Introduction Capillarity( ) (flow ceased) Capillary effect ( ) surface and colloid science, coalescence process,

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2 Introduction Capillarity( ) (flow ceased) Capillary effect ( ) surface and colloid science, coalescence process,

3 Introduction Capillary forces in practical situation

4 Capillary Model A Capillary Model system, 2, 1 various interfacial tensions 2 the geometry of the solid-liquid-liquid interface 3 the geometry of solid surface at the three-phase boundary line

5 Capillary Model A Capillary Model Contact angle: -

6 Capillary Model A Capillary Model ( ) system (hydraulic) ( ) (curvature) (hydrostatic head) system system

7 A Capillary Driving Forces in Liquid Fluid Systems, surface tension bulk ,, -, hydrostatic pressure

8 A Capillary Driving Forces in Liquid Fluid Systems 1806 Laplace P 1 P 2 = P = σ ( 1/ r1 + 1/ r2 ) = P cap (61), P 1 P 2 r 1 r 2 r 1 = r 2 = r, 61 P = 2σ r (62) (62)

9 A Capillary Driving Forces in Liquid Fluid Systems r dr, 8 r dr ( 63) π ( r + dr) = 4π ( r + 2rdr + dr ) 4πr + 8πrdr

10 A Capillary Driving Forces in Liquid Fluid Systems W = σda (63) σda, P 1 P 2, dr 2σ P1 P2 = (62a) r

11 A Capillary Driving Forces in Liquid Fluid Systems system, system P 1 P 2, P 1, P 2 flat surface, r1 = r2 =, P = concave( ), P > 0 convex, P < 0 0,, capillary pressure

12 A Capillary Driving Forces in Liquid Fluid Systems? : density : 1 surface tension : 10 mn m -1 diameter : 01 cm top bottom hydrodynamic pressure difference 98 mj m -2 62, 2000 mj m -2 r = 10-4 cm 101 X 10 5 mj m -2 r = 10 nm 101 X 10 7 mj m -2 drop,

13 Solid--Liquid--Fluid Systems: The Effect of Contact Angle 64 a b, bc = ab cosθ - interface ab, - interface 0, G = σ SV A SV + σ SL A SL + σ LV A LV (64) σ = σ + σ SV SL LV cos θ (65) vapor Young's equation

14 Solid--Liquid--Fluid Systems: The Effect of Contact Angle Young's equation σ = σ + σ SV SL LV cos θ (65) θ σ LV Force balance σ SL σ SV σ LV cosθ ab cosθ G = σ SV A SV + σ SL A SL + σ LV A LV = 0 A A A SV SL LV = -ab = + ab, ab cosθ

15 Capillary Flow and Spreading Processes, duplex film drop lens

16 Capillary Flow and Spreading Processes, G = ( δ G / δaa ) daa + ( δg / δaab ) daab + ( δg / δab ) dab (66) A substrate, B liquid, da = da = A B da AB ( δ G / δa ) = σ, ( δg / δa ) = σ, ( δg / δa ) = σ A A B B AB AB ( δg / δab ) liquid B solid A spreading A B spreading coefficient, S B/A, SB = σ σ σ / A A B AB (67)

17 Capillary Flow and Spreading Processes work of cohesion work of adhesion, B A work of adhesion B work of cohesion S = W B / A AB - W BB (68) spreading free energy, spreading + spreading, S B/A, cohesive force, drop lens : low surface tension hydrocarbon high surface tension clean glass, mercury spreading spreading teflon, paraffin wax spreading drop lens

18 Capillary Flow and Spreading Processes system, bulk properties,,,,, spreading thermodynamics : benzene water benzene ; -1 water : σ B σ AB = 289 mn m = 350 mn m 67 spreading coefficient : -1-1 = 728 mn m, σ B -1 S B / A = = 89 mn m

19 Capillary Flow and Spreading Processes saturate, 622 mn m -1-1 S B / A( B) = = 17 mn m A(B) B A lens benzene ( ) -1 σ B ( A) = 288 mn m -1 S B / A( B) = = 90 mn m spreading, -1 S B / A( B) = = 16 mn m benzene spreading surface tension initial spreading - retraction - lens formation

20 Capillary Flow and Spreading Processes 3, - interface lens formation, oil-water, interfacial tension spreading

21 Geometrical Consideratins in Capillary Flow Capillary flow, -, σ LV,,, P cap LV P cap, P cap yielding yielding, yielding,,,

22 Geometrical Consideratins in Capillary Flow 65 vapor (V) Lamellae (L) Plateau region (P) L, P (convex) P cap, L P cap (Plateau) > P cap (Lamellae) flow from L to P L P, Lamellae,

23 Geometrical Consideratins in Capillary Flow P cap (Plateau) > P cap (Lamellae) flow from L to P Yielding oil recovery, (cell),

24 Measurement of Capillary Driving Forces P cap interface, 66 -

25 Measurement of Capillary Driving Forces contact angle( ) θ, r r, - R, = r/cosθ 61, B -2σcosθ/r P cap (A)- P cap (B) A P cap (A) = 0, ρ gh P cap (B) ρ, g, h ρ gh = 2σ cosθ r (69) θ=0 o, σ = ρghr / 2 (610)

26 Measurement of Capillary Driving Forces 67, r r' B A A P cap = 2σ cosθ (1/ r 1/ r') (611)

27 Measurement of Capillary Driving Forces system solid-vapor ( A SV ) solid-liquid ( A SL ) (dg) (three phase boundary) ds dg/ds = σ LV da LV /ds - σ LV cosθda SL /ds (612) σ LV θ,

28 Measurement of Capillary Driving Forces dg/ds < 0, dg/ds P cap, (notch), interlacing system Fiber 2

29 Complication of Capillary Flow Analysis,, ( ( ),, ), (gradient),, hysterisis

30 Surface Tension Gradients and Related Effects solid-liquid and/or liquid/vapor σ LV σ LV Marangoni flow, Marangoni ( ), σ LV hot spot" ( 69)

31 Surface Tension Gradients and Related Effects

32 Surface Tension Gradients and Related Effects system evaporation, LV LV σ LV,, Marangoni flow σ LV,

33 Surface Tension Gradients and Related Effects, system SLV LV, SL SL, σ LV σ SL σ SL swelling Swelling, σ SL swell, monomeric unit swell σ SL θ,

34 Contact Angle Effects system,, ( ), (surface roughness),, advancing contact angle, θ A,, receding contact angle, θ R, contact angle hysteresis

35 Contact Angle Effects contact angle hysterisis, Receding angle Advancing angle

36 Contact Angle Effects contact angle hysterisis,,, 611, contact angle hysteresis

37 Contact Angle Effects hysteresis SLV hysteresis (curvature) (smooth) 90, 90 o, composite empirical 17

38 Contact Angle Effects capillary system o hysteresis θ A, θ R 0 system empirical adjustment 612 θ A θ R dg/ds = σ LV da LV -σ /ds - LV σ LV cosθ da cosθ da R SL( R) SL( A) (613) SL(A) SL(R) advancing receding 67, θ A θ R, θ A, P cap 0 A /ds /ds

39 Dynamic Contact Angle Effects hysterisis, dynamic advancing contact angle, θ AD advancing contact angle θ A θ AD θ A static θ A dynamic contact angle, - (self-limiting) SLV A SL SLV R, θ AD 17

40 Rates and Patterns of Capillary Flow, (Laminar), (volume rate) capillary system Poiseiuille's equation, dv/dt (ml sec -1 ) dv/dt = πr 4 P/ 8η l (614) r, η, l t P (linear rate), dl/dt = r 2 P/ 8η l (615) system P P cap

41 Rates and Patterns of Capillary Flow 612 dg/ds, P P cap 67, (LV interface A (in cm 2 ), B B ds, -dg/ds (in dynes) B, A B (dynes cm -2 ) 615 dl/dt = 2σ LV r cosθ/ 8η l (616)

42 Rates and Patterns of Capillary Flow system r hydraulic radius hydraulic radius -, A r, resistance factor, r/η

43 Practical Capillary Systems Introduction, wetting repellency,

44 Practical Capillary Systems Wetting in Woven Fibers and Papers,, m 3-8cm 3-4 (order) SLV

45 Practical Capillary Systems Wetting in Woven Fibers and Papers,,, wetting reagent

46 Practical Capillary Systems Wetting in Woven Fibers and Papers, σ LV 40 mnm -1 (728) 1/2 (foaming problem fluorocarbon silicone ) Contact angle

47 Practical Capillary Systems Wetting in Woven Fibers and Papers 61 data Surface tnesion σ LV θ (dl/dt),, σ LV θ SL LV

48 Practical Capillary Systems Wetting in Woven Fibers and Papers Cynlinder,

49 Practical Capillary Systems Waterproofing or Repellaency Control, waterproofing repellency, Fluorocarbon silicone θ A >90 o : θ R >90 o : θ A <90 o :,

50 Practical Capillary Systems Waterproofing or Repellaency Control, nylon polyester - 2,

51 Practical Capillary Systems Waterproofing or Repellaency Control 613 detergency, SL 1 L 2 system ceramic

52 Practical Capillary Systems Waterproofing or Repellaency Control agitation, displacement -, ( ) σ LL ( ), θ A/water θ R/oil θ A/water 90,, θ

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