Questions about Viscosity

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Questions about Viscosity
NCRH Frankfurt, April 2007 L.P. Csernai,
University of Bergen
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In superstring theory, based on analogy between
black hole physics and equilibrium
thermodynamics, ... there exist solutions called
black branes, which are black holes with
translationally invariant horizons. ... these
solutions can be extended to hydrodynamics, ...
and black branes possess hydrodynamic
characteristics of ... fluids viscosity,
diffusion constants, etc. In this model the
authors concluded that ? / s
1 / 4p And then they speculate that in
general ? / s gt 1 / 4p or ? / s gt 1.
They argue that this is a lower limit
especially for such strongly interacting systems
where up to now there is no reliable estimate for
viscosity, like the QGP. According to the
authors the viscosity of QGP must be lower than
that of classical fluids.
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lt1
Kovtun, et al., PRL 2005
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Why Perfect QGP Fluid Core Hadron Gas Corona
May Reproduce Data?
? shear viscosity, s entropy density
TH and Gyulassy (05)?
Kovtun,Son,Starinets(05)?

• Absolute value of viscosity

• Its ratio to entropy density

!
Rapid increase of entropy density near Tc could
validate hydro at RHIC/LHC Deconfinement Signal ?!
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Origin of the news
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Why viscosity ?

• Viscosity leads to dissipation, it slows down,
  weakens, averages out flow phenomena, - helps to
  approach global equilibrium in a system. (No
  problem, the flow is present and strong in HI
  physics ? viscosity is not too strong to
  eliminate the flow !!! )
• Viscosity prevents random, irregular, turbulent
  motion and instabilities, makes the flow LAMINAR,
  i.e. well defined and coherent, while too low
  viscosity leads to instabilities and turbulence.
  (Yes, flow seems to be regular and systematic in
  HI reactions ? viscosity is large enough !!! )
• Strictly speaking Perfect fluid is absolutely
  unstable ! LL

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RT instabilities in Tokamak

• The figure above shows three-dimensional
  isosurfaces of the pressure as the instability
  develops along ridges dominantly aligned along
  the ambient magnetic field.

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Stability, Reynolds number
- kinematic viscosity
In an ideal fluid any small perturbation
increases and leads to turbulent flow. For
stability sufficiently large viscosity and/or
heat conductivity are needed! Re ?
1000 - 2000 (Calculations are also stabilized
by numerical viscosity!)
- density
- viscosity
- length
- velocity
Measured Lijuan Ruan / STAR scaling A, E of
dimensionless v2 fluctuations , can be compared
to constant Re contours. If the two are similar
viscous effects are dominant in these
fluctuations, and viscosity (or Re) can be
extracted. (If not, Initial State (IS)
fluctuations and FD fluctuations should be
separated complex theroretical task.)
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Re studies in HICs
Theoretical D. Molnar, U. Heinz, et al., ?
50 500 MeV/fm2c Re ? 10 100 Exp. 50
800 MeV/nucleon energies 80sBonasera,
Schurmann, Csernai scaling analysis of flow
parameters. Re ? 7 8 !(more dilute, more
viscous matter) In both cases ?/s ? 1
(0.5 5) ,This is a value large enough to keep
the flow laminar in Heavy Ion Collisions !!! NS
Star-quakes / Spin-up of rotation is observed ?
? finite
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Stability, Reynolds number
Interesting and important in RFD detonation
fronts are stabilized by radiation and heat
conductivity. E.g. - Rocket propulsion-
Implosion, fission- and fusion reactions- Heavy
Ion reactions
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Preventing turbulence
The instability of deflagration- (flame-) front
is not desirable at supersonic fronts. With
increasing temperature the radiation becomes
dominant and stabilizes the flame front.
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(Kovtun, et al., PRL 2005)

• With Kapusta and McLerran we have studied these
  results and assumptions and found that
• ? vs. T has a typical decreasing and then
  increasing behaviour, due to classical reasons
  (Enskog21)
• ?/s has a minimum exactly at the critical
  point in systems, which have a liquid-gas type of
  transition
• ? vs. T shows a characteristic behaviour in
  all systems near the critical point (not only in
  the case of He).

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Viscosity vs. T has a minimum at the 1st order
phase transition. This might signal the phase
transition if viscosity is measured. At lower
energies this was done.
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Viscosity Momentum transfer
Via VOIDS
Via PARTICLES
Liquid
Gas
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Prakash, Venugopalan, .
Helium (NIST)
QGP (Arnold, Moore, Yaffe)
This phenomenon can help us to detect
experimentally the critical point ? can be
determined from (i) fluctuation of flow
parameters and from (ii) scaling properties of
flow parameters.
Water (NIST)
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• Viscosity at this meeting
• Formulation of dissipative processes in RFD,
  the physical processes governing these processes
  and their stabilityL. Turko, A.K. Chaduri, T.
  Koide, P. Van, A. Muronga, ..
• Fluid dynamical models and the role of viscosity,
  numerical and parametric, and lack of viscosity
  in really perfect fluid, ANALYTIC
  solutionsI. Mishustin, T. Csorgo, M. Nagy, M.
  Chojnacki, U. Ornik, D. Strottman, I. Arsene, M.
  Gyulassy, B. Betz, E. Molnar, G. Denicol, P.
  Mota,
• Other subjects, important but not strongly
  related to viscosity, like freeze-out, initial
  states, role of EoS,
• All these are needed for experimental study of
  Vicsosity.

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1st measurement of viscosity

• Roy Lacey et al.
• C. Nonaka adiabatic expansion goes close to
  the CEP.
• Low viscosity point can be reached in expansion
• Using Cs. Cs.s perfect FD model results,
  Tc, m.f.p, Cs, - ? was estimated as ?/s0.09

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The prediction is strongly based on model FD
estimates. This is unavoidable both in AE scaling
in flow analyses and in v2 value
estimates. Thus, reliable 3d CRFD models are
vital with known physical (parametric) and
numerical (computational) viscosity.
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Numerical viscosity

• Shock test asymptotic states are exactly known
  from an EoS.
• Stationary shock profile should develop in a
  stable CRFD model

Ls
M. Chojnacki Mathematica WR
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Estimate viscosity in a planar shock frontThe
front is standing in the calculational frame, and
a stationary profile develops after some time,
then
Measure this!
D. Strottman, P. Romatschke, U. Ornik, ..
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• Other questions related to numerical viscosity
• Dissipation and entropy production may be
  eliminated by brute force in CFD. However,
• Coarse graining, (finite cell size) eliminates
  SHORT wave-length flow patterns by averaging
  these out. The energy of these should be
  dissipated and transformed to heat.
• If entropy increase is prevented (or forced to a
  given value), due to energy conservation, this
  extra energy is returned to the fluid in the form
  of LONG wavelength fluid motion! (see talk of
  Gabriel Denicol or instabilities in T. Motas
  talk.)
• This can only be realistic if the physical
  process is such, that - short wavelength
  fluctuations die out due to some other reason
  - this other process is well represented by
  the method..

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Other tests

• We need analytic test cases for the given EoS!!!
  (Also viscous test cases!)
• Both for viscosity and for forced entropy
  conservation do the test!
• Shock waves, discontinuities
• Harmonic waves, wavelength vs. cell size
• Bjorken model,
• Unfortunately all these examples require
  non-confined boundary and initial conditions,
  thus different from a collision !