NonNewtonian viscous fingering modeled by the phasefield method

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Non-Newtonian viscous fingering modeled by the
phase-field method

• Roger Folch
• Molecular Simulation II group
• DEQ

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formation of patterns on interfaces
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example of diffuse interfacephase separation
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When the interface is abrupt in the traditional
formulation,use the phase-field method
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Free boundary problemswithout a phase
transformation, e.g. fluid flow (immiscible
fluids)
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our model phase-field equation (Folch et
al., PRE 60,1724, 1999)
non-conserved Ginzburg-Landau
cancels C
advection
F
vn
e
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complete model
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order-parameter model for vesicles under flow
(Biben Misbah, LSP Grenoble)
red cells
Experiments (bulk) Podgorski et al., LSP
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• membrane area conservation ? (e.g. Biben et al.,
  PRE 2005)
• enclosed volume conservation (e.g. Folch et al.,
  PRE 1999)

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a fluid-fluid interface2-d biphasic flow
viscous fingering instability
(Hele-Shaw cells)
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Rotating Hele-Shaw cell
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Viscous fingering with a Non-Newtonian
fluid,e.g., shear-thinning
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finger width selection
finger width

• dimensionless surface tension

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tuning the timescales