Characterization of Pore Structure: Foundation

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Characterization of Pore Structure Foundation

• Dr. Akshaya Jena
• Director of Research
• Porous Materials, Inc., USA

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Topics

• Pore structure

• Characteristics of pore structure
• Characterization techniques
• Extrusion Flow Porometry
• Liquid Extrusion Porosimetry
• Mercury Intrusion Porosimetry

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Topics

• Nonmercury Intrusion Porosimetry

• Vapor Adsorption
• Vapor Condensation
• Conclusions

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Pore Structure
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Pore Structure
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Characteristics of Pore Structure
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Characteristics of Pore Structure
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Characteristics of Pore Structure
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Characterization Techniques
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Extrusion Flow Porometry (Capillary Flow
Porometry)
Principle Displacement of a wetting liquid from
a pore

• Wetting liquid

• Flows spontaneously into pores

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Extrusion Flow Porometry (Capillary Flow
Porometry)
Principle Displacement of a wetting liquid from
a pore

• For displacement of wetting (gs/lltgs/g) liquid
  from a pore by a gas

• Work done by gas Increase in interfacial free
  energy

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Extrusion Flow Porometry (Capillary Flow
Porometry)

• For all small displacement of liquid

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Extrusion Flow Porometry (Capillary Flow
Porometry)
p d V gs/g dSs/g gs/l dSs/l gl/g dSl/g p
differential pressure dV infinitesimal increase
in volume of the gas in the pore dSs/g
infinitesimal increase in interfacial area

• For a wetting liquid
• p gl/g cos q (dSs/g/dV)
• (dSs/g/dV) measure of pore size

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Extrusion Flow Porometry (Capillary Flow
Porometry)

• For most pores size not defined

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Extrusion Flow Porometry (Capillary Flow
Porometry)
Definition of pore diameter, D dS/dV(pore)

• dS/dV(cylindrical opening of diameter, D)
• 4/D
• D 4gl/g cos q/p

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Extrusion Flow Porometry (Capillary Flow
Porometry)

• Test Method
• Dry Curve
• Flow rate, F versus p for a dry sample

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Extrusion Flow Porometry (Capillary Flow
Porometry)
Test Method

• For viscous flow
• F ??/(256m l ps)?iNiDi4pi pop
• ? a constant
• m viscosity of gas
• l thickness
• ps standard pressure
• Ni number of pores of diameter Di
• p differential pressure, inlet pressure, pi
  minus outlet pressure, po

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Extrusion Flow Porometry (Capillary Flow
Porometry)

• Dry curve normally concave upward

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Extrusion Flow Porometry (Capillary Flow
Porometry)

• Others possible shape of dry curve because of
• High pressure

• Nonviscous flow
• Tortuous paths for flow
• High flow rate
• Pore diameter
• Interaction of sample with liquid

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Extrusion Flow Porometry (Capillary Flow
Porometry)

• Wet Curve
• F versus p for a wet sample

• Initially there is no gas flow

• The largest pore is emptied first and gas flow
  begins
• With increase in differential pressure smaller
  pores are emptied and gas flow increases
• When all pores are empty wet curve converges with
  the dry curve with the dry curve

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Extrusion Flow Porometry (Capillary Flow
Porometry)

• Equipment

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Extrusion Flow Porometry (Capillary Flow
Porometry)

• Measurable Characteristics
• Through pore Throat Diameter
• The technique measured only the throat diameter

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Extrusion Flow Porometry (Capillary Flow
Porometry)

• The largest pore diameter (Bubble Point Pore
  Diameter)

• Bubble point pressure in F vs p plot.

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Extrusion Flow Porometry (Capillary Flow
Porometry)
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Extrusion Flow Porometry (Capillary Flow
Porometry)

• Mean flow pore diameter

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Extrusion Flow Porometry (Capillary Flow
Porometry)

• Pore diameter range
• Largest - Bubble point pressure
• Lowest - pressure at which wet and dry
  curves meet

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Extrusion Flow Porometry (Capillary Flow
Porometry)

• Distribution
• F ??/ (256? l ps) ?iNiDi4pipop

• (F w,j / Fd,j) g(D,N, )w,j/g(D,N,)d,j
• Cumulative filter flow
• (F w,j / Fd,j)x100

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Extrusion Flow Porometry (Capillary Flow
Porometry)
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Extrusion Flow Porometry (Capillary Flow
Porometry)
Flow distribution over pore diameter

• fF - dFw/Fd)x100/dD

• ?(Fw/Fd)x100 D1?D2-fFdD

• Area in a pore size range flow in that size
  range

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Extrusion Flow Porometry (Capillary Flow
Porometry)
Fractional pore number distribution

• Fractional pore number Ni/??iNi

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Extrusion Flow Porometry (Capillary Flow
Porometry)

• Liquid permeability
• Computed from flow rate at average pressure using
  Darcys law

• F k (A/ml)(pi-po)

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Extrusion Flow Porometry (Capillary Flow
Porometry)

• Gas permeability
• Computed from flow rate at STP

• F k (A/2mlps)(pipo)pi-po
• Can be expressed in any unit Darcy Gurley Fraz
  ier Rayls

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Extrusion Flow Porometry (Capillary Flow
Porometry)

• Envelope Surface Area
• Based on Kozeny-Carman relation

• F l/p A P3/K(1-P)2S2m ZP2p/(1-P) S
  (2ppr)1/2
• F gas flow rate in volume at average pressure,
  p per unit time

• p average pressure, (pipo)/2, where pi is
  the inlet pressure and po is the outlet
  pressure

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Extrusion Flow Porometry (Capillary Flow
Porometry)
Envelope Surface Area
F gas flow rate in volume at average pressure,
p per unit time

• p average pressure, (pipo)/2, where pi is
  the inlet pressure and po is the outlet
  pressure
• l thickness of sample
• p pressure drop, (pi - po)
• A cross-sectional area of sample
• P porosity (pore volume / total volume)
• 1-(rb/ra)

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Extrusion Flow Porometry (Capillary Flow
Porometry)
Envelope Surface Area
rb bulk density of sample ra true density
of sample

• S through pore surface area per unit volume
  of solid in the sample
• m viscosity of gas
• r density of the gas at the average pressure,
  p
• K a constant dependent on the geometry of the
  pores in the porous media. It has a value close
  to 5 for random pored media
• Z a constant. It is shown to be (48/13p).

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Extrusion Flow Porometry (Capillary Flow
Porometry)

• Summary
• Flow Porometry measures a large variety of
  important pore structure characteristics.

• Results particularly relevant for filtration
  media
• Toxic materials, high pressures subzero
  temperatures not used
• A highly versatile technique

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Extrusion Porosimetry

• Principle
• Prevention of gas from flowing out after
  displacing wetting liquid in pore
• Place membrane under the sample

• Largest pore of membrane ltSmallest pore of
  interest in sample p(to empty sample pores)ltp(to
  empty membrane pores)
• D 4 gl/g cos q/p

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Extrusion Porosimetry

• Displaced liquid flows through membrane measured

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Extrusion Porosimetry

• Gas that displaces liquid in sample pores does
  not pass through membrane

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Extrusion Porosimetry

• Test method
• Differential pressure yields pore diameter

• Extruded liquid (weight or volume) gives pore
  volume

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Extrusion Porosimetry

• Equipment

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Extrusion Porosimetry

• Measurable Characteristics
• Through pore volume

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Extrusion Porosimetry

• Through pore diameter

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Extrusion Porosimetry

• Through pore volume distribution
• Distribution function

• fv -(dV/d logD)

• Area in any pore size range volume of pores in
  that range

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Extrusion Porosimetry

• Through pore surface area
• Integration of Equationp gl/g cos q (dSs/g/dV)

• S ?p dV/(gl/g cos q)
• Not very accurate
• Sensitive to pore configuration
• Over estimates volume of pore throat

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Extrusion Porosimetry

• Liquid permeability
• From liquid flow rate

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Extrusion Porosimetry

• Summary
• Only technique that permits measurement of
  through pore volume

• Does not use toxic materials, high pressures and
  subzero temperatures.

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Mercury Intrusion Porosimetry

• Principle
• Intrusion of a non-wetting liquid in to pore
• Non-wetting liquid cannot enter pores
  spontaneously
• gs/l gtgs/g

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Mercury Intrusion Porosimetry

• Pressurized liquid can enter pores

• Work done by the liquid Increase in interfacial
  free energy
• (p-pg) dV (gs/l -gs/g) ds ?P (-gl/g cos
  q) (dS/dV)

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Mercury Intrusion Porosimetry

• From definition of pore diameter(dS/dV) pore
  (dS/dV) circular opening of diameter, D 4/Dp
  -4gl/g cos q/D

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Mercury Intrusion Porosimetry

• Test Method
• Measured intrusion pressure yields pore diameter

• Measured intrusion volume of mercury yields pore
  volume

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Mercury Intrusion Porosimetry

• Equipment

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Mercury Intrusion Porosimeter

• Measurable Characteristics
• Through and blind pore volume

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Mercury Intrusion Porosimetry

• Through and blind pore diameter

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Mercury Intrusion Porosimetry

• Through and blind pore diameter

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Mercury Intrusion Porosimetry

• Through and blind pore diameter

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Mercury Intrusion Porosimetry

• Pore Volume distribution
• fv -(dV/d log D)

• Area in a size range Pore volume in that range

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Mercury Intrusion Porosimetry

• Through and blind pore surface are

• S 1/(-gl/g cos q) ?p dV

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Mercury Intrusion Porosimetry

• Surface area not very accurate
• Wide parts of ink-bottle pores measured as pores
  with neck diameter

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Mercury Intrusion Porosimetry
Surface area not very accurate

• For very small pores, large pressure increases
  cause small increases in volume. The integral is
  less accurate.

• At high pressures, correction terms in the small
  volume of small pores is appreciable

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Mercury Intrusion Porosiemtry
Extrusion volume and hysteresis
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Mercury Intrusion Porosimetry
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Mercury Intrusion Porosimetry

• Summary
• Almost any material can be tested - mercury in
  non-wetting to most materials

• No flow characteristics are measurable
• Uses toxic materials and high pressures

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Non-Mercury Intrusion Porosimetry

• Principle
• Exactly same as mercury intrusion porosimetry

• Non-wetting intrusion liquid is NOT MERCURY
• Water
• Oil
• Application liquid

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Non-Mercury Intrusion Porosimetry

• Measurable Characteristics
• All characteristics measurable by mercury
  intrusion porosimetry - measurable

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Non-Mercury Intrusion Porosimetry
Measurable Characteristics

• Advantages over Mercury Intrusion Porosimetry
• No toxic material used

• An order of magnitude low pressures used

• Smaller pores measurable
• Can measure one kind of pores in a mixture like
  the mixture of hydrophobic and hydrophilic pores

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Non-Mercury Intrusion Porosimetry

• Summary
• Can measure all characteristics measurable by
  Mercury Intrusion without using any toxic
  material or high pressures

• Can detect one kind of pore in a mixture

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Vapor Adsorption

• Principle
• Physical Adsorption

• Weak van der Waals type interaction with surface
• Multi-layer adsorption

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Vapor Adsorption

• BET theory of physical adsorption
• p/(po-p)W 1/(WmC) (c-1)/WmC(p/po)

• W amount of adsorbed gas
• Wm amount of gas that can form a monomolecular
  layer
• C a dimensionless constant
• (A1v2/A2v1) exp (E-L)/RT

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Vapor Adsorption

• p/po-p)Wversus(p/po)-linear

• Wm 1/(intercept)(slope)
• Surface area
• S WmNoa
• No Avogadros number
• a cross-sectional area of the adsorbed gas
  molecule

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Vapor Adsorption

• Chemisorption
• Chemical interaction between the gas and the
  surface

• Only one layer of molecules gets bonded to the
  material

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Vapor Adsorption

• Model for chemisorption (Langmuir)

• p/W 1(KWm)p1/Wm
• p pressure of gas
• W amount of adsorbed gas
• K Ko exp(E/RT)
• Wm amount of adsorbed gas for a completed
  monomolecular layer

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Vapor Adsorption

• Test Method
• Sample maintained at constant temperature

• Volumetric method
• A known amount of gas is introduced in to the
  sample chamber of known volume
• Amount of gas left in the sample chamber is
  computed from change in gas pressure

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Vapor Adsorption
Test Method

• Gravimetric method

• Weight gain of sample in the sample chamber is
  measured

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Vapor Adsorption

• Equipment

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Vapor Adsorption

• Measurable Characteristics
• Through and blind pore surface area
• Multipoint surface area

• p/(po-p)Wversus(p/po)linear in the range 0.05lt
  (p/po)lt0.35
• Plot of p/(po-p)Wversus (p/po)

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Vapor Adsorption
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Vapor Adsorption

• Single point surface area
• Assuming large C, Wm, is computed from a single
  measurement

• Good approximation for large C

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Vapor Adsorption

• Chemisorption
• Chemisorption of many chemicals measurable

• Water
• Carbon monoxide
• Carbon dioxide
• Poisonous chemicals
• Many others
• Over a wide range of temperature and pressure

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Vapor Adsorption
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Vapor Adsorption

• Summary
• Technique determines surface area accurately

• Both through pore and blind pore surface areas
  are measured.

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Vapor Condensation

• Principle
• Condensation of vapor in pore

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Vapor Condensation
? Gv(p)?l (pore) dV(?Gv(p)?l(bulk)/V)dS?G
ss/v?s/l 0

• dV volume of condensed liquid
• V molar volume of liquid
• dS solid/liquid interfacial area

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Vapor Condensation
dV(?Gv(p)?l(bulk) ?Gv(p)?v(po) RT ln
(po/p)

• ?Gss/v?s/l (gs/l - gs/v)
• ln(p/po) -4Vgl/v cos q/RT/D

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Vapor Condensation

• Definition of pore diameter (dS/dV) Pore
• (dS/dV)Cyliderical opening of diameter,
  D 4/D
• ln(p/po) -4Vgl/v cos q/RT/D

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Vapor Condensation

• Test method
• Measures relative vapor pressure (p/po)

• Measures amount of condensed vapor At a given
  pressure

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Vapor Condensation

• Equipment

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Vapor Condensation

• Measurable Characteristics
• Through and blind pore volume
• Condensation occurs in through blind pores

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Vapor Condensation

• Through and blind diameter
• Diameter of pore from condensation
• ln(p/po) -4V gl/v cos q/RTD

• Prior to condensation, pores contain adsorbed
  films
• True pore radius, rp
• rp (D/2)t
• t thickness of adsorbed layer

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Vapor Condensation
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Vapor Condensation

• Pore Volume Distribution
• Distribution function fvfv -(dV/dD)

• Area in any pore diameter range volume of pores
  in that range

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Vapor Condensation

• Pore structure of materials containing very small
  pores
• Type of pores

• Macropores gt0.05mm
• Mesopores 0.002-0.05mm
• Micropores lt0.002mm

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Vapor Condensation
Pore structure of materials containing very small
pores

• Capability
• Technique 0.2-0.00035mm

• Validity of relations ? 0.0015mm
• For micropores data need to be analyzed using
  other models

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Vapor Condensation

• Adsorption and desorption isotherms and hystersis

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Vapor Condensation
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Vapor Condensation

• Shape of adsorption curve ? many factors

• Large number of larger pores ? High adsorption at
  high pressure
• Large number of small pores ? saturation
• Strong interaction of adsorbate with the adsorbed
  ? increasing adsorption

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Vapor Condensation
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Vapor Condensation

• Summary
• Measure volume and diameter of very small through
  and blind pores

• No other technique can measure such
  characteristics

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Conclusions

• Extrusion Techniques
• Two recent techniques Extrusion Flow Porometry
  Liquid Extrusion Porosimetry have been
  discussed in detail

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Conclusions

• The techniques are capable of measuring a wide
  variety of pore structure characteristics of
  through pores including fluid flow
  characteristics, which other techniques cannot
  measure

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Conclusion

• All characteristics particularly relevant for
  filtration are measurable

• The techniques do not use toxic materials, high
  pressures or subzero temperatures

102
Conclusion

• Mercury Intrusion Techniques
• The widely used mercury intrusion porosimetry has
  been briefly discussed

• This technique can measure pore volume and pore
  diameters of through and blind pores in almost
  any material

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Conclusion

• Fluid flow characteristics cannot be measured

• Uses very high pressures and mercury, which is
  toxic

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Conclusion

• Non- Mercury Intrusion Techniques
• The novel technique non-mercury intrusion
  porosimetry has been discussed

• This technique can measure pore volume and
  diameter of through and blind pores like mercury
  intrusion porosimetry

105
Conclusion

• No toxic material is used and pressure required
  is almost an order of magnitude less.

106
Conclusion

• Gas adsorption condensation techniques
• The widely used gas adsorption and condensation
  techniques were discussed briefly

• These techniques can measure surface area, pore
  diameter and pore volume of through and blind
  pores
• Characteristics of very small pores are measurable

107
Conclusion

• Flow properties are not measurable

• Many require subzero temperatures

108
Thank You