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

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Presentation on theme: "University of Lyon, France Nanoscale Interfacial Phenomena in Complex Fluids - May 19 - June 20 2008 E. CHARLAIX Introduction to nano-fluidics."— Presentation transcript:

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

2 1. 1. Flows at a nano-scale: where does classical hydrodynamics stop ? 2. 2. Liquid flows on smooth surfaces: the boundary condition 3. 3. Liquid flows on smooth surfaces: experimental aspects 4. 4. Flow on patterned surfaces 5. 5. Effect of boundary hydrodynamics on other surface transport properties 6. 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 Nanofluidic devices Miniaturization increases surface to volume ratio: importance of surface phenomena  manipulation and analysis of biomolecules. with single molecule resolution  specific ion transport 50 nm channels Wang et al, APL 2002 500 nm Nanochannels are more specifically designed for : Microchannels… …nanochannels

6 Large specific surface (1000m 2 /cm 3 ~ pore radius 2nm) catalysis, energy/liquid storage or transfo, … Mesoporous materials 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 10nm

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

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

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

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

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

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

14 Horn & Israelachvili, J. Chem Phys 1981 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

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 K ∆(t) = F static (D) + F hydro (D, D) Drainage of confined liquids : Chan & Horn 1985 t tsts D(t) DD L(t) Run-and-stop experiments Inertia negligible :

18 Lubrication flow in the confined film z(x) x u(x,z)  Hypothesis  Properties Pressure gradient is // Ox Average velocity at x: Velocity profile is parabolic Quasi-parallel surfaces: dz/dx <<1 Newtonian fluid Low Re Slow time variation: T >> z 2 / z2z2 12  dPdP dxdx U(x)= -   fluid dynamic viscosity No-slip at solid wall  Mass conservation 2  xz U(x) = -  x 2 D  Reynolds force (D< { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/13/3893378/slides/slide_18.jpg", "name": "Lubrication flow in the confined film z(x) x u(x,z)  Hypothesis  Properties Pressure gradient is // Ox Average velocity at x: Velocity profile is parabolic Quasi-parallel surfaces: dz/dx <<1 Newtonian fluid Low Re Slow time variation: T >> z 2 / z2z2 12  dPdP dxdx U(x)= -   fluid dynamic viscosity No-slip at solid wall  Mass conservation 2  xz U(x) = -  x 2 D  Reynolds force (D<> z 2 / z2z2 12  dPdP dxdx U(x)= -   fluid dynamic viscosity No-slip at solid wall  Mass conservation 2  xz U(x) = -  x 2 D  Reynolds force (D<

19 Drainage of confined liquids : run-and-stop experiments K (D - D  ) = F static (D) + D 6  R 2 D t tsts D(t) DD L(t) ∆(t) D > 6nm D(t) - D  D(t) KD  6  R 2 ln = (t - t s ) + Cte

20 Chan & Horn 1985 (1) D(t) - D  D(t) KD  6  R 2 ln = (t - t s ) + Cte D > 50 nm : excellent agreement with macroscpic hydrodynamics Various values of D  : determination of fluid viscosity  excellent agreement with bulk value Chan et Horn, J. Chem. Phys. 83 (10) 5311 (1985)

21 Chan & Horn (2) D ≤ 50nm : drainage too slow Reynolds drainage Sticking layers Hypothesis: fluid layers of thickness D s stick onto surfaces D - 2D s D 6  R 2 F hydro = - Excellent agreement for 5 ≤D≤ 50nm OMCTS tetradecane hexadecane Molecular size DsDs 7,5Å 13Å 4Å 7Å 4Å 7Å

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

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

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

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

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: How can one describe flows ? Liquid-solid transition ? Liquid-glass transition ?

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) Methods to cleave mica without particules have been designed (Franz & Salmeron 98, recleaved mica). They seem to be removed by water

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

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

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 N layers transition N -1 layers No flow Average velocity V(x) x P=Cte Hypothesis : transition region moves at velocity r(t) Lubrication flow in the N-layers region Constant pressure P o in the non-flowing N-1 layers region (Assumes some linear friction law for the flow in the thin film) Hydrodynamic limit: r(t)

36  + lubrication x o : maximum extend of the layered region A o =  x o 2 maximum area of the layered region A =  r 2 actual area of the N-1 layers region  Constant pressure in the non-flowing region :  Mass conservation : d : layer thickness Nd : flowing film thickness

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

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

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

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

41 N Discrete model describes very well the thickness variations of µ  d2d2 =0.3

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 intrinsic friction 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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