Vesicles under flow

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Soft matter, complex fluids and morphogenesis
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CNRS and Univ. J. Fourier Grenoble I
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DyFCoM Dynamique de Fluides Complexes et
Morphogenèse
chercheurs et enseignant-chercheurs
expérimentateurs, théoriciens, 1 Mathématicien
appliqué
Morphogenèse croissance, phénoménologie, rides
sur le sable
contraintes, géophysique.
Fluides complexes vésicules, fluides
viscoélastiques, plasticité, mousse,
globules rouges, cellules,
rhéologie
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A l échelle du site Grenoblois PPF Dynamique
des Systèmes Complexes
Physique, Mécanique, Géophysique, Mathématiques
appliquées
Equipements communs, recherche pluridisciplinaire
(thèses, postdoc en commun, groupes de
travail.) et une rencontre scientifique par an
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Cell crawling
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Actin Polymerization at bead/layer interface
K. John, P. Peyla, K. Kassner, C. Misbah
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Biomimetic entities vesicles

• Simple enough to lend themeselves to experimental
  control
• Sound modelling
• Sound cooperation between experiments, theory,
  and numerical simulations

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Giant Unilamellar Vesicles (GUV)
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A simple model of cell membrane
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Even a unique vesicle is complex!

• Several types of motions and dynamics
• deformability change drastically rheology
• link between underlying dynamics and rheology

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Catastrophes
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Nonlinear dynamics of sand ripple formation
Z. Csahok, A. Valance, F. Rioual
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ATG Intability (Asaro-Tiller,1972 -Grinfeld, 1986)
Quantum dots formation
pyramid-shaped quantum dots grown from indium,
gallium, and arsenic. Each dot is about 20
nanometers wide and 8 nanometers in height.
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Misbah C., Renard F., Gratier J.P., Kassner K.,
Geoph. Res. Lett., 31, L6618 (2004). J.
Schmittbuhl, F. Renard, J. P. Gratier, and R.
Toussaint Phys. Rev. Lett. 93, 238501 (2004)
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Complex Fluids
One of the most exciting area of modern science
Link between micro and macroscales, generic
constitutive laws are lacking, largely
inexplored area by physicists
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Microfluidics
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La microfluidique
La taille de lobjet devient comparable à celle
du canal Rg ou d ? H gt
importance de l hydrodynamique, des interactions
avec la paroi, adhésion....
Macromolécules
Diamètre d
Cellules, vésicules contraintes par le
confinement gt influence sur la rhéologie
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Microfluidique de Fluides complexes (polymères
en solution) P. Peyla et C. Misbah
Boules level set, et interboules ressort
 imateriel 
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Polymères Nuds et leur topologie
O. Pierre-Louis
Inclure dans l étude de la rhéologie?
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Simulation 3D d écoulements complexes (M. Ismail)
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Dynamics and rheology of Suspension of vesicles
and cells (Danker, Ismail, Maitre,
Cottet,Bonnetier, Raoult, Misbah) Rheology of
polymers, microfluidics (Peyla, Misbah) Rheology
of foams (Graner, Saramito) Models of cell
motility (John, Fourcade, Peyla,
Misbah) Rheology of the crust (Misbah,
Renard) Morphogenesis in nonequilibrium systems
(Pierre-Louis, Misbah) gtgtgtgtgtgt present in
condensed and soft matter, complex fluids,
biology
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Catastrophes, and patterns are unavoidable
Patterns in cells (e.g. asters) Pattern in nature
in general Pattern are intimately linked to
nonequilibrium dissipative structures Patterns
occur in complex fluids (add complex to
complex) Bifurcations and catastrophes are the
rule
(growth, nanotsructures, chemistery, sand
ripples.
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Modelling

• Boundary integral formulation
• Phase-field
• Analytical, scaling arguments, pertubrative
• Large scale numerical simulations

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Modeling migration of vesicles
Stokes equations
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Integral formulation
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Phase field models
Sharp interface
Diffuse interface
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Diffuse membrane model, advected field
Biben, Misbah
EPJB, 2002, Phys. Rev. E 2003
Integral formulation limited to linear bulk
equations not
systematic for topology changes
somewhat difficult to handle
An advected-field is akin to phase-field
Idea do not treat explicitly the boundary
(membrane)
Is an advected field (colour function)
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Minimum in 1D
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AF across the vesicle
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Lift of vesicles, their tumbling and their
rheology
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Lift force
Cantat, Misbah Phys. Rev. Lett. 1999., and EPJE
2003, EPL, 2004
M. Abkarian, C. Lartigue, A. Viallat. Phys.
Rev. Lett. 2002
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Lift force
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air
Ball translation
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air
Ball translation
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air
Ball translation
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air
Increase of pressure (Bernoulli)
Ball translation
Drop pressure (Benouilli)
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air
Increase of pressure (Bernoulli)
Lift force
Ball translation
Drop pressure (Benouilli)
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Reverssibility of the stokes equations
is also a solution
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Mirror image
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Mirror image
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Mirror image
Blue arroworange one
No lateral deviation
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2. Dynamics near soft walls

• Blood vessels covered with glycocalyx
• Lift force maintaining cells away from walls
• Increase resistance to flow
• Regulate hematocrit

J. Beaucourt, T. Biben C. Misbah, Europhys.
Lett. 2004
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Glycocalyx (glycosylated molecules) 1) direct
specific interaction 2) prevents undesirable
adhesion.
Available data indicate Cw close to 0.1 in
postcapillary venules
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2. Dynamics near soft walls
J. Beaucourt, T. Biben and C. Misbah , Euro.
Phys. Lett.(2004).
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Theory/experiments symbosis
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Pendulum analogy
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Pendulum analogy
Fixed points
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Stable
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Unstable
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Saddle
Node
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Close to critical point
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Analytical theory
Small deformation theory
1) solve Stokes equations inside and ouside, with
BC 2) Use inextensibility constraint 3) Close
self-consistently the equations.
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Shape preserving RCte
Tumbling if
Good agreement with full numerical analysis
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An other fixed point
Stability of which
Oscillation (eigenvalue purely imaginary
coexistence with tumbling
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Tank-treading motion Tumbling if viscosity
contrast is high enough (saddle-node
bifurcation) Vacillating-breathing (coexistence
with tumbling)
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Results from the equations
They exhibit tank-treading, tumbling and VB
depending on the parameters
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Averages
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Averages
membrane force
membrane normal
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Averages
membrane force
membrane normal
Rheology is contained in this term
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Results
stress
Strain rate
and
Coeff. Depend on
Wrotation
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Shear thinning and normal stress differences
Rheology depends on underlying dynamics (in
progress with G. Danker)
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Rheology of a dilute suspension
A. Einstein, Annln. Phys. 19, 289 (1906)
Corrections. Annln. Phys. 34, 591 (1911).
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Rheology of a dilute suspension
A. Einstein, Annln. Phys. 19, 289 (1906)
Corrections. Annln. Phys. 34, 591 (1911).
C. Misbah, Phys. Rev. Lett. (January 2006).
Area
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Rheology of a dilute suspension
A. Einstein, Annln. Phys. 19, 289 (1906)
Corrections. Annln. Phys. 34, 591 (1911).
C. Misbah, Phys. Rev. Lett. (January 2006).
Area