik

• like r

e res esponse e  pe perfect fluid flow di dissipation = fr frictional fl fluid co continuum flow remains no non-Newtonian in in lim limit to it towards d dis issip ipatio tionle less p perfe fect flu t fluid id flo flow