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Dynamic Water Transport in a Pigmented Porous Coating Medium: Novel Study of Droplet Absorption and Evaporation by Near-Infrared Spectroscopy Carl-Mikael Tåg,*,† Mikko Juuti,‡ Kimmo Koivunen,§ and Patrick A. C. Gane§,| Forest Pilot Center Oy, FI-21200 Raisio, Finland, VTT Technical Research Centre of Finland, P. O. Box 1199, FI-70211 Kuopio, Finland, School of Science and Technology, Faculty of Chemistry and Materials Sciences, Department of Forest Products Technology, Aalto UniVersity, P. O. Box 16300, 00076 Aalto, Finland, and Research and DeVelopment, Omya DeVelopment AG, CH-4665 Oftringen, Switzerland
The dynamic wetting of, and absorption into, model porous coatings in the form of compressed particulate pigment tablets by monocomponent, dual-component, and multicomponent liquid droplets has been studied by observation of apparent contact angle and near-infrared spectroscopy to identify the liquid water/moisture content. The absorption of the liquids was studied in a corresponding vapor-saturated environment. Liquid evaporation was determined for the tablets at both equilibrium starting pore saturation and under limited volume-filling conditions as evaporation proceeds. The changes in water and moisture content within the coatings as a function of time were also determined gravimetrically to relate the water uptake and evaporation being observed to changes in the near-infrared spectral data. Model and commercial offset printing fountain solutions were compared with respect to both absorption and evaporation. For the solutions containing isopropyl alcohol in water, a nonlinear behavior in the water response in the near-infrared spectra during absorption is observed as a function of time, which can be related to the fast evaporation of the alcohol. The nonlinear region was followed by a decline in water and moisture content as the penetration/evaporation of the water phase proceeded. Comparing the near-infrared water volume dependency in the upper layers of the structure with weight loss during evaporation showed that the mechanism of liquid transport to the surface-air interface reflected the logarithmic volume distribution of pore sizes, as might be expected from capillarity considerations and pore condensation hysteresis. 1. Introduction In many industrial applications, such as the printing and coatings industry, wetting of porous materials by liquids includes not only the bulk liquid absorption but also its evaporation and surface spreading. By understanding these phenomena, valuable information can be obtained for improved process control, runnability, and printability, in which absorption of liquid and subsequent drying play important quality and economic roles. Knowledge of the position of the wetting front and the distribution/degree of pore filling within the structure is crucial in describing the transport phenomena involved. These factors also combine and play a major role in processability; for example, print defects such as blistering and waving (fluting of the sheet), which are closely related to an uneven moisture profile in the paper during drying, can be predicted and controlled by understanding the mechanisms of absorption and evaporation. The moisture content has a great influence on the dimensional stability of paper.1 The moisture content has been shown to have clear effects on the calendering response, print quality, friction, and structural dimensions of paper, such as waviness and curl. The moisture content of paper is dependent on the surrounding humidity, temperature, paper weight, and the hygroscopic properties.2 Enomae and LePoutre showed the effect of moisture content (relative humidity (RH) change) on gloss and the gloss relaxation mechanisms, where the latter was addressed to the time lag observed.3 In the same paper the role of moisture * To whom correspondence should be addressed. † Forest Pilot Center Oy. ‡ VTT Technical Research Centre of Finland. § Aalto University. | Omya Development AG.
diffusion into the bulk and its effect on swelling behavior of the coated paper with respect to the base paper was discussed. Laudone et al. claimed that shrinkage occurring during drying, for pigmented coatings far above the critical pigment volume concentration, is caused by capillary forces acting as the water recedes within the pigment structure while polymeric binders can permit release of or retain these stresses.4 Different mechanisms for structural changes have also been proposed, such as the recovery of fibers, but also surface condensation of water occurring at high humidity levels.5 The internal liquid and vapor contents of paper are rapidly removed during the drying process in several printing technologies, such as heatset web offset, thermal drying of inkjet, etc., which can lead to distortion due to mechanical stresses, which disrupt the internal or surface structure and ultimately may even break the paper. The paper quality, and thus composite structure, is obviously critical when considering the rate of liquid and vapor removal in relation to storage of, and retained, moisture inside the reel. The storage environment of the reels, with respect to the subsequent surrounding conditions of the printing house, plays a dominant role. In the case of coated paper, the interrelation between liquid and vapor transmission within the porous coating, thus defining the transport of moisture to and from the underlying base paper by permeation, capillarity, and diffusion, becomes the major controlling factor with respect to paper stability. The impact of the paper environment on the physical and chemical stability of printed and unprinted paper is well-reported in the literature. When considering the absorption rate of ink and fountain solution components into porous paper coatings, the pore size in relation to pore density must also be considered.6 However, as this work shows, pore density in the coating surface is not sufficient to describe the offset in behavior from the assumed
10.1021/ie1000289 2010 American Chemical Society Published on Web 04/08/2010
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Lucas-Washburn square root of t dynamic. A compensation with respect to a root t offset is required,6 so the work shows the unsuitability of assuming perfect capillaries operating at equilibrium. Thus, it is necessary to consider the short time scale dynamics within a rapidly changing geometrical network of pores.7,8 Porous pigmented structures and the absorption rate and volume dependency of porous network structures9 have previously been used to determine the absorption rate of vehicle components of flexographic inks10 and the imbibition rate of offset inks.11 It has been found that the imbibition rate of low-viscosity fluids can be correlated to short time scale inertiacontrolled absorption into the porous network structure of the coating layer. The interplay between preferential plug flowlike filling of the finest pores and the inertially retarded filling of larger pores defines the absorption dynamic on the nanosecond time scale. Further longer time uptake into the bulk structure continues this nanoscale interplay at each and every geometrical connective feature within the structure, while simultaneously superposing the viscous drag of the permeable network. This was demonstrated by Ridgway and Gane7 adopting an algorithm based on the Bosanquet equation12 applied to a model porous network, concluding that pores up to a given diameter in a porous network fill rapidly while bigger features remain bypassed and tend to remain unfilled under conditions of limited supply volumes of fluid. This confirmed the observations made by Schoelkopf et al. studying liquid uptake from an applied droplet into tablet structures of porous pigmented coating.8 Pigment tablets have also been used for the analysis of the thermal conductivity properties of calcium carbonate based coatings showing that an even binder distribution, ensuring connectivity, leads to a greater thermal conductivity.13 The mechanism of the evaporation of pure liquids is very well documented in the literature, but the phenomenological understanding of the evaporation of multicomponent liquids, under the confines of a porous network structure, is lacking. Furthermore, the evaporation of liquids has to a great extent been studied on smooth homogeneous nonporous materials, but here the evaporation of liquid mixtures is investigated from heterogeneous porous structures. The link between thermal conductivity and the heat-induced transport of vapor is therefore fundamental to the study of drying efficiency, so it is imperative to develop the measurement techniques required to establish the distribution of liquids within porous media in real time. In literature, the evaporation of droplets has been modeled in terms of mass transfer by the rate at which vapor is transported from the liquid front through pores and further to the atmosphere. The transport within the structure is normally described by molecular diffusion. Roberts and Griffiths also discuss the role of droplet size and temperature in their proposed evaporation model.14 Shokri et al. distinguish the drying of hydrophobic and hydrophilic porous media.15 The same authors conclude that the evaporation rate often exhibits a transition from constant rate capillary liquid flow to vapor diffusion by comparing evaporative mass loss and drying front depths. In the first case, liquid pathways connect the receding drying front with evaporating surface, and in the second phase, at a certain drying front depth, gravity overcomes capillary driving forces, leading to diffusion-supported evaporation. Near-infrared (near-IR) spectroscopy has previously been used to determine the moisture content and z-directional moisture profiles of paper coatings.16 By application of near-IR analysis it has been found that the drying strategy during coating shows clear differences in the water penetration and the immobilization of the coating.17 Since the IR absorption bands of water are
easily determined in the near-infrared spectral region, the measuring of moisture contents of various samples has gained a lot of interest in the field.18 The moisture content of paper can of course also be measured with other techniques, such as gravimetry,19 but the advantages with the near-IR technique are that it can measure the whole spectrum of a sample very rapidly, so it can, in principle, be used for online process evaluation. The near-IR reflection wavelength has a limited penetration depth into the sample, but a dual side measurement is also possible in the case of paper samples.20 In the work reported here, the wetting behavior of a series of liquid mixtures was determined by droplet absorption measurements in the absence of external pressure, such that surface wetting and capillarity are the driving forces. The dynamic of absorption is vitally important to the problem at hand, as it occurs within the time scale of the subsequently applied drying in practice. Therefore, it is important to understand the distribution of liquid within the porous structures, and this is provided by considering models that are not following classical Washburn dynamics. It is for this reason that much attention is given to the pore network description and the impact of geometrical changes in the structure causing rapid changes in the liquid acceleration and hence inducing inertial effects acting on the short time scale within the local structure of the network. These effects determine the liquid distribution. The aim of this study is to present the experimental findings concerning the moisture content of pigment tablets, as a result of water imbibition and, primarily, during subsequent evaporation, by using near-infrared measurement technology together with a determination of the wetting properties of different liquid mixtures, as might be encountered on a printing press. The aim of the work is also to initiate the near-IR method and to link it with the distribution aspects. The studied liquids were monocomponent, dualcomponent, and multicomponent liquids containing water and either isopropyl alcohol or a surfactant as the main additive component. The liquid series was chosen in order to compare commercial fountain solutions with model solutions having only the main component present together with water. Water alone was used as a reference. The strengths in using near-IR techniques to investigate the liquid water and moisture response of pigment structures are presented. The liquid water transport was studied under controlled conditions as a function of time. 2. Experimental Section The test liquids and their surface tensions are described in Table 1. The liquid mixtures were prepared before the measurements in order to maintain a homogeneous solution mix. A microbalance (Mettler-Toledo Inc., Columbus, OH) was used to monitor the amount of liquid added with a microsyringe. The surfactant used in the study involving alcohol-free fountain solution was an acetylenic glycol based nonionic surfactant (Dynol 607, 2,5,8,11-tetramethyl-6-dodecyn-5,8-diol ethoxylate) delivered from Air Products and Chemicals, Inc. The surfactant is pure in a molecular sense and based on the so-called Gemini technology. Gemini surfactants possess more than one hydrophobic tail and hydrophilic headgroup, and are thus more surface-active than the corresponding conventional surfactants of equal chain length. The VOC content is 1.45 wt % (EPA Method 24), and the surfactant hydrophilic-lipophilic balance (HLB) is 8. The HLB was determined by taking the hydrophilic portion of the surfactant on a molecular weight basis divided by 5, giving a HLB value between 1 and 20.21 The cloud point occurred at 17.2 °C in water determined at a concentration of 5 wt %. The solubility limit in water is 0.032 wt %. The Dynol
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Table 1. Test Liquids and Their Surface Tensions liquid samples deionized water, reference 10% IPA-water solution 1% surfactant-water solution IPA based heat set fountain solution (fount 1) Heatset alcohol-free fount 2017 (fount 2) Heatset alcohol-free fount 2072 (fount 3)
manufacturer
concentration/%
Millipore Inc., Billerica, MA Air Products and Chemicals Inc., Allentown, PA VEGRA Gesellschaft fu¨r Herstellung and Vertrieb von Produkten fu¨r die grafische Industrie mbH, Aschau am Inn, Germany Flint Group, Luxembourg Flint Group (address above)
607 surfactant does not form micelles; i.e., when the surfactant concentration is increased, at one point the solution will “oil out”, meaning that the solubility limit is reached. Ground calcium carbonate (GCC, Hydrocarb 60 ME (a product of Omya AG, Oftringen, Switzerland) polyacrylate dispersed marble pigment having 60% (w/w) finer than 2 µm) was the chosen pigment for the model structures, which additionally contained 2 parts per hundred (pph) styrene acrylic latex, Acronal S360D (a product of BASF, Ludwigshafen, Germany) based on 100 pph pigment by weight to provide structural stability. The use of only two parts of binder emphasizes the effect of the pore structure alone. This is applied purposefully in this case to allow correlations to be made with structural parameters alone, since latex has a marked effect on the colloidal interactions in the coating color which are reflected in the final coating structure.22 Tablets were formed from this pigment-binder formulation by dewatering the slurry mix (65% (w/w) solids content) under 20 bar pressure in a cylindrical steel die. After forming, the tablets were dried overnight in 60 °C. A more detailed description of the preparation of the tablets can be found in ref 23. From the large ready-made tablets some smaller plugs were drilled with the dimensions of height 15 ( 3 mm and diameter 8 mm. The dimensions of the tablet are magnitudes thicker than that of a coating layer. However, for coated paper, the impact of capillarity will be strongest in the coating layer compared with the base paper. Therefore, the major impact on the near-IR measurement will be seen in terms of liquid content in the coating, especially at higher coat weights. The pore structure of the tablet was probed by mercury intrusion porosimetry. The mercury intrusion data were corrected for mercury compression, penetrometer expansion, and sample skeletal compression using Pore-Comp (a software program developed by the Environmental and Fluid Modeling Group at the University of Plymouth, U.K.).24 The density of the tablets was determined to be 1.85 g cm-3, and the total specific pore volume was shown to be 0.16 cm3 g-1. In each experiment, a droplet was put on the pigment tablet surface. Since the tablet cores had a large diameter of 8 mm, a constant base diameter of the droplets put on the surface without the influence of any edge effects was guaranteed. Different droplet volumes creating different interface shape characteristics were also tested. Deegan et al. have concluded that droplets of similar base radius should exhibit similar evaporation rates, with all other conditions being constant.25 This can be considered as an important foundation for the later understanding of the relationship between water weight loss from the porous structure, during the evaporative stages of drying, and the volume-dependent near-IR absorbance. The tablet was weighed during each near-IR measurement of the water/moisture distribution during liquid absorption to calculate the mass of evaporated liquid as a function of time. The weighing as a function of time was correlated to the nearIR measurement once the surface droplet has disappeared due to absorption. The measurements were performed inside a chamber in order to have a closed environment defined by the
surface tension/(mN m-1)
10.0 1.0
72.9 40.9 27.6
6.0 IPA + 3.5 Vegra 3232i
49.8
3.0 3.0
45.2 43.7
vapor pressure of the liquid(s) involved (Figure 1). Two repetitive measurements were performed. The surrounding laboratory conditions were 50% RH and T ) 23 °C. 2.1. Surface Tension Measurements. The surface tensions of the liquids were measured with a bubble tensiometer (SensaDyne PC9000 Instrument Division, Mesa, AZ). The method description is described in ref 26. Three repetitive measurements were performed over a 5 min measuring time in order to achieve reliable results. The temperature was recorded during the measurement (T ) 23-24 °C). The surface tensions were measured at a bubble rate of 1 bubble s-1 for water which constituted a semistatic measurement. 2.2. Contact Angle Measurements. In the case of porous absorbing surfaces, it is recognized that it is not possible to determine a true contact angle due to the probability of liquid passing laterally within the subsurface, so influencing the threephase contact at the apparent wetting front; i.e., the liquid droplet boundary is in contact with solid, air, and further liquid. Nonetheless, an affinity for liquid surface spreading or contraction can be determined. Thus, the apparent contact angle evolution as a function of time was monitored with a highspeed camera (KSV Instruments Ltd., Helsinki, Finland). In the measurements, a droplet is put on the substrate sample surface and the spreading takes place without any external pressure. The measuring procedure is described in more detail in ref 26. The volume of the droplets was 1.5 µL, corresponding to a sphere radius of ∼2 mm at t ) 0.1 s. The results are given as a mean of five measurements. The standard deviation of the measured apparent contact angle values was less than 2°. This consistency reflects also the reproducibility of the basal contact area between the droplet and the surface for each given liquid and combinations thereof. 2.3. Near-Infrared Measurements. The water-induced nearIR absorptive reflectance from the GCC pigment tablets was studied using a spectrophotometer (Tec5 AG, Oberursel, Germany). The measurement system is based on a fiber-optic light source, a single-point probe, and a spectrograph. It consists of a halogen lamp as a light source and a near-IR spectrometer as well as reflectance probe with fiber-optic illumination and detection. The measurement probe is a diffuse reflectance probe containing optics which project the illuminating light from the
Figure 1. Schematic picture of the near-IR measurement setup.
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Figure 2. Porous solid-liquid apparent contact angles, Θ (deg) as a function of time, t (s).
source fiber onto the sample and the detector probe collects the backscattered light into the detection fiber. The measurement is different from a typical spectroscopic measurement; namely, the probe unit spectrophotometer provides the possibility to carry out dynamic (real time) measurements of IR reflection from a sample such as a pigment tablet to form a full-scale near-IR spectrum. By using mechanical clamps and stands for the probes, it is possible to choose the angle of incidence and a range of detection angles between 0 and 45°. The radiation source of the device adopts the extended InGaAs (990-2000 nm) technique. The diameter of the incident irradiating beam spot from the probe to the sample surface was 4 mm, and the acceptance angle of the detector was less than 2°. Full near-IR spectra were measured and analyzed with the spectrophotometer. Spectralon (Labsphere Inc., North Sutton, NH), a PTFE-based material with high reflectance, was used as a white reference for the diffuse reflectance measurements. In Figure 1, a schematic picture of the measurement system is shown. The near-IR diffuse reflectance was measured from a series of pigment tablets, dried, and wetted by the six different solutions. The near-IR spectrograph measures diffuse reflectance spectra from the paper surface. Two repetitive measurements were made and no significant variation in the diffuse reflectance between them was observed, indicating good repeatability. The dynamic diffuse reflectance reported in this paper is the integrated diffuse irradiance from the sample detected in the plane of light incidence. The time step for the running integration was chosen to be 5 s. The measurements revealed differences in liquid water/moisture contents as a function of time between the different mixtures of the commercial and model offset fountain solutions. Since the power capacity of the IR source fiber was low and the detector integration time correspondingly long, the heating of the tablet during the measurements was considered negligible. The measurement geometry of the diffuse reflectance measurements, as shown in Figure 1, was chosen to be 45/0, and the distance between the probe and sample was 10 mm. The left-hand image (I) describes the situation as the droplet has been applied on the surface (geometry for contact angle measurements) and the right-hand image (II) as the liquid droplet has penetrated into the tablet (geometry for the near-IR measurements). The value t ) 0 refers to the situation when the droplet has penetrated into the substrate. 3. Results In Figure 2, the wetting of the probe liquids is simply exemplified by plotting the apparent contact angle versus time. One can observe a strong initial decrease in apparent contact
Figure 3. Dynamic near-infrared diffuse reflection spectrum of the unwetted and the wetted pigment tablet, as exemplified by the surfactant solution. The spectrum is not baseline-corrected but slightly noise-smoothened. The point t ) 0 refers to the situation where the droplet has penetrated into the tablet and no further exposed volume remains on the surface.
angle as the droplet comes into contact with the tablet surface. In this regime, the spreading is closely related to the surface structure and chemistry of the sample. The fastest decline is observed for the surfactant solution, and for both of the commercial surfactant based fountain solutions. The differences in apparent contact angle values are also attributed to the interfacial tension between the liquids and the solid and any lateral subsurface liquid spreading. Highly evaporative liquids cause surface tension gradients which change the spreading and imbibition behavior. The difference in the apparent contact angle values between the commercial heatset offset fountain solution (fount 1) and the IPA-water mixture is attributed to the presence of other unknown additive(s) in the fount 1 formulation. The slowest wetting of the tablet is obtained by the deionized water, it creating the highest solid-liquid interfacial tension. In Figure 3, the dynamic near-IR diffuse reflectance spectrum of the dry and wetted pigment tablet is presented. The spectra at different wetting times give an estimate of the relative moisture content in the pigment tablet. The selection of the absorption bands of water in the near-IR region for the moisture predictions was simple since both of the water absorption bands are well-defined at the wavelengths of 1450 and 1950 nm. In the analysis, both regions were analyzed since the 1950 nm band has a better sensitivity to water and since the 1450 nm water band is not disturbed by any partly overlapping cellulose band (1490 nm). The results showed the same behavior in both of the regions, and thus only the 1450 nm peak is presented in this paper. Furthermore, the 1450 nm water absorption band displayed a slightly lower noise level than the 1950 nm peak. It can be observed that a small water peak is detected also for the “dry” tablet, describing the tablet moisture content in ambient air conditions. The relative differences of the curves reveal the rate of penetration and evaporation. As the evaporation and penetration of the liquid becomes slower, an apparent increase in reflectance (decrease in absorbance) is observed. An effort was made to analyze the initial absorption of the liquids into the pigment tablet with the near-IR technique. The droplet was placed, as described above, on the tablet surface and an immediate absorption occurred. In the measurements, different droplet volumes creating different interface shape characteristics were tested, this obviously affecting the reflection in the measurements. Hence, it was difficult to determine the initial absorption. However, the repetitive measurements showed no drastic differences, suggesting that the capillarity is extremely rapid and defined by the contact area.
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second stage to the other components. The faster decline for fount 1 than that of the 10% IPA solution can likely be attributed to other unknown additive(s) in the fount 1 mixture. 4. Discussion
Figure 4. Liquid penetration of a droplet into and evaporation from the porous tablet as measured by near-IR absorbance, A. The presented water absorbance band in the near-IR diffuse reflection spectrum is 1450 nm. The point t ) 0 refers to the time when the liquid droplet is no longer on the surface but absorbed in the bulk and adsorbed on the surface layer.
In Figure 4 the penetration and evaporation of the studied liquids inside the tablet (below and from the tablet-air interface surface) are presented. Once again, the point t ) 0 represents the situation where the droplet is no longer existing on the surface but is absorbed within the structure and adsorbed on the uppermost surface layer. Also gravimetric measurements have been made, and those findings are presented later on in order to verify the observations determined with the nearinfrared technique. We see in Figure 4 that initially there is observed an almost stable regime, which corresponds to the situation where further liquid transport has reached an equilibrium filling level of the surface pores and further transport is controlled by diffusion. At t ) 200-300 s, depending on the liquid, the evaporation stage dominates as liquid near the surface can no longer be replenished. This phase includes both further liquid transport inside the tablet and evaporation from the inside of the tablet to the surface and then to the atmosphere. The point where the initial penetration starts to level out corresponds to the maximum surface moisture content. It should be noted that the drop in absorbance is partly due to transport restriction further inside the tablet (deeper than near-IR detection limit) and the evaporation from the tablet surface. At t ) ∼500 s, depending on liquid, the leveling of the curve corresponds to the state where the liquid has penetrated deeper than the near-IR detection limit and the moisture evaporation slows down. The strongest change in intensity in Figure 4 is observed for the 1% surfactant solution. According to the contact angle wetting measurements, the surfactant solution immediately wets the pigment tablet, and hence the rapid change in intensity is referred to as fast penetration into the tablet. The surfactant acts to reduce the surface tension of water, so the vapor pressure differential across the liquid-vapor boundary is reduced. Compared to alcohol-based solutions, it is supposed that the surfactant does not evaporate from the tablet but adsorbs to the pigment surface.26 The adsorption of species on the surface influences the surface chemistry, and hence the adhesion and the interaction with other substances will also be affected. The same evolution in liquid water and moisture change is observed for the two alcohol-free fountain solutions. The slow penetration and evaporation of water is observed as an almost linear curve. In the samples containing isopropyl alcohol (10% IPA and fount 1), linear regions up to 150 s are observed, which can be related to the fast evaporation of the alcohol. The linear region is followed by a decline, which is interpreted as the penetration/ evaporation of the water phase. The first region is thus related to the evaporation of the more volatile component and the
The liquid water and moisture content of pigment tablets wetted by different liquid mixtures (all containing water) has been analyzed by near-infrared spectroscopy. The absorption and surface wetting of the studied liquids were investigated with contact angle measurements. Considering, for example, printing processes, wetting is primarily affected by a nip pressure and pressureless diffusion plays only a minor role compared with the action of capillarity. However, for local moisture distribution determination, diffusion is of key importance once the initial pore equilibrium filling of the surface structure has occurred. Thus, the liquid water and moisture movement occur partly as capillary flow and partly as vapor diffusion through the void spaces of the tablet contributing to subsequent penetration further into the matrix on a longer time scale. Test liquids consisting of model fountain solutions were compared to commercial ones and water. Both IPA- and surfactant-based systems were investigated. The strong point of the use of IPA is that it is 100% miscible with water and does not form micelles. It is surface-active and therefore reduces the surface tension. It is homogeneously distributed in the liquid phase and therefore aids interfacial wetting. Surfactant-based fountain solutions are mostly glycol or glycol-ether-based nonionic surfactants,27 and much lower quantities are required to achieve functionality.28 The dynamic efficiency of the surfactants is critical in order for new wetting surfaces to be created sufficiently rapidly. The surfactant-based fountain solutions present stronger absorption behavior than that of the IPAbased ones. The increased wetting force can be related to the fast wetting front diffusion of surfactants, and since they are nonionic, they may inhibit the swelling of the hydrophilic dispersing agent on the pigment surface as well as providing better wetting of the binder present. These assumptions require further work to confirm, and one should note that the wetting studies were performed under nonimpact conditions, i.e., no external pressure applied. One way to characterize the rate of absorption in porous systems is to model the structure as a bundle of uniform capillaries.29 Analysis of the capillary imbibition pressure and the viscous drag leads to the Lucas-Washburn equation,30 which relates the penetration depth at a certain time into a capillary with a given radius, the viscosity and the surface tension of the liquid, and the effective contact angle between the liquid and the capillary wall. However, the inner surface of porous materials such as paper is never perfectly smooth or chemically homogeneous, and this has a strong effect on the wettability and the rate at which liquids imbibe. The mechanism of liquid absorption into porous pigment structures has been investigated in detail by Gane et al.9 It has been shown that it is the smaller voids in the matrix which contribute to the strong absorption properties.7 The same workers also studied the moisture pickup of calcium carbonate tablets using pigments of different size distributions.31 As the liquids come into contact with the sample, the structure of the swellable matrix associated with adsorbed polyacrylate dispersant on the carbonate surface is changed, i.e., when hydrophilic and hygroscopic dispersant agent is present.7,31 Hence, it is the porous permeability and surface structure relationship which controls the saturated absorption/evaporation capacity.
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Figure 5. Near-IR moisture against weighed moisture for the fount 1 solution. The initial point refers to the time when the droplet has penetrated into the tablet, t ) 0, and the final point at t ) 400 s.
In Figure 5, data of near-IR reflectance signal strength loss is plotted against weight loss and the relationship is exemplified for the fountain solution, fount 1 and water. It is easy to follow the progress of the imbibition and evaporation of the fount 1 solution compared to water away from the surface layers of the pigment matrix, and we note the linear trend between the weight loss and the logarithmic decline of the near-IR reflectance signal. From near-IR measurement alone one cannot tell if the signal decline, exemplified in Figures 3-5, is all due to surface water removal by evaporation or a combination of rapid further deep absorption plus evaporation, although instinctively transport competition is to be expected. The close to linear declination of the data in Figure 6 relating weight loss and the log of the reciprocal near-IR reflectance, however, demonstrates that the reduction in combined liquid and tablet weight is linear and thus defined by evaporation of the liquid from a constant surface area under constant surface saturation conditions, whereas the fall in near-IR reflectance is exponential. Thus, the near-IR signal, being sensitive to surface layer phenomena only (
