Flow in two-dimensions: novel fluid behavior at interfaces

Transcription

1 Flow in two-dimensions: novel fluid behavior at interfaces M. Dennin U. C. Irvine Department of Physics and Astronomy and Institute for Surface and Interfacial Science

2 Research Overview Fluid Instabilities (convection) Complex Fluids (foams/granular) Interfacial Flows (Langmuir Monolayers) pattern formation spatiotemporal chaos domain growth control/stabilization flow behavior jamming effective T micro vs. meso 2D fluids interfacial physics bio. applications tech. applications

3 Outline Introduction to monolayers Experimental Methods Three outstanding issues: Large changes in viscosity Nonlinear behavior Anomalous pressure dependence

4 Langmuir Monolayers

5 Langmuir Monolayer History 1) 18 th century BC: Babylonians spread oil for divination 2) 1770: Benjamin Franklin experiments with damping of surface waves 3) 1800 s: Rayleigh works on surface tension 4) Turn of the century: Agnes Pockels develops the Langmuir trough in her kitchen 5) Early 1900 s: Langmuir provides detailed explanations of thickness of layers and orientation of molecules. He develops the Langmuir film balance to measure surface tension.

6 Langmuir monolayers today Technology: sprays, emulsions, foams, etc. (direction we are exploring) Biology: membranes (direction we are exploring) Rheology: liquid crystals, not simple Newtonian fluids (area of focus)

7 Big Change: Rich Phase Behavior liquid crystal phases (LC) are very common. Surface Pressure: Π= γ w - γ where γ is surface tension.

8 Experimental Methods: characterization of fluid properties Velocity profiles Steady state viscosity Complex shear modulus

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10 microscope Torsion pendulum Movable barrier

11 Schematic of Apparatus A: outer barrier, or fingers B: torsion pendulum C: fixed inner cylinder

12 Velocity Profile Couette flow: v θ (r) = Ar + B/r (Newtonian Fluid) Non-Newtonian fluid: many cases still have analytic solutions

13 Track particles Brewster Angle Microscope Images Monolayer without shear Monolayer under shear

14 Newtonian

15 Non-Newtonian

16 Viscosity and Shear Modulus Rotate outer cylinder: constant rate of strain ( γ ) Angular displacement of rotor: provides a measurement of the stress (σ) Oscillate inner rotor with known torque => known stress, measure strain response (γ)

17 Measured Quantities Steady state viscosity: η = σ / γ Time dependent shear modulus: Gt () = σ ()/ t γ () t Complex Shear modulus: G * ( ω) = σ( ω)/ γ ( ω) * G = G + ig

18 Interesting Questions Long time scales (kinetics at an interface) Nonlinear properties (relation between viscosity and complex shear modulus) Interesting pressure dependence

19 Introduce Ca 2+ into the system Fraction of negative charges depends on ph

20 Top view of monolayer Monolayer is in a hexatic liquid crystal phase

21 Ghaskadvi, Carr, and Dennin, J. Chem Phys. (1999) 1 Viscosity (g/s) 0.1 ph = 2.6 ph = 3.4 ph = 4.1 ph = 6.1 Viscosity as a function of time for different ph values time (hr)

22 Ghaskadvi, Carr, and Dennin, J. Chem Phys. (1999) G' & G" (dyne/cm) 10 1 ph = 5.5: Linear measurement 0.1 G' G" time (hr)

23 Ghaskadvi, Carr, and Dennin, J. Chem Phys. (1999) Viscosity (g/s) Ca concentration mm mm mm mm Viscosity for different bulk concentrations of Ca ions, at ph = time (hr)

24 Relations between η and G Cox-Merz : G ( ω) G * ( ) 1 ( ) ηγ = + ω G ω= γ η ω Simple Linear relation: ηγ ( ) = G ( ω) ω ω = γ Amplitude dependence of G? (Ghaskadvi, et al., Langmuir 1997)

25 Results for 2OH TCA (a) Π = 32 dyne/cm (b) Π = 48 dyne/cm viscosity (g/s) viscosity (g/s) Twardos and Dennin, Langmuir (a) (b) shear rate or frequency (s -1 ) η* and G"/ω (g/s) η* and G"/ω (g/s)

26 Results for C21 (a) Π = 10 dyne/cm, T = 18 o C L 2 phase (b) Π = 20 dyne/cm, T = 18 o C near transition (c) Π = 20 dyne/cm, T = 14 o C L' 2 phase Twardos and Dennin, Langmuir 2003 viscosity (g/s) viscosity (g/s) viscosity (g/s) (a) (b) (c) shear rate or frequency (s -1 ) η* and G"/ω (g/s) η* and G"/ω (g/s) η* and G"/ω (g/s)

27 Anomalous Pressure Behavior Peak in viscosity as a function of pressure: - Associated with ordering of the headgroups: Ghaskadvi, et al., Langmuir (1997) and Ghaskadvi and Dennin, Langmuir (2000) - Associated with tilt angle: Brooks, et al., Langmuir (1999)

28 Definition of G(t) t dγ σ () t = G( t t') dt' dt ' Assume a model for G(t): Gt () = G e i + G 0 i t / λ e

29 Some Results: 2 OH TCA 60 Pressure (dyne/cm) Phase Transition around Π = 26 dyne/cm Trough Area (cm 2 )

30 Peak in G(t) G 0 (dyne/cm) G 0 λ λ (s) Pressure(dyne/cm)

31 Complex Shear Modulus G' (dyne/cm) 10 1 G''(dyne/cm) Pressure (dyne/cm) Pressure(dyne/cm) Different symbols correspond to different frequencies.

32 Summary Langmuir monolayers exhibit a range of surprising behavior. Interesting kinetics in interfacial systems. Surface viscosity is not simple. - interesting shear rate/frequency dependence - interesting surface pressure dependence

33 Thanks to Undergraduates: Sharon Carr John Lauridsen Jonathan Moore Postdoctoral Researchers: Rajesh Ghaskadvi John Collins Graduate Students: Michael Twardos Funding: NSF CTS , Petroleum Research Fund, Research Corporation, Sloan Fellowship