Contact Angles of Porous Media by Liquid Extrusion and Comparison

Ind. Eng. Chem. Res. 2005, 44, 1381-1389

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Contact Angles of Porous Media by Liquid Extrusion and Comparison to Measurements from a Novel Inclined-Plate Technique Jaideep Chatterjee* and Swati Agarwal Unilever Research India, C/O Hindustan Lever Research Centre, B D Sawant Marg, Chakala, Andheri (E), Mumbai, India 400 099

Most techniques for characterization of the pore structure of porous media, such as mercury porosimetry, liquid extrusion porosimetry, and permporometry, among others, require the estimation of a capillary pressure. The estimation of capillary pressure requires the knowledge of liquid contact angles with the porous material. This paper demonstrates the use of liquid extrusion for estimating the liquid-porous medium contact angle. It then demonstrates the estimation of the advancing and receding contact angles for the same system with a modified inclined-plate technique. In this technique, a critical drop mass is experimentally estimated, at a fixed plate tilt angle, as compared to estimating the critical tilt angle for a fixed drop mass. Comparison between the contact angles measured by these techniques shows that the inclinedplate technique gives lower receding and higher advancing contact angles. It is concluded that higher surface roughness of the coated inclined plate is the cause of the above discrepancy and that the liquid-extrusion-based technique yields the better estimate of the liquid-porous material contact angle. This paper also demonstrates that surfactant solutions can be used in liquid extrusion methods, provided their concentration is high enough to ensure that the “extruded” liquid surface tension does not change from its original value. Introduction Accurate characterization of porous media is needed in various industrial processes and applications. These include tertiary oil recovery, membrane technology, textile technology, and filtration among others. Many techniques have been and continue to be proposed for the characterization of porous media. Some of the most enduring methods for the characterization of porous media with pores in the micron size range are based on liquid intrusion or extrusion. In these techniques, a nonwetting liquid such as mercury is pressurized into the porous medium, and the pressure applied to ensure liquid intrusion is measured and used to infer pore sizes, assuming a high value for the liquid-solid contact angle. Although many reservations for the above technique have been reported,1,2 the technique is still applied.3 Liquid extrusion porosimetry is often preferred, as it does not entail the use of mercury and the associated environmental issues or the need for very high pressures. In this method, a spontaneously wetting liquid, such as water, is allowed to wet the porous medium, and is subsequently pressurized out of the medium by an inert gas such as N2/air. The gas pressure is measured to infer the pore sizes present in the medium. Miller and Tyomkin4 have reviewed liquid porosimetric techniques and have demonstrated their application to woven and nonwoven fabrics. A drawback of these techniques is that the contact angles (advancing and/or receding) of the liquid in the porous medium are needed to accurately obtain the pore sizes from this * To whom correspondence should be addressed. Tel.: 91-22-28276227. Fax: 91-22-28352839. E-mail: [email protected].

method. Hence, the liquid-porous medium contact angle needs to be known a priori to apply these techniques for the characterization of porous media. However, it is also possible to estimate the contact angles, advancing by the intrusion technique and receding by the extrusion technique, using the above methods.5,6 This method of contact angle estimation for powders is quite old7 and continues to be used because of its wide applicability. In this method, a completely wetting liquid is used to obtain the pore sizes of a porous plug of the powder or granular medium. Then, the liquid whose contact angle on the porous medium is to be measured is forced into or out of the medium, and the measured pressure is used to estimate the relevant contact angle by the following equations

∆P1 )

2σ1 cos θ1 r

cos θ1 )

σ2∆P1 σ1∆P2

(1) (2)

where ∆P is the capillary pressure; σ is the surface tension; θ is the contact angle, either advancing or receding; and r is the effective capillary radius. It has been shown by White8 that the effective pore radius can be interpreted in terms of properties of the porous medium, such as porosity, specific area, and mass density, which might be a more accurate description of the term r. The above equations assume, however, that the pores have a circular cross section and that liquid 2 makes a contact angle of 0° with the porous material. The kinetics of liquid penetration can also be used to characterize porous media by measuring the

10.1021/ie0401408 CCC: $30.25 © 2005 American Chemical Society Published on Web 01/12/2005

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time versus distance of penetration, along with liquid properties such as surface tension and viscosity. The simplest of these techniques uses the Lucas-Washburn equation9,10 for penetration into an empty horizontal capillary. More recently, Marmur and Cohen11 have demonstrated that the kinetics of liquid penetration using a vertical capillary model can be used to characterize porous media with variations in pore size. However, these techniques also involve the liquid-solid contact angles. In addition, the kinetic techniques become doubtful if the liquid phase contains surfaceactive agents. In addition to the above approaches, a wide variety of techniques are currently being used for characterizing pore structure.12-19 Another technique that is used for membrane pore size characterization is permporometry.20 Even though this technique uses variations in pressure of a vapor to induce capillary condensation in the membrane and then measures diffusive flux of an inert gas across the membrane to characterize its pores, it too requires the solidcondensed liquid contact angle. The above discussion highlights the significance of the liquid-solid contact angle for characterization of the pore structure/size distribution of porous media. It is well recognized that the three-phase contact angle for a given system can vary between an upper limit, called the advancing contact angle, and a lower limit called the receding contact angle.21,22 Contact angle hysteresis is responsible for the retention of liquid droplets on inclined solid surfaces.23,24 A discussion of contact angle hysteresis and its causes can be found in ref 25. The use of an inclined solid surface to measure the advancing and receding contact angles is well-known.26 In this method, the tilt of the solid on which the contact angle is to be measured is increased to the point at which the drop begins to slide down the surface. The angles made by the advancing and receding ends of the drop just prior to this critical point are the advancing and receding angles, respectively. Using thermodynamic arguments, Furmidge24 showed that, at the critical inclination, the following force balance applies

mg sin R ) wσ(cos θR - cos θA)

(3)

where m is the mass of the drop, g is the acceleration due to gravity, R is the angle of inclination of the plate with respect to the horizontal, σ is the surface tension of the liquid, θA is the advancing contact angle, θR is the receding contact angle, and w is the wetted width of the drop. A detailed analysis of the shape of a liquid drop on an inclined surface has been reported.27 The application of the above method usually involves measuring the advancing and receding contact angles by recording the drop profile up to the critical inclination. It can also be applied, however, by measuring the critical mass at which the drop begins to slide at a fixed angle of inclination. This approach might be easier to apply, as the search for the critical inclination can take time which might cause a reduction in drop mass by evaporation. The mass of the drop can be increased accurately by using a high-precision syringe pump. In this paper, the above modification of the inclined-plate technique has been used to measure advancing and receding contact angles on powdered and granular media, as discussed in the following sections. These values of contact angle are compared to those obtained by the liquid extrusion technique. Potential causes of the

Figure 1. Schematic of the method by which advancing and receding contact angles were measured on an inclined surface.

differences in receding contact angles measured by these two techniques are discussed, and an application of the measured contact angles for pore structure characterization is discussed. Experimental Section Measurements on an Inclined Plate. The porous media whose contact angles with water were measured consist of powdered activated carbon, formed into a solid block by sintering with a small amount of a suitable binder material. Identical powder was applied and spread on a microscope glass slide. The granular/ powdered material was spread on the glass slide, which was then heated to obtain a fixed coat, a couple of millimeters thick, on the flat glass slide. A schematic of the inclined-plate technique used for measuring the advancing and receding contact angles directly is shown in Figure 1. Water drops were formed on the powderedcarbon-coated glass slide by a syringe pump in which the injection rate could be varied down to 0.1 mL/h. The pumping rate was set at 0.07 mL/min in the syringe pump. Drop volume was varied by changing the duration of drop formation from 10 to 50 s. The drops were formed with the syringe tip just above the coated plate surface so that the drops “grew” on the plate rather than falling onto it. Drops were deposited with the plate at a horizontal position. It was observed that a drop of 13 µL did not slide down the plate, even when the angle of inclination was increased to 90°. This indicated a very high contact angle hysteresis, which led to increasing the drop volume in steps, as no further increases in inclination angle were possible. Figure 2 shows the recording of the drop profiles for drops of volume 15 ((1) µL (Figure 2a) and 23 µL (Figure 2b). Figure 3 shows similar recorded images of drops whose volumes were 29 and 35 µL, and Figure 4 shows recordings for drop volumes of 43 and 47 µL. All of these recordings were obtained with the plate inclination at 90° to the horizontal, that is, with the plate in the vertical position. A 50× magnification of the drop was obtained by using an optical microscope, and the image was imported into a PC with standard image “grabber” hardware. The rotation of the images was subsequently changed for measuring of the angles. The contact angles were obtained by imposing a computer-generated right triangle with an acute angle tip touching the three-phase contact angle line at the edge of the drop such that the hypotenuse formed a tangent to the drop profile at the three-phase contact line. The ratio of the base to the height of the right triangle was obtained by using standard features in image analysis software. Such values were used to determine the measured contact angles. An attempt was also made to measure the contact angles of a 4% solution of sodium dodecyl benzene sulfonate (SDBS) in water and heptane by the above technique. However, it was observed that a drop could not be formed because the above liquids spontaneously

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Figure 2. Angles of the front and back edges measured with drop volume ) (a) 15 and (b) 23 µL.


wetted and spread into the porous material coating, which did not occur with water. Measurements Based on Liquid Extrusion. Figure 5 shows a schematic of the apparatus used for conducting the liquid/water extrusion experiments on the basis of which the contact angles were measured. A compressed air cylinder (dry) with pressures over 100 kg/cm2 was used to supply air for the measurements (item 1 in Figure 5). Stainless steel (0.25-in.) tubing was used for most connections. Air entry into the measurement system was controlled with an air pressure regulator (item 2 in Figure 5). This regulator was capable of varying the chamber pressure in steps of ∼0.5 cm on a water column. The pressure regulator is connected to an airtight cylindrical stainless steel

chamber (item 3 in Figure 5) with an internal arrangement for holding the porous block in a manner such that fluid passing through the chamber can only pass through the porous block. A pressure transducer (item 4 in Figure 5) was fitted on the pressure chamber to measure the air pressure on the inlet side of the porous block. The range or full scale of the pressure transducer was 200 cm of water column and, as per the manufacturer’s certificate, had a linearity of 0.2% of full scale or 0.4 cm. The repeatability of the pressure transducer reading was 0.05% of full scale or 1 mm of water column, and the hysteresis was below 0.5% of the full-scale reading. The porous block of the granular/powdered material whose contact angle was to be measured was fixed in the chamber in the manner described above

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Figure 5. Schematic of the apparatus by which contact angles were measured by liquid extrusion: 1, compressed air cylinder; 2, pressure regulator; 3, pressure chamber; 4, pressure transducer; 5, porous block; 6, water trap; 7, moisture separator; 8, flow meter; 9, open to atmosphere.

(item 5 in Figure 5). The outlet from the porous block was connected to a liquid trap, which collected liquid at the bottom while allowing unhindered air flow through it (item 6 in Figure 5). The liquid trap was made of glass and graduated in milliliters, and the connection to the trap was through translucent silicone tubing. Downstream of the liquid trap is a moisture trap. The moisture trap was a transparent-walled column filled with activated silica gel (item 7 in Figure 5). The purpose of the moisture trap was to protect the flow sensor downstream at the end of the apparatus (item 8 in Figure 5), which is used to measure the air flow rate through the system. The air flow meter (thermal air flow meter from Bronkhorst) is open to the atmosphere. The range or full scale of the air flow meter was 30 normal liters per minute (at STP), and it had an accuracy of 2% of full scale. The porous block was soaked in distilled water, and its surface tension was measured to be 72 dyn/cm with a Du-Nuoy ring tensiometer from Kruss. The soaking was for 18 h, which ensured that all void spaces within the porous matrix were filled with water. Occasionally, at the end of the soaking period, water was forced into the block by the use of a suction pump capable of generating 1 mmHg absolute pressure. The porous block did not show any increase in mass immediately after this treatment, as compared to the mass measured after

soaking. This indicated that soaking had filled all void spaces in the block. The wet block was placed and clamped into the airtight chamber. The pressure on the inlet side was increased in small steps of 2-3 cm of water column. The initial pressure increase did not produce any air flow through the system, as verified by the flow meter reading. It was observed that some water collected in the water trap even while the air flow meter reading was still zero. At a critical value of pressure (above the porous block), water was displaced from the largest through-pore, and air flow started through the system, with the flow measuring system showing some finite nonzero value. The pressure at this point is the capillary pressure required to displace water from the narrowest section of the largest through-pore and represents ∆P1 in eq 2. Air pressure is subsequently increased in steps, so that the liquid is displaced from the smaller pores also, and the air pressure vs air flow curve is recorded. The porous block was subsequently dried and resoaked in a 2.8% solution of sodium lauryl ethoxy sulfonate (SLES), an anionic surfactant. The surface tension of this solution was measured with a Du-Nuoy ring tensiometer to be 30 mN/m. This high concentration of surfactant was used to ensure that there were no dynamic effects due to adsorption of surfactant within the porous block, which would cause some depletion of surfactant. The above concentration used ensured that the dynamic surface tension of the liquid in the porous matrix would not drop below the above value. The surface tension of the soaking solution was measured after prolonged soaking of the porous block and did not show any significant increase, suggesting that surfactant adsorption had not depleted the surfactant level enough to produce an increase in surface tension. Because liquid ingress into the porous block is significantly enhanced by the low surface tension, the soaking time requirement in this case was greatly reduced. The porous block was placed inside the pressure chamber, and the critical pressure required to

Ind. Eng. Chem. Res., Vol. 44, No. 5, 2005 1385

begin gas flow through the system was measured following the procedure described above. In this case, however, it was expected that some foam would be generated, which would be indicative of air breakthrough, as opposed to a finite value of air flow registered by the flow meter. Surprisingly, no foam could be observed, and a breakthrough pressure could be recorded (70 cm of water column) after which a gradual increase in air flow was recorded. The surface tension of liquid collected in the trap was measured to verify that no surfactant depletion had occurred. This liquid collected in the trap showed a surface tension of 54 mN/m, indicating that, contrary to expectations, significant depletion of surfactant had occurred within the pores of the porous block. This suggested that a higher surfactant concentration was required to reliably estimate the contact angle of water with the porous block. The block was washed and subsequently soaked in a 4% solution of sodium dodecyl benzene sulfonate. Here also, the soaking time required was reduced because of the low surface tension. The surface tension of the soak solution after soaking was measured and did not show any significant increase from the original value of 32 mN/m. When the extrusion experiment was performed, foam appeared indicating breakthrough. The liquid collected in the liquid trap in this case did not show any increase in the surface tension over 32 mN/m, verifying that surfactant depletion within the porous block had not affected the liquid surface tension. This value of surface tension along with the pressure required to cause foam breakthrough can be used to estimate the contact angle of water with the porous block. This critical pressure represents ∆P2 in eq 2. The above experiments were repeated with more sintered carbon blocks. The experiment was also repeated with a porous block made of glass spheres, formed into a sintered block with a small amount of hydrophilic binder. The water breakthrough pressure and the surfactant/foam breakthrough pressure were measured, to verify the validity of the technique for measuring contact angles, as the contact angle of water on glass is known. Figure 6 shows optical microscope images of the glass spheres and the carbon particles that were used in these experiments to form the porous blocks. The results of these experiments are discussed in the following section. Results Figure 7 shows a plot of the angles measured by the inclined-plate technique for the front and back edges for increasing values of the drop volume/mass. It was expected that the angle of the back edge would decrease and the angle of the front edge would increase with increasing values of drop mass/volume. This trend is shown by the data. The angles of the front edge and the back edge for subcritical drop sizes are expected to be within the range defined by the advancing and receding contact angles. These are not the advancing and receding contact angles for the system. Only when the drop size is critical can the above angles be interpreted as the advancing and receding contact angles. Table 1 lists the values of the angles of the front and back edges for different drop volumes, and Table 2 reports the contact angles measured on a horizontal plate, as a function of drop volume. The validity of eq 3, the force balance on the inclined plate, at the critical tilt

Figure 6. Optical microscope images of the primary particles used to form the porous blocks: (a) glass beads (50 µm), (b) carbon particles (100-250 µm).

angle or critical drop mass can now be checked with the above values. However, an analysis of this is taken up later in the Discussion section. Judging from the observation that a drop of 4% solution of SDBS in water and heptane could not be formed on the porous powder coat, as it spontaneously wetted and disappeared over the surface, it was inferred that the contact angle for these systems was 0°. As mentioned in the previous section, the liquidextrusion-based contact angle measurement was performed for four distinct blocks. A porous block formed from glass beads (50 µm) and hydrophilic binder was used to establish the validity of the experimental technique with surfactant solutions. The critical breakthrough pressure was measured for the block, first with water and then with a 2.8% SLES solution. Glass was used because the contact angle of water and the above surfactant solution on glass is expected to be 0°. The critical breakthrough pressure with water was measured to be 185.1 cm of water column. This high value is due to the small particle size of the primary particles used to make up the porous block, as shown in Figure

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Figure 7. Variation in the angles of the front and back edges measured by the inclined-plate technique and the contact angles measured on a horizontal plate for different drop volumes. Table 1. Measured Angles of the Front and Back Edges for Different Drop Volumes angle (deg) vol (µL)

front edge

back edge

15 21 23 26 29 35 43 47

114 110 119 115 109 105 138 137

56 54 63 49 47 49 40 40

Table 2. Contact Angles Measured on a Horizontal Plate for Different Drop Volumes vol (µL)

CA (deg)

cos(CA)

23 26 29 35

85 82 80 82

0.09 0.14 0.17 0.14

6. The breakthrough pressure for the 2.8% SLES solution, signified by the appearance of foam, was 78 cm of water column. The values of the critical pressures for each porous block, for different liquids studied, along with the surface tensions of the liquids are reported in Table 3. These values were used to calculate the cosine of the receding contact angle of water with the porous block by eq 2. The calculated values of the receding contact angle are also included in Table 3. The contact angle of water on the glass spheres was estimated by this technique to be 8.6°. However, as mentioned in the earlier section, in this liquid extrusion technique, the air pressure was manually increased in incremental steps, and the correct value of the breakthrough pressure could be anywhere between the last recorded pressure and the pressure at which breakthrough was observed. In this case, the last recorded pressure before breakthrough was 76.4 cmH2O, and breakthrough was observed at 78 cmH2O. Back calculations show that a pressure of 77.125 cm would cause the contact angle to be exactly 0°. Hence, the deviation of the above estimated value of the water contact angle on glass from 0° arises from the manually regulated input pressure and is not inherent in the technique. The diameter of the largest pore (from which the liquid is pushed out at the critical pressure) can be estimated using eq 1, and

because the porous medium remains unchanged, these values should match for the two liquids used. These values are also included in Table 3, and the values are 15.9 µm using variable values for water and 15.7 µm using the values obtained for 2.8% SLES. Next, the water contact angle on a porous block of powdered carbon was measured by using the extrusion technique. First, the breakthrough pressure with water was estimated, then, a 2.8% solution of the anionic surfactant SLES was used. As described in the Experimental Section, this concentration was initially expected to be sufficient to prevent the liquid surface tension from rising during the experiment, as the concentration was expected to remain well above the CMC, even after surfactant depletion, which would occur due to surfactant adsorption on carbon. However, this was not the case, and even though the surface tension of the surfactant solution after soaking remained at 30 mN/m, the surface tension of the extruded liquid turned out to be 54 mN/m. Because the estimation of the water contact angle on the porous medium requires the second liquid surface tension, the above measurement resulted in an ambiguity, as the two value of surface tension would result in two very different contact angles. The values of the critical pressures and the average of the two above surface tensions are reported in Table 3. Also included in Table 3 is the water contact angle on the porous carbon medium, estimated by using an average value for the surface tension, which was 49.8°. The above experiment was repeated with a 4% solution of the anionic surfactant SDBS. In this case, however, the surface tension of the extruded liquid was very close to the surface tension of the original surfactant solution. This value of surface tension could be used in eq 2, along with the experimentally measured critical breakthrough pressures, to obtain an unambiguous value of the water contact angle. The measured values of the breakthrough pressures and the liquid surface tensions are reported in Table 3; using these values, the contact angle was estimated to be 50.4°. The values of the largest pore diameter for this porous block were estimated using eq 1, and are included in Table 3 for the three liquids used, showing excellent agreement. To further verify the above estimate of the contact angle, the measurements were repeated on a new porous carbon medium, which was first wetted with water followed by a 4% solution of SDBS. The values of the critical pressures measured and the liquid surface tensions are listed in Table 3. Also included is the calculated value of the water contact angle on the above porous medium, based on the measured values and eq 2. The contact angle estimate for this porous medium is 49.4°. Figure 8 shows the measured air flow rates, at different values of the chamber inlet side pressure, through the dry porous block, the water-filled porous block, and the porous block filled with 4% solution of SDBS. As expected, the air flow rate through the dry porous block increases with applied inlet side pressure over the entire range. However, for the water-filled block, there was no air flow through the porous block until the applied inlet pressure was 62 cm of water column. Similarly, for the 4% SDBS solution, the initial increase in applied inlet side pressure could not produce air flow through the pores, and a minimum pressure of 42.3 cm of water column was required to start foam

Ind. Eng. Chem. Res., Vol. 44, No. 5, 2005 1387 Table 3. Experimentally Measured Critical Breakthrough Pressures for Different Blocks with Different Liquids along with Their Surface Tensions and the Values of the Receding Contact Angles of Water on These Porous Media Estimated Using Eq 2 porous block

liquid

pressure (cmH2O)

surface tension (mN/m)

glass spheres (50 µm) glass spheres (50 µm) act carbon medium 1 act carbon medium 1 act carbon medium 1 act carbon medium 2 act carbon medium 2 act carbon medium 3 act carbon medium 3

water 2.8% SLES water 2.8% SLES 4% LAS water 4% LAS water heptane

185.1 78.0 77.5 70.0 54.0 62.0 42.3 53.5 24.0

72 30 72 42 32 72 32 72 21

flowing through the porous block. By inserting the above values for critical pressure and the measured surface tensions in eq 2, the receding contact angle for water on the porous materials was estimated to be 49.4°. The values of the largest pore diameter estimated for this porous block for the two liquids used are reported in Table 3 and show excellent agreement. Although the use of surfactant solutions in the liquid extrusion technique gives consistent values of the receding contact angle, the reliance on visual observation of foam coming from the porous block to obtain the critical breakthrough pressure leaves some room for doubt. Hence, a pure liquid with much lower surface tension but without any potential dynamic effects was also used for estimating the water-carbon medium contact angle. A different porous block was formed from the carbon particles, and the pressure for extruding water from its largest through-pore was measured to be 53.5 cm of water column. This difference in critical pressure for this block was entirely due to changes in the block pore sizes, which could not be very accurately controlled during the block-forming process. The block was subsequently dried and soaked in heptane. The pressure required to extrude heptane from the largest throughpore was measured to be only 24 cm of water column. Judging from the observation that heptane spontaneously wetted the powdered carbon surface, a contact angle of 0° for the heptane-powdered carbon system was assumed, according to which, the water-powdered carbon contact angle was estimated by eq 2 to be 49.4°. The relevant values for this system are also reported in Table 3. It is worth noting that the diameter of the

cos(ΘR)

receding CA of water (deg)

0.99

8.6

0.65 0.64

49.8 50.4

0.65

49.4

0.65

49.4

estimated pore diameter (µm) 15.9 15.7 24.4 24.5 24.2 30.5 30.9 35.3 35.7

largest through-pore, calculated using eq 1, with the breakthrough pressure and contact angle for water (50°) is 35.3 µm. This diameter estimated by the critical pressure for heptane and its contact angle (0°) is 35.7 µm. Conversely, if the water contact angle of 50° is used in eq 2, then the heptane contact angle from the measured values of the critical pressures is 8°. These values show a high degree of consistency and confirm the water-carbon porous medium contact angle measured with the surfactant solutions. Figure 9, shows the air flow through this porous medium when it is dry, water-wet, and heptane-wet, which clearly shows the critical pressure values. Once again, the values of the largest pore diameter for this block, obtained separately with the two liquids used, show excellent agreement and are reported in Table 3.

Figure 9. Variation of air flow rates through a porous block at different values of the inlet side pressure for (1) the dry block, (2) the water-filled block, and (3) the heptane-filled block.

Discussion

Figure 8. Variation of air flow rates through a porous block at different values of the inlet side pressure for (1) the dry block, (2) the water-filled block, and (3) the block saturated with 4% solution of SDBS in water.

As mentioned above, eq 3 can be used to validate the contact angles measured by the inclined-plate technique, as the drop mass, tilt angle, drop width, and surface tension are known for this system. Using estimates of the above quantities and the receding and advancing angles of 40° and 138°, respectively, the critical drop mass is estimated to be 67 µL, which is significantly larger than the experimental value of 47 µL. However, if the receding angle measured by the liquid extrusion method is used (50°) in eq 3, then the advancing angle needs to be 115° to make the critical drop volume equal the experimentally measured value of 47 µL. The angle measured by the extrusion technique appears to satisfy eq 3 better and is more likely to be the correct value.

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Although the above analysis indicates that the liquidextrusion-based measurement technique is more likely to yield the correct value of contact angles, it does not explain the cause of the observed difference in the measured values. The reason for the difference can be found from the large body of literature on the effect of surface roughness on measured advancing and receding contact angles. Ray and Bartell,28 on the basis of a study of water contact angles on paraffin wax, reported that the advancing contact angle increased and the receding contact angle decreased with increasing surface roughness. Subsequently, Bartell and Shepard29 studied the contact angles of several other liquids on paraffin wax and found the same effect of increasing surface roughness on the measured advancing and receding contact angles. The same conclusion was also reached by Dettre and Johnson30 and Allan and Roberts31 with different liquids on fluorocarbon films. These results show that increasing roughness has the same impact on contact angle hysteresis, irrespective of the chemical nature of the system. It should be noted, however, that extreme roughness can induce wicking of the liquid on the surface, causing it to spread spontaneously, and should be distinguished from the above. In the granular/powdered system studied in this paper, it is very likely that the coating of the material on the plane glass slide is a significantly more rough surface than the surface of the internal pore structure created by forming the material into a porous block. Hence, the advancing angle measured by the inclined-plate technique is higher than the actual value, whereas the receding angle measured by the same is lower than the correct value. This also suggests that the higher value of the receding contact angle measured by the liquid extrusion technique (50°) is more likely to be correct, as indicated by analysis based on eq 3 as well. With the value of the receding contact angle for water (50°) measured by the liquid extrusion technique, the pore sizes and volume distribution within the porous block formed by the powdered material can be estimated by using water alone. It is interesting to note that, for each of the four porous blocks used in the experiments, the value of the largest pore obtained from the different liquids used agree to within 0.5 µm, which points to the high consistency and accuracy of the liquid-extrusionbased technique. This paper has also shown that surfactant solutions can be used in liquid extrusion porosimetry, even when the material is highly adsorbing, if sufficiently high concentrations are used to ensure the absence of any dynamic effects. This is very useful because the use of pure liquids such as common solvents, in addition to safety and environmental concerns, is more likely to cause irreversible damage to the porous block. We observed that, when the block that was used with heptane was subsequently dried and the extrusion experiments were repeated, the critical pressures dropped significantly, indicating that the pore sizes had increased as a result of prolonged exposure to heptane. In conclusion, this paper demonstrates that the liquidextrusion-based technique is more robust and gives consistent and reliable values of receding contact angles compared to the inclined-plate technique, which is subject to variability largely caused by roughness of the inclined surface.

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Received for review May 4, 2004 Revised manuscript received December 2, 2004 Accepted December 7, 2004 IE0401408

Contact Angles of Porous Media by Liquid Extrusion and Comparison

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