*4.3. Case 3—Signal Decrease Due to Swelling*

θ If capillary penetration is possible, a signal decrease is caused by entrapped, resonating air bubbles, as explained above. However, paper samples where capillary penetration is not possible because they are heavily sized (θ > 90◦ ) can still exhibit a decrease in signal transmission. Air bubbles cannot be the reason for the decrease in this case, as there is no liquid entering the substrate pores. This can be shown when again comparing the flat and the grooved sample holder. Figure 6a shows the ULP curve of a sized copy paper with water on the flat sample holder, where the air within the sample is entrapped at the backside. The signal first increased until it reached a maximum that was followed by a slow decrease. The shape of the curve was not changed when using a grooved sample holder that allows the air to escape (Figure 6b). Thus, enclosed air bubbles could not be the reason for the signal decrease in this case.

Air bubbles cannot be the reason for a signal decrease if capillary penetration is not possible, since there is no liquid front advancing through the sample. However, as mentioned earlier, water can still enter the sample via vapor and surface diffusion, as well as penetration within the paper fibers (which are porous). In that way, water will diffuse into the fibers, filling voids within the fibers, causing them to swell. The filling of the voids should lead to an increase in the speed of sound in the fibers. That would lead to an increase in the fibers' wave impedance and consequently to an increased reflection coefficient for air–fiber boundaries. As the fibers are still surrounded by air, this would explain the slowly decreasing ultrasound signal.

**Figure 6.** ULP curves of sized paper in contact with water. (**a**) AKD (alkyl ketene dimer) sized paper on flat sample holder—air is entrapped. (**b**) Sized copy paper on grooved sample holder (measurement from [16])—air can leave the sample on the backside via the grooves. Both papers have contact angles of about 100◦ with water, thus no capillary penetration. The signal decrease is created by fiber swelling, diffusion, or surface transport of liquid into the substrate (in this case usually paper).

Figure 7 shows the last stage of penetration of water into a sized paper. The first two stages were equivalent to the first two stages of case 1 (Figure 3—top and middle row). Initially there was an air film at the paper surface at which the ultrasound signal was reflected to a large extent. As the liquid wetted the surface and the air film disappeared, ultrasound transmission increased. For a non-swelling substrate–liquid combination the signal would not decrease again. For paper in contact with a fiber swelling liquid like water, however, the fibers will take up some liquid, ultimately leading to a decrease in the signal. In that case, the time of the maximum intensity can be interpreted as the time at which swelling of the fibers starts [33].

**Figure 7.** Liquid uptake of a surface hydrophobized paper (no capillary penetration). (**a**) ULP curve of an AKD sized paper in contact with water. (**b**) Graphical illustration of the water uptake into the fibers by vapor and surface diffusion as well as intra-fiber liquid penetration (third stage of liquid uptake; stages one and two are equivalent to Figure 3b, digits 1 and 2). The density increase within the fibers leads to a higher ultrasonic reflection at the fiber-pore interfaces and thus to a decrease of the signal.

Results that confirmed that fiber swelling was the reason for the decrease in ultrasound transmission for surface hydrophobized (sized) papers are shown in Figure 8. First, Gabriel [6] found that ultrasound transmission and wet expansion are strongly correlated especially for sized and coated papers (Figure 8a) and that they show exactly the same development over time. The wet expansion of a paper sheet is

directly related to the swelling of the fibers within. Therefore, this correlation is a strong indication that the decrease of the ULP curve for hydrophobized papers is indeed related to swelling of the fibers.

**Figure 8.** ULP measurement results underlining the effect of fiber swelling on ultrasound transmission. (**a**) Ultrasound transmission intensity I and wet expansion for a coated printing paper in contact with water. Ultrasound transmission and wet expansion are strongly correlated. (**b**) Temperature dependence of ULP measurements of sized copy paper in contact with water. The high temperature dependence indicates a high influence of the vapor pressure and thus diffusive water transport into the fibers (both adapted from [6]).

Second, Gabriel [6] also found that the ULP results are highly dependent on the temperature of the test liquid. In Figure 8b 20 percent ultrasound intensity was reached after about 14 s when measuring water at 23 ◦C, while it took less than half the time to reach the same relative intensity at 43 ◦C. The faster decrease at higher temperatures indicates faster water uptake of the fibers. One reason for that might be the lower viscosity of the liquid. More dramatic, however, is the increase in saturation vapor pressure, which increased exponentially with temperature. Therefore, Gabriel [6] concluded that the sharper decrease and thus faster liquid uptake at higher temperatures is caused by the intensified water vapor diffusion into the sample and the fibers. This is another indication that the decrease of the ULP curve of a surface hydrophobized (sized) paper is determined mainly by the transport of the liquid into the fibers.
