Course + Lectures notes + additional info

Transcription

1 Course + Lectures notes + additional info Examination : oral 3 days (to be determined)

2 Week 1: Intro tu :45 15:30 dr.ir. L. Pel Introduction + porosity th :45 10:30 dr.ir. L. Pel Capillary forces I Week 2: Capillary forces + Darcy tu :45 15:30 dr.ir. L. Pel Capillary forces II th :45 10:30 dr.ir. L. Pel Darcy + Dupuit Week 3 tu :45 15:30 dr.ir. L. Pel Unsaturated absorption th :45 10:30 Public holiday Week 4 tu :45 15:30 dr.ir. H.Huinink Multiphase transport th :45 10:30 No course due to conference visit Week 5 tu :45 15:30 No course due to conference visit th :45 10:30 No course due to conference visit Special subjects Week 6 tu :45 15:30 T. Arends Moisture transport in wood th :45 10:30 dr.ir. L. Pel Drying + Fire spalling Week 7 tu :45 15:30 prof. H. van Duijn Density driven flow th :45 10:30 dr.ir. L. Pel Component transport

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4 Porosity BE AWARE Transport Permeability Ability to hold water Ability to transmit water Size, Shape, Interconnectedness Porosity Permeability

5 How is the moisture distributed??

6 WHY?

7 SURFACE TENSION

8 What s going on at the surface of a liquid?

9 What s going on at the surface of a liquid? Let s take a look!

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29 Particles that make up a liquid are in constant random motion; they are randomly arranged.

30 You might expect the particles at the surface, at the micro level, to form a random surface, as shown below.

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32 But how do intermolecular forces influence the surface? = intermolecular attractions COHESION

33 Under the surface, intermolecular attractions pull on = intermolecular attractions individual molecules in all directions COHESION

34 = intermolecular attractions COHESION

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36 At the surface, pull on the molecules is laterally and downward; there is negligible intermolecular attractions above the molecules (from the medium above, such as air). SO, the net force on surface molecules is downward.

37 The result of this downward force is that surface particles are pulled down until counter-balanced by the compression resistance of the liquid:

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40 Surface molecules are compressed more tightly together, forming a sort of skin on the surface, with less distance between them compared to the molecules below=surface skin

41 Surface molecules also form a much smoother surface than one would expect from randomly moving molecules.

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44 This explains the characteristic rounded shape that liquids form when dropping through the air: The molecules are all being pulled toward the center.

45 This explains the characteristic rounded shape that liquids form when dropping through the air: The molecules are all being pulled toward the center.

46 The overall result of this asymmetric force on surface molecules is that: The surface of the liquid will rearrange until the least number of molecules are present on the surface In other words the surface area will be minimized A sphere has the smallest surface area to volume ratio The surface molecules will pack somewhat closer together than the rest of the molecules in the liquid The surface molecules will be somewhat more ordered and resistant to molecular disruptions Thus, the surface will seem to have a "skin" The "inward" molecular attraction forces, which must be overcome to increase the surface area, are termed the "surface tension"

47 Surface tension is the intensity of the molecular attraction per unit length along any line in the surface Surface tension = N/m

48 Zero gravity

49 Surface Tension Emperor penguin huddle, Antarctica Doug Allan/Naturepl.com

50 Thomas Young In 1804: founded the theory of capillary phenomena on the principle of surface tension. He also observed the constancy of the angle of contact of a liquid surface with a solid, and showed how to deduce from these two principles the phenomena of capillary action. The Young Laplace equation is the formula for capillary action independently discovered by Laplace in Born Thomas Young 13 June 1773 England Died 10 May 1829 (aged 55) Young was the first to define the term "energy" in the modern sense. Fields Religion Physics, Physiology, Egyptology Quaker

51 Formation of a Surface Separation of liquid to create a new surface requires work to overcome cohesion forces

52 Surface Energy of Liquids The work (w) required to create a new surface is proportional to the # molecules at the surface, and hence the area (A): δw = γ δa Where : γ is the proportionality constant defined as the specific surface free energy. It has units of (energy/unit area, J/m 2 ). γ acts as a restoring force to resist any increase in area, for liquids it is numerically equal to the surface tension.

53 Units of measurement Surface Tension Surface Energy (force/unit length) (energy/unit area) (N/m) (J/m 2 ) 1 Joule = 1 Nm (Nm/m 2 ) (N/m) For Liquid/Liquid Interface, usually termed For Gas/Liquid interface usually termed Interfacial Tension Surface Tension

54 γ = 2F l

55 DEMO movie

56 Surface Tension Measurement -- Drop-- Release of a Liquid drop from a capillary

57 Drop-weight Method Here the liquid is allowed to flow out from the bottom of a capillary tube. Drops are formed which detach when they reach a critical dimension, the weight of a drop falling out of a capillary is measured As long as the drop is still hanging at the end of the capillary, its weight is more than balanced by the surface tension A drop falls off when the gravitational force mg determined by the mass of the drop is no longer balanced by the surface tension mg = 2πr c γ

58 Surface Tension Measurement -- Wilhelmy Plate -- γ cos( θ) γ = surface tension θ = contact angle wt total = total weight = wt total (wt 2l plate b) wt plate = plate weight b = buoyancy force l = width of plate Normally platinum is used to have q 0 and plate just touches liquid so buoyancy is small

59 Surface Tension Measurement -- Ring--

60 W tot = W ring + 4πRγ F where W ring is the weight of the ring, R is the radius of the ring, and g the surface tension. 2R Still commonly used but values may be as much as 25% However, the shape of the liquid supported by the ring is complex and the direction of tension forces are non-vertical. The correction factor should be introduced.

61 The surface or interfacial tension F γ = βf 4πR 2R Oil oil r Where β is the correction factor, calculated from the equation of Zuidema and Waters water ( β ) 2 4b 1 F a = + c 2 2 π R 4πR ( ρ ρ ) Where ρ 1 and ρ 2 are the densities of the lower and upper phases; a=0.725, b= m -1 s 2 ; c= r/r 1 2 (Liquid-Vapor) (Liquid-Water) The first column shows the surface tension Between a liquid and its own vapor

62 Surface tension (10-3 Nm -1 ) alcohol 23 benzene 29 glycerol 62 mercury 500 milk 45 water 73 influence surfactants (soap) (often dynes/cm dyne=10-5 N)

63 Water high surface tension??? asymmetrical molecule: dipole moment hydrogen bonding: Water is polar so there are intermolecular forces (dipole-dipole interaction and H bonding) that must be overcome polar liquid

64 Floating paperclip DEMO

65 Water strider mass Mass: F=m 10 Surface tension F= mass,max~ 0.15 gram=150 mgr (~10 mgr)

66 Nature: all sizes

67 The relation between the maximum curvature force F s = γp and body weight F g = Mg for 342 species of water striders. P = 2(L1+L2+L3) is the combined lengths of the tarsal segments. Hu, Chan & Bush (Nature, 424, 2003).

68 42: above 38: feet slightly lower 35: feet lower 33: feet broken through surface, head & body still dry 31: feet & body even lower 30: feet & body under water

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70 Surface tension ships DEMO

71 Walking over water? movie

72 Pressure in droplet /soap bubble droplet ( Pi Po ) π r 2 = 2π r γ P i P o = 2γ r P o P i bubble P i P o = 4γ r

73 Balloons: what will happen?

74 Pressure in balloon versus time burst Valid model system

75 P out Pressure buble: P in P = 4γ r r

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77 Porous material porosity Surface tension Contact angle

78 Droplets on materials One fluid wets the surfaces of the formation rock (wetting phase) in preference to the other (non-wetting phase). Gas is always the non-wetting phase in both oil-gas and water-gas systems. Oil is often the non-wetting phase in water-oil systems.

79 Cohesive and Adhesive Forces Water on: Water is said to wet glass Teflon Glass Adhesive attraction between water and teflon is low and the cohesive forces among the water molecules pull the water molecules into spheres Adhesive attraction between water and glass is high and water is pulled onto the glass TiO 2 -Silicone film before UV irradiation TiO 2 -Silicone film after UV irradiation

80 Liquid surface border equilibrium γ cosθ + γ = γ LG SL GS cosθ = γ γ γ GS LG SL

81 Contact angle cosθ = γ γ γ GS LG SL

82 Contact angle: θ cos θ Spreading Complete wett. Partial wetting γ SL = γ SV Negligible wett. Non-wett. (a) (b) (a) is the case of a liquid which wets a solid surface well, e.g. water on a very clean copper. Perfect wetting. (b) is the case of no wetting, contact angle =180 o. This represents water on teflon or mercury on clean glass.

83 Extremes

84 The lotus effect(~150 o ) Water droplet on lotus leaf, with adhering particles Contaminating stain powder removed by rinsing with water The Lotus Effect is based on surface roughness caused by different microstructures together with the hydrophobic properties of the epicuticular wax (~150 o )

85 Cassie Baxter model cos θ * = r f cosθ + f f y 1 Apparent contact angle

86 A droplet on an inclined superhydrophobic surface does not slide off; it rolls off. When the droplet rolls over a contamination, the particle is removed from the surface if the force of absorption of the particle is higher than the static friction force between the particle and the surface. Usually the force needed to remove a particle is very low due to the minimized contact area between the particle and the surface. As a result, the droplet cleans the leaf by rolling off the surface.

87 WATER-WET ROCK θ Water σ ow Oil σ os σ ws Solid σ os 0 < θ < 90 Adhesive tension between water and the rock surface exceeds that between oil and the rock surface.

88 OIL-WET ROCK Water σ ow Oil σ os 90 < θ < 180 The adhesion tension between water and the rock surface is less than that between oil and the rock surface. θ σ ws σ os Solid Reservoir rock is oil-wet if oil preferentially wets the rock surfaces.

89 Experimental setup for measuring contact angles

90 Contact angle hysteresis Young eq. predicts single value for intrinsic c. a. but Range of stable apparent an be measured experimentally: => hysteresis maximum - advancing minimum receding Advancing contact angle (θ A < θ R ) is always larger than or equal to the receding contact angle raindrop Roughness Θ r hysteresis Chemical contamination or heterogeneity of solid surface Θ a Solutes in the liquid (surfactants, polymers) may deposit a film on solid surface

91 Oil drop in water : lens

92 Oil drop in water γ WA γ OA Air Θ 3 Θ 1 Θ 2 Oil γ OW Water Force balance for both horizontal and vertical direction γ wa cosθ3 = γ oa cosθ1 + γ ow cos γ γ + γ wa < lens oa γ γ + γ wa oa ow ow θ > spreading 2

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94 Porous material porosity Surface tension Contact angle Capillary pressure +

95 Pressure???? ds dn r 1 r 1 r 2 r 2 r 2 Small curved surface element

96 Forces: small curved surface element ds dn r 1 r 1 r 2 r 2 r 2

97 Forces: small curved surface element γ wn ds ds dn γ wn dn γ wn dn r 1 r 1 γ wn ds r 2 r 2 r 2

98 Pressure difference γ wn ds ds p w dsdn dn γ wn dn p n dsdn γ wn dn r 1 r 1 γ wn ds r 2 r 2

99 p w dsdn γ wn ds p n dsdn γ wn ds r 1 r 1

100 p w dsdn γ wn ds p n dsdn α ½dn? γ wn ds r 1 r 1 α

101 γ wn ds p w dsdn p n dsdn r 1 r 1 α α ½dn F? γ wn ds p p = tot sinα = = F A 2 2r = dn r 1 dn dsγ 1 r 1 1 = + r1 wn dn ds γ dn ds 1 r 2 γ wn wn

102 Water in a fine glass capillary tube Capillary Pressure? Water wets the surface of the glass, and is pulled upwards to form a curved surface, or meniscus. P = 2γ r Capillary tube R r Negative pressure : suction R=r 1 =r 2 =r

103 Better Capillary tube R r θ R=r 1 =r 2 =R/cosθ p c = p n p w = 2 γ cosθ wn r

104 Short cut Capillary tube R r Work: = γds = ( pn pw) dv p c = ( p p ) n w sphere p c = γ 2γ = r ds dv

105 EXAMPLE: Water in a fine glass capillary tube Because the pressure on the concave side is lower than that on the convex side (P in < P out ), water rises within the capillary tube. Fluid rises in the capillary until the pressure due to the weight of the column of fluid in the capillary is equal to the pressure difference across the meniscus: P meniscus = P water = ρgh Where: h = height of capillary rise g = force due to gravity ρ = density of water

106 EXAMPLE: Water in a fine glass capillary tube since: 2γ Pmeniscus = = r ρgh we get: h max = 2γ gρr Washburn equation

107 Washburn equation

108 Liquids in Contact with a Solid Surface The adhesive forces (liquid-glass) are greater than the cohesive forces (liquid-liquid) The liquid clings to the walls of the container The liquid wets the surface Cohesive forces (liquid-glass) are greater than the adhesive forces The liquid curves downward The liquid does not wet the surface

109 NOTE: The contact angle between the fluid and the capillary wall determines whether: (a) capillary rise (b) capillary depression P 2 γ = < 0 r P = 2 γ > 0 r

110 Definition water contact surface Hydrophillic Hydrophobic

111 example

112 Maximum height??? h max = 2γ gρr

113 Soil Type Capillary Rise (m) Clay >10 Fine Silt 7.5 Coarse Silt 3.0 Very Fine Sand 1.0 Fine Sand 0.50 Medium Sand 0.25 Coarse Sand 0.15 Very Coarse Sand 0.04 Fine Gravel 0.015

114 Cellular concrete Capillary rise Water level

115 Rising damp city of Venice

116 Capillary suction Capillary suction

117 Related phenomena

118 Sugar cube in coffee movie

119 Lungs It takes some effort to breathe in because these tiny balloons must be inflated, but the elastic recoil of the tiny balloons assists us in the process of exhalation Baby: The alveoli of the lungs are collapsed in the fetus and must be inflated in the process of inhalation

120 Wet Moist Dry

121 Water in porous material Underpressure => shrinkage soil, glass beads, dikes, beach

122 movie

123 10 x 10 cm 0.1 μm Hyundai Pony kg

124 Force of plates F = 2γ r S F = = 14600N > 9240N

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126 Crystallization pressure limestone airflow Na 2 SO 4 solution Movie of Eric Doehne Getty Science 1 month in 52 secs movie

127 Gypsum crystals growing in a pore space

128 Crystallization pressure θ r p crystal P c pressure P c = 2γ cosθ cl r p

129 Surface tension crystal Na 2 CO 3 γ=0.09 Nm -1 Na 2 SO 4 7H 2 0 Damage crystal γ very low Na 2 SO 4 10H 2 0 γ=0.10 Nm -1 P = 0.04 r 0.0 P = r 0.06 P = r e.g. fired-clay brick :3 MPa [Pa [Pa [Pa m] m] m] damage < 12 nm non < 20 nm

130 MIP: Mercury Intrusion Porosimetry Non-wetting fluid Mercury θ=140 o, γ= Nm -1

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133 MIP: Mercury Intrusion Porosimetry Assumes pores in porous material shaped like cylindrical tubes Working principle Assuming a cylindrical pore model, the relation between the pressure applied and the pore size is described by the Washburn equation: r = Where: r = radius of the pore intruded by the mercury, γ= surface tension of the mercury, θ= contact angle between the mercury and the material tested p= pressure applied 2 γ cosθ Hg P THIS IS A MODEL

134 Inject mercury into pores to measure pore size and pore size distribution. MIP cylindrical pores MODEL OF MATERIAL

135 cumulative r V = f ( r) dr o pore size distribution f ( r) = dv dr

136 cumulative r V = f ( r) dr o pore size distribution f ( r) = dv dr

137 Advantages Results obtained quickly (minutes,hours) Method is reasonably accurate Very high range of capillary pressures Disadvantages Ruins core / mercury disposal Hazardous testing material (mercury) Conversion required between mercury/air capillary data to reservoir fluid systems

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139 Self study Capillary instability The force g = r forces fluid from the throat, decreasing r leading to collapse. Joseph Plateau, in 1873, observed experimentally that a falling stream of water of length greater than approximately 3.13 times its diameter will form droplets while falling.

140 Surface Tension with Temperature low T high T Weaker intermolecular forces Increase of surface area Lower Surface Tension Water molecule representative Surface tension decreases at approximately one percent per 4 o C

141 Temperature gradient T 1 < T 2 Water moves to lower temp