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Strong Roughening of Spontaneous Imbibition Fronts

Strong Roughening of Spontaneous Imbibition Fronts. Z. Sadjadi 1 , H. Rieger 1 S. Grüner 2 , P. Huber 2. 1 Theoretical Physics, Saarland University 2 Experimental Physics, Saarland University. ComPhys11, Leipzig 24.-26.11.2011.

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Strong Roughening of Spontaneous Imbibition Fronts

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  1. Strong Roughening of Spontaneous Imbibition Fronts Z. Sadjadi1, H. Rieger1 S. Grüner2, P. Huber2 1 Theoretical Physics, Saarland University 2 Experimental Physics, Saarland University ComPhys11, Leipzig 24.-26.11.2011

  2. Imbibition:Displacement of one fluid by another immiscible fluid in a porous matrix Physical processes involved: Ink in paper towel Oil-air interface in an artificial microstructure

  3. Spontaneous imbibition in nanoporous Vycor glass [S. Grüner, P. Huber (2010)] Network of nano-pores R0 ~ 5 ∙10-9m Lightscattering Experiment: front height front width

  4. Lucas-Washburn law for spontaneous capillary rise Capillary / Laplace Pressure: PL Lucas-Washburn

  5. Height evolution of imbibition frontin nano-porous Vycor glass h(t) ~ t1/2 - Lucas-Washburn as expected since on average

  6. Kinetic Roughening: Standard scaling Height difference fluctuations:

  7. Roughness of the imbibition front Front Width / Roughness Height difference fluctuations   const. (time independent)

  8. Theory • Interface roughening, KPZ • Cellular automata: Directed percolation depinning • Microscopic simulations (lattice Boltzmann) • Phase Field Models • … • Models with surface tension in the imbibition front • display a growing correlation length • and a roughening exponent  << 0.5 • independent pores with constant (not ok) radius:  = 1/2 • independent pores with randomly varying (ok) radius:  = ¼ • lattice gas model with in porous medium with high porosity (not ok):   0.5 Ergo: Theoretical description must contain A) pore aspects B) network aspects

  9. Pore network model with quenched disorder Pipe radii: Network of cylindrical pipes with random diameter (<10nm) • Liquid reservoir in contact • with lower system boundary Filling height in each pipe: Hagen- Poiseuille Rules at junctions / collisions mass balance at each node i Boundary conditions: pi = 0 for bottom node layer pmeniscus = plaplace = 2/r  Compute all node pressures pi(t) Integrate for step t:

  10. Time evolution snapshots: Define height h(x,t) at lateral coordinate x: Average over all menisci in column x

  11. Computer simulation results (disorder averaged): Kinetic Roughening Lucas- Washburn • = 0.45 •  0.02 Height- difference Fluctuations C(l,t) for fixed t Correlation length =O(1) „Finite size scaling“: No dependence on lateral size

  12. Conclusion • Rougheningofimbibition front in vycorglass = 0.46  0.01 … • … in porenetworkmodel = 0.45  0.02. • Absence of lateral correlations uncorrelatedmeniscuspropagation • Low porositymaterials, poreaspectratio > 2: • New (?) universalityclass • Expectedcrossoverforporeaspectratio < 1: • hydrodynamics in junctionsimportant, • influenceofsurfacetensionwithinimbibition front important

  13. Titel

  14. Titel

  15. Imbibition: theory Phase field models (Alava et al.) Directed percolation Depinning (DPD) Lattice gas model (Tarjus et al)

  16. Lattice gas model for an aero-gel •  0.5 BUT: High porosity  surface tension relevant  lateral correlations

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