Cellulose (2016) 23:2249–2272
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operation. Sample preparation by freeze-drying and freeze fracturing can remedy this problem for certain resolutions (Belle et al. 2015a, 2016; Pye et al. 1965; Washburn and Buchanan 1964). Thomson used the fluorescence resonance energy transfer method to examine cellulose surfaces (Thomson 2007), which in future may be an additional option for the determina- tion of phenomena occurring on the fiber surface. These methods enable the visualization of even the smallest changes on fiber surfaces. Whether and to what extent the nanometer scale fiber surfaces have a direct and verifiable influence on the IWWS will only become evident when the two other size ranges are considered, the micrometer and macro scale because of the strong interactions among all three levels.
h: height of a liquid column; c : surface tension liquid- fiber surface; h : contact angle of water with fiber surface; q : density of liquid; g: gravity; r: radius of capillary The formula shows that as ‘‘r’’ decreases, the capillarity increases. In practice, this relationship can be simplified as displayed in Eq. 4, highlighting the fact that capillary forces are mainly controlled by the thickness of the water film (Lyne and Gallay 1954a, b). Simplified calculation of capillary forces F C 4 Þ F C : capillary force; D: water film thickness between two fibers 1 D ð The applicability of this theory can be observed during sheet forming. As during the dewatering process the gross of the sheet volume is removed in terms of water, the distances between the fibers decrease, resulting in lower water film thickness, and thus in increasing capillary forces. The resulting capillary force increases. The idealistic model rep- resentation of fibers as two cylinders that approach each other during the dewatering process states that the greater the amount of water removed, the closer the fibers come to each other, increasing capillary forces and holding the fibers together (Wa˚gberg and Annergren 1997). Lyne and Gallay showed this in trials with glass fibers (Lyne and Gallay 1954b). However, this model assumes rigid, smooth bodies, and therefore is only a rough approximation of the true phenomenon (Wa˚gberg 2010). This is because fibers have a certain morphology, are flexible, present in various deformed or swollen states, and are very coarse, especially in wet conditions (Belle et al. 2015a; Feiler et al. 2007; Heinemann et al. 2011). Calculations based on the capillary theory showed lower values than one order of magnitude compared to measured values (Miettinen et al. 2007; Tejado and van de Ven 2010). This shows that besides the capillary force other forces interact and contribute to the IWWS. It is proposed that especially the con- formability of the fibers in the network leads to frictional connection that contributes significantly to the IWWS.
Micrometer level (fiber morphology)
At the micrometer level, processes between fibers, fillers and additives are studied more closely. First, the interaction between fibers and water is explained by capillary forces and the processes of swelling, gel formation in the proximity of fibers, and hornification. Subsequently, the influence of the fiber characteristics on the IWWS is discussed, including the surface roughness and the complex fiber morphology com- prising fiber fractures, fibrils and fines particles. This discussion includes both, the beating and blending of fibrous materials and the measurement techniques used to assess the fiber characteristics.
Capillary forces
Besides drainage pressure and suction in the wire section the capillary forces are acting for the fiber and fibril approach, and as a result are a major factor affecting the IWWS in the early stages of paper dewatering (Campbell 1933; Israelachvili 2006a; Kendall 2001b; Page 1993; Persson et al. 2013; Rance 1980; Schubert 1982; van de Ven 2008; Williams 1983). The capillarity describes the properties of liquids in narrow spaces. Equation 3 shows the formula for the capillarity: Capillarity
2 c cos h q gr
h ¼
ð
3 Þ
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