emulsions, and foams March 21 22, 2009

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1 Wetting and adhesion Dispersions in liquids: suspensions, emulsions, and foams ACS National Meeting March 21 22, 2009 Salt Lake City Ian Morrison 2009

2 Ian Morrison 2009 Lecure 2 - Wetting and adhesion 1

3 The molecular origin of surface tension The free energy to stretch a surface is: Δ F = σ ΔA L Where σ L is the surface tension. To increase surface area, molecules must be pulled from the bulk. This increase requires work. Ian Morrison 2009 Lecture 2 - Wetting and adhesion 2

4 Reduction of surface tension by adsorption The free energy to stretch this surface is also: Δ F = σ Δ A L But σ L is the surface tension reduced by the adsorption of surfactant. To increase surface area, molecules must be pulled from the bulk. This increase requires work. Because surfactants go to the surface spontaneously, the work is less. Ian Morrison 2009 Lecure 2 - Wetting and adhesion 3

5 Surface tension is a pull Ian Morrison 2009 Lecure 2 - Wetting and adhesion 4

6 Coalescence of droplets + The change in energy is: Δ F = F F final initial = σ ( A A ) = σ Δ A < 0 final initial Therefore the drops coalesce spontaneously. Ian Morrison 2009 Lecure 2 - Wetting and adhesion 5

7 Coalescence of droplets with emulsifier When droplets covered with emulsifier coalesce, some emulsifier must be desorbed. This requires work. + Δ F = σ Δ A + work of desorption If the emulsifier is strongly adsorbed, the work to remove it is large, and the drops do not coalesce. Ian Morrison 2009 Lecure 2 - Wetting and adhesion 6

8 Spreading on a substrate The energy change per unit area for liquid 2 (top) to spread across the surface 1 (bottom) is: Δ F = ( σ + σ σ ) Surfactants reduce the two terms positive terms allowing the drop to spread. Ian Morrison 2009 Lecure 2 - Wetting and adhesion 7

9 Detergency more than one mechanism! Requires only that the energy of surfactant adsorption is greater than the energy of the new liquid surface created. Requires that the surfactant lower the new solid/liquid interface to be less than the previous solid/oil interface. Requires spontaneous absorption of oil into micelles. Holmberg et al. pp Ian Morrison 2009 Lecure 2 - Wetting and adhesion 8

10 Different contact angles on different solids Ian Morrison 2009 Lecure 2 - Wetting and adhesion 9

11 Contact angles independent of shape Mercury drops on glass.* Drops vary in size from 4 to 24 grains (1 grain = 64.8 mg) The contact angle of 140 o is the same for each drop, independent of drop size. The observation is that the contact angle depends on the materials but not the particular geometry. * Bashforth and Adams, Ian Morrison 2009 Lecure 2 - Wetting and adhesion 10

12 Contact angles reflect solid-liquid interactions Young and Dupré (independently) assert this simple idea: σ lv σ sv θ σ sl That three tensions balance; Or similarly, That three energies balance. σ = σ cosθ + σ sv lv sl or σ sv σsl = σlvcosθ Ian Morrison 2009 Lecure 2 - Wetting and adhesion 11

13 The Young-Dupre applied to adhesion The work of adhesion is the separation to create two new surfaces from one interface: σ sl σ lv σ sv W adh = σ + σ σ sv lv sl Inserting the Young-Dupré idea gives: W adh = σ cosθ + σ lv lv Ian Morrison 2009 Lecure 2 - Wetting and adhesion 12

14 Contact angle hysteresis High energy spots low contact angles. Low energy spots high contact angles. Advancing liquids are held up by low energy spots and show high contact angles. Receding liquids id are held by high h energy spots and show low contact angles. Ian Morrison 2009 Lecure 2 - Wetting and adhesion 13

15 Motion of liquids due to surface energies Capillary flow Motion as a consequence of shape. Key idea: pressure drop across a curved surface Marangoni flow Motion as a consequence of variation in surface tension. Ian Morrison 2009 Lecure 2 - Wetting and adhesion 14

16 Laplace pressure - 1 Overpressure inside a drop of oil o in water w. If the surface is perturbed from a sphere: δw = p odv o p wdv w + σ o / wda For a sphere: 2 dvo = 4π R dr = dvw da = 8π RdR Pierre Simon, Marquis de Laplace At equilibrium: δ W = 0 p p =Δ p = o w 2σ ow / R ( de Gennes, 2004, Fig. 1.5 Ian Morrison 2009 Lecture 2 - Wetting and adhesion 15

17 Laplace pressure - 2 For oil/water For a 1μm drop: Δ p = 2σ ow / R R 3 Nm Nm Δp 6 10 m 4 610Pa 0.6 atm For drops (or bubbles) bbl of different sizes, the internal pressures will be different. The smaller is at a higher pressure and so molecules inside it will diffuse into the larger. An effect called Ostwald ripening. A more general form of the Laplace equation is Where R 1 and R 2 are the principle radii of curvature. 1 1 Δ p = σ + R R 1 2 Ian Morrison 2009 Lecture 2 - Wetting and adhesion 16 de Gennes, 2004, pp 6f

18 The capillary length The Laplace pressure can be written as: 1 1 Δ p = σ + = κσ R1 R2 Hydrostatic pressure can be written similarly: where κ -1 is a curvature. 1 Δ p = ρ gκ where κ -1 is a height. The capillary length is defined when these two pressure are equal σ 1 1 = ρ gκ 1 or κ = σ ρg κ Typically σ J m ρ 1 gm / cm 10 kg/ m and g = 9.8 m/ s 2 So that 1 κ 1 mm Gravity is generally neglected for sizes smaller than the capillary length. de Gennes, 2004, p. 33f Ian Morrison 2009 Lecture 2 - Wetting and adhesion 17

19 Capillary adhesion The large radius of curvature, R, is in the plane of the plates. The smaller one is perpendicular and opposite in sign: H ( θ ) 2cos e 2cos 2 cos The Laplace pressure is: 1 θe σ θe Δ p = σ R H H The force pushing the plates together is the 2 2σ cosθ F = π R e drop area times Laplace pressure. H For R= 1 cm, H = 5μm, and θ = 0 the pressure is about 1/3 atm and the force 10 N. (What is the stable state? What are the dynamics?) de Gennes, Ian Morrison 2009 Lecture 2 - Wetting and adhesion 18

20 Capillary rise is an example of Laplace pressure Ian Morrison 2009 Lecure 2 - Wetting and adhesion 19

21 Capillary rise because of Laplace pressure The curvature inside the tube depends on the radius and the contact angle: 2cos θ R The pressure is lower! inside the liquid. The balance is the capillary rise: 2σ L cosθ R = ρ gh Ian Morrison 2009 Lecure 2 - Wetting and adhesion 20

22 The break-up of a jet is also: Mathilde Reyssat, Harvard 2007 Ian Morrison 2009 Lecure 2 - Wetting and adhesion 21

23 Capillary pressure determines nucleation Ian Morrison 2009 Lecure 2 - Wetting and adhesion 22

24 Controlled nucleation of bubbles Ian Morrison 2009 Lecure 2 - Wetting and adhesion 23

25 Laplace pressure creates Ostwald ripening Δ p σ = r The pressure inside > pressure outside 2 This equation implies that in an emulsion with a range of drop sizes or a foam with a range of bubble sizes, material diffuses from small drops to large drops. Also, this equation implies that bubbles are difficult to nucleate. Ian Morrison 2009 Lecure 2 - Wetting and adhesion 24

26 Small particles also ripen ln P Po = 2σV rrt m If the particles have any solubility, small particles become smaller and the large particles become larger. The effect is described by the Kelvin equation. c ln = c0 2σV rrt m Ian Morrison 2009 Lecure 2 - Wetting and adhesion 25

27 Marangoni flow Marangoni flow flow resulting from local differences in surface tension. Causes of Variation in Surface Tension Local temperature differences. Local differences in composition due to differential evaporation. Electric charges at surfaces. Local compression or dilatation of adsorbed films. Ian Morrison 2009 Lecure 2 - Wetting and adhesion 26

28 Liquid flows from a low surface tension region Ian Morrison 2009 Lecure 2 - Wetting and adhesion 27

29 Liquid flows to a high surface tension region. Ian Morrison 2009 Lecure 2 - Wetting and adhesion 28

30 Tears of Wine + σ σ EthOH/H O 2 Ian Morrison 2009 Lecure 2 - Wetting and adhesion 29

31 Flow due to surface tension differences Ian Morrison 2009 Lecure 2 - Wetting and adhesion 30

32 Liquid flows away from a hot spot Ian Morrison 2009 Lecure 2 - Wetting and adhesion 31

33 Liquid flows to a cold spot Ian Morrison 2009 Lecure 2 - Wetting and adhesion 32

34 Ian Morrison 2009 Lecure 2 - Wetting and adhesion 33