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University of Lyon, France

Nanoscale Interfacial Phenomena in Complex Fluids - May 19 - June 20 2008. Introduction to nano-fluidics. E. CHARLAIX. University of Lyon, France. 1. Flows at a nano-scale: where does classical hydrodynamics stop ?.

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University of Lyon, France

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  1. Nanoscale Interfacial Phenomena in Complex Fluids - May 19 - June 20 2008 Introduction to nano-fluidics E. CHARLAIX University of Lyon, France

  2. 1. Flows at a nano-scale: where does classical hydrodynamics stop ? 2. Liquid flows on smooth surfaces: the boundary condition 3. Liquid flows on smooth surfaces: experimental aspects 4. Flow on patterned surfaces 5. Effect of boundary hydrodynamics on other surface transport properties 6. Capillarity at a nano-scale

  3. Flows at a nano-scale: Where does classical hydrodynamics stop ? (and how to describe flow beyond ?)

  4. OUTLINE • Why nano-hydrodynamics ? • Surface Force Apparatus: a fluid slit controlled at the Angstrom level • First nano-hydrodynamic experiments performed with SFA • Experiments with ultra-thin liquid films solid or glass transition ? a controversy resolved

  5. 500nm Nanofluidic devices Microchannels… …nanochannels 50 nm channels Wang et al, APL 2002 Miniaturization increases surface to volume ratio: importance of surface phenomena Nanochannels are more specifically designed for : • manipulation and analysis of biomolecules . with single molecule resolution • specific ion transport

  6. Mesoporous materials Large specific surface (1000m2/cm3~ pore radius 2nm) catalysis, energy/liquid storage or transfo, … 10nm Water in mesoporous silica (B. Lefevre et al, J. Chem. Phys 2004) Water in nanotubes Koumoutsakos et al 2003 H. Fang & al Nature Nanotech 2007

  7. Electrokinetic phenomena Colloid science, biology, nanofluidic devices… Electrostatic double layer 3 nm 300 nm Electric field electroosmotic flow Electro-osmosis, streaming potential… are determined by nano-hydrodynamics at the scale of the Debye length

  8. Tribology : Mechanics, biomechanics, MEMS/NEMS friction Rheology and mechanics of ultra-thin liquid films First measurements at a sub-nanometric scale: Surface Force Apparatus (SFA) Bowden & Tabor J. N. Israelachvili The friction and lubrication of solids Clarendon press 1958 Intermolecular and surface forces Academic press 1985

  9. OUTLINE • Importance • Surface Force Apparatus : a slit controlled at the Angstrom level • First nano-hydrodynamic experiments performed with SFA: • Experiments with ultra thin liquid films solid or glass transition ? a controversy resolved

  10. Surface Force Apparatus (SFA) Tabor et Winterton, Proc. Royal Soc. London, 1969 Israelachvili, Proc. Nat. Acad. Sci. USA 1972 Ag D mica Ag Optical resonator

  11. Franges of equal chromatic order (FECO) Tolanski, Multiple beam Interferometry of surfaces and films, Clarendon Press 1948 Spectrograph Source of white light l

  12. D=28nm contact l (nm) r : reflexion coefficient n : mica index a : mica thickness D : distance between surfaces l Distance between surfaces is obtained within 1 Å

  13. Force measurement In a quasi-static regime (inertia neglected) Piezoelectric displacement

  14. The Oscillating force in organic liquid films Static force in confined organic liquid films (alkanes, OMCTS…). Oscillations reveal liquid structure in layers parallel to the surfaces Horn & Israelachvili, J. Chem Phys 1981

  15. Electrostatic and hydration force in water films Horn & al 1989 Chem Phys Lett

  16. OUTLINE • Importance • Surface Force Apparatus : a slit of thickness controlled at the Angstrom level • First nano-hydrodynamic experiments performed with SFA: thick liquid films (Chan & Horn 1985) • Experiments with very thin liquid films solid or glass transition ? a controversy resolved

  17. D(t) L(t) D¥ t ts Drainage of confined liquids : Chan & Horn 1985 Run-and-stop experiments Inertia negligible : K ∆(t) = Fstatic (D) + Fhydro (D, D)

  18. 2pxz U(x) = - p x2 D z2 dP U(x)= - 12h dx Lubrication flow in the confined film • Hypothesis Newtonian fluid z(x) Quasi-parallel surfaces: dz/dx <<1 u(x,z) Low Re ( Re ≤ 10-6) x Slow time variation: T >> z2/n No-slip at solid wall • Properties Pressure gradient is // Ox Velocity profile is parabolic h: fluid dynamic viscosity Average velocity at x: • Mass conservation • Reynolds force (D<<R):

  19. D(t) ∆(t) L(t) D¥ t ts D > 6nm 6p hR2 D D(t) -D¥ 6p hR2 ln =(t - ts ) + Cte D D(t) KD¥ Drainage of confined liquids : run-and-stop experiments K (D -D¥) = Fstatic (D) +

  20. D(t) -D¥ 6p hR2 ln =(t - ts ) + Cte D(t) KD¥ Chan & Horn 1985 (1) D > 50 nm : excellent agreement with macroscpic hydrodynamics Various values of D¥ : determination of fluid viscosity h excellent agreement with bulk value Chan et Horn, J. Chem. Phys. 83 (10) 5311 (1985)

  21. Hypothesis: fluid layers of thickness Ds stick onto surfaces 6p hR2 D Fhydro = - Excellent agreement for 5 ≤D≤ 50nm D - 2Ds Reynolds drainage OMCTS tetradecane hexadecane Molecular size 7,5Å 4Å 4Å Ds 13Å 7Å 7Å Chan & Horn (2) D ≤ 50nm : drainage too slow Sticking layers

  22. Including static force in dynamic equation yields drainage steps BUT Occurrence of steps is NOT predicted by « sticky » Reynolds + static forces Chan & Horn (3) D ≤ 5 nm: drainage occurs by steps Steps height = molecular size

  23. Draining confined liquids with SFA: conclusion • Efficient method to study flows at a nanoscale • Excellent agreement with macroscopic hydrodynamics down to ~ 5 nm (6-7 molecular size thick film) • « Immobile » layer at solid surface, about 1 molecular size Israelachvili JCSI1985: water on mica George et al JCP 1994: alcanes on metal Becker & Mugele PRL 2003: D<5nm • In very thin films of a few molecular layers macroscopic picture does not seem to hold anymore

  24. OUTLINE • Importance • Surface Force Apparatus : a slit of thickness controlled at the Angstrom level • First nano-hydrodynamic experiments performed with SFA : • Experiments with ultra thin liquid films solid or glass transition ? a controversy resolved

  25. Velocity Shearing ultra-thin films (1) McGuiggan &Israelachvili, J. Chem Phys 1990 Strain gauges Frictional force Solid or liquid behaviour depending on V, V/D, history very high viscosities, long relaxation times Flattened mica surfaces ‘Continuous’ solid-liquid transition

  26. Shearing ultra-thin films (2) Granick, Science 1991 hbulk= 0.01 poise Shear force thickness area velocity Dodecane D=2,7nm Giant increase of viscosity under confinement Shear-thinning behaviour OMCTS D=2,7 nm Confinement-induced liquid-glass transition

  27. Shearing ultra-thin films (3) Klein et Kumacheva, J. Chem. Phys. 1998 High precision device with both normal and shear force tangential motion confined organic liquid Shear force response Confinement-induced solid-liquid transition at n=6 layers times

  28. Flow in ultra-thin liquid films: questions In very thin films of a few molecular layers macroscopic hydrodynamics does not seem to hold anymore What is the liquid dynamics: Liquid-glass transition ? Liquid-solid transition ? How can one describe flows ?

  29. OUTLINE • Importance • Surface Force Apparatus : a slit of thickness controlled at the Angstrom level • First nano-hydrodynamic experiments performed with SFA : • Experiments with ultra thin liquid films solid or glass transition ? a controversy resolved

  30. Langmuir 99

  31. Nano- particules are present on mica surfaces when cut with platinum hot-wire They affect significantly properties of ultra-thin sheared films (Zhu & Granick 2003, Heuberger 2003, Mugele & Salmeron) They seem to be removed by water Methods to cleave mica without particules have been designed (Franz & Salmeron 98, recleaved mica).

  32. Drainage of ultra-thin films Becker & Mugele Phys. Rev. Lett 2003 Direct imaging with SFA recleaved mica (particle free) OMCTS molecule Ø 9-10 Å Monochromatic light

  33. Layering transitions F. Mugele & T. Becker PRL 2003 Drainage occurs by steps corresponding to layering transitions 2 layers 3 layers Each step is the expulsion of a single monolayer The heigth between each steps is the size of a OMCTS molecule

  34. http://pcf.tnw.utwente.nl/people/pcf_fm.doc/ The growth of the N-1 layers region gives information on the flow in the N-layers film.

  35. Persson & Tossati model for the dynamics of the layer expulsion No flow Average velocity V(x) P=Cte x N -1 layers r(t) N layers transition transition region moves at velocity r(t) Hypothesis : • Constant pressure Po in the non-flowing N-1 layers region • Lubrication flow in the N-layers region (Assumes some linear friction law for the flow in the thin film) Hydrodynamic limit:

  36. Mass conservation : d : layer thickness Nd : flowing film thickness • + lubrication xo : maximum extend of the layered region • Constant pressure in the non-flowing region : Ao = p xo2maximum area of the layered region A= p r 2 actual area of the N-1 layers region

  37. 4 3 3 2 2 1 2 1 PT model: Ao measured Po determined from load Po = Load / Ao One ajustable parameter for each curve : µ PT model describes very well the dynamics of a monolayer expulsion with an ad hoc friction coefficient µ depending on the flowing film thickness

  38. N Comparison with macroscopic hydrodynamics Macroscopic hydrodynamic: (with no-slip at wall) N Ad hoc friction model meets hydrodynamic friction at large N For N≤5 layers, discrepancies with macroscopic hydrodynamic occur. Effective friction is larger than predicted by hydrodynamic.

  39. i -1 i i+1 i Discrete layers flow model N-1 P=Cte N transition Force balance on one layer of thickness d and length dx F x x+dx F Hydrodynamic limit:

  40. Solving discrete layers flow model 1≤ i ≤N • Assume two different friction coefficients mi,i±1 = m ll liquid-liquid friction m1,0 = mN,N+1 = m ls solid-liquid friction • Solve for 1D flow : mass conservation Velocity of transition region, measured N+1 equations give Vi and dP/dx as a function of m ll and m ls • Adjust m ll and m ls so that Ad hoc friction coefficient of the PT model

  41. h d2 N =0.3 Discrete model describes very well the thickness variations of µ

  42. Results of Becker & Mugele 2003 • Flow in ultra-thin films is very well described by a lubrication flow with . ad-hoc friction coefficient depending on the film thickness. • For N≤5 layers the friction coefficient is slightly larger than predicted by . macroscopic hydrodynamics with no-slip b.c. • The dependence of the ad-hoc friction with the film thickness is well . accounted by 2 intrinsicfriction coefficients, one for liquid-liquid friction . and one for liquid-solid friction • Liquid-liquid friction is close to the value of hydrodynamic limit • Liquid-solid friction is about 20 times larger than liquid-liquid friction

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