Influence of the Processes Parameters on the Properties of The ...

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Chapter 3. Analytical Methods and Designs <strong>of</strong> Experiments 6.2.1.3 Lucas-Washburn’ Method This approach is also known as <strong>the</strong> capillary rise method. It determines <strong>the</strong> contact angle by analyzing <strong>the</strong> capillary rise <strong>of</strong> liquids into a porous powder. It is a very simple and universally applicable method and is <strong>the</strong>refore commonly used. The set up <strong>of</strong> <strong>the</strong> experiment is done by adding a porous powder to a glass tube with a filter on <strong>the</strong> bottom. The glass tube with powder is densified and attached to <strong>the</strong> tensiometer. The liquid with known density (ρ), viscosity (η), and surface tension (γ LV ) is placed at <strong>the</strong> bottom <strong>of</strong> <strong>the</strong> tensiometer and its level is subsequently raised until contact with <strong>the</strong> filter <strong>of</strong> <strong>the</strong> glass tube is registered (cf. Figure 3.23). Via capillary forces, <strong>the</strong> liquid rises through <strong>the</strong> porous powder and <strong>the</strong> increase in weight is measured by <strong>the</strong> tensiometer, resulting in a graph <strong>of</strong> <strong>the</strong> square mass plotted against <strong>the</strong> time. The equation that fits this graph is [Dang-Vu and Hupka, 2005; Kiesvaara and Yliruusi, 1993]. l s /t = ( r.Cos (3.15) where l s is <strong>the</strong> front <strong>of</strong> <strong>the</strong> liquid; t is <strong>the</strong> time; l is <strong>the</strong> superficial tension <strong>of</strong> <strong>the</strong> liquid, r is <strong>the</strong> capillary radius; θ is <strong>the</strong> contact angle and η is <strong>the</strong> liquid viscosity. Figure 3.23: Principle <strong>of</strong> <strong>the</strong> absorption Wasburn’ method. 6.2.1.4 Surface Tensions <strong>of</strong> Classical Liquids The liquids used must be characterized such that <strong>the</strong> polar and dispersive components <strong>of</strong> <strong>the</strong>ir surface tensions are known. Classical liquids chosen in experiments are ei<strong>the</strong>r polar as pure water and ethylene glycol or apolar as -bromonaphtalene (cf. Table 3.1). Table 3.1: Surface tensions <strong>of</strong> various liquids. Liquids γ L (mJ/m 2 ) γ d L (mJ/m 2 ) γ nd L (mJ/m 2 ) γ − L (mJ/m 2 ) γ + L (mJ/m 2 ) Water 72.75 21.75 51.00 25.20 25.50 Glycerol 64 34 30 3.92 57.4 Formamide 58.00 39.00 19.00 2.28 39.60 Ethylene Glycol 48.00 29.00 19.00 1.92 47.00 Diiodomethane 50.80 50.80 0.00 0.00 0.00 bromonaphtalene 44.40 44.40 0.00 0.00 0.00 [Oss, 2006, 1994] 6.2.2 Surface Energy <strong>of</strong> Solids 6.2.2.1 Young-Dupré’ Equation The determination <strong>of</strong> <strong>the</strong> surface energy <strong>of</strong> a solid sample (γ SV ) is difficult since <strong>the</strong>re is no direct method to measure it. The result will remain an estimation <strong>of</strong> <strong>the</strong> actual value [Mykhaylyk et al., 2003]. In 1805, Young described <strong>the</strong> relation between <strong>the</strong> contact angle and <strong>the</strong> different surface tensions (Figure 3.24 and equation 3.19): - 80 -
Chapter 3. Analytical Methods and Designs <strong>of</strong> Experiments Figure 3.24: Vectorial equilibrium for a drop <strong>of</strong> a liquid resting on a solid surface to balance three forces. SV SL LV Cos (3.16) SV SL cos (3.17) LV where γ LV denotes <strong>the</strong> interfacial tension due to <strong>the</strong> liquid-gas surface, γ SL refers to <strong>the</strong> interfacial tension due to <strong>the</strong> solid-liquid surface and γ SV indicates <strong>the</strong> interfacial tension <strong>of</strong> <strong>the</strong> solid-gas surface. In Young-Dupré equation, two parameters can be measured directly: <strong>the</strong> liquid surface tension (γ LV ) and <strong>the</strong> contact angle (θ). The two o<strong>the</strong>r parameters (γ SV and γ SL ) have to be derived. The contact angle measurements give 3 informations: The affinity <strong>of</strong> a liquid to a solid surface: if water is used to measure <strong>the</strong> contact angle, one can deduce <strong>the</strong> hydrophobic (great angle) or hydrophilic (small angle) character <strong>of</strong> <strong>the</strong> surface. If several reference liquids are used, <strong>the</strong> surface energy <strong>of</strong> <strong>the</strong> solid can be calculated, discriminating between polar and dispersive components. The most common models used are <strong>the</strong> Good & Van Oss and <strong>the</strong> Owens & Wendt models. The measure <strong>of</strong> <strong>the</strong> hysteresis between advancing angle and recessing angle give informations on non homogeneity <strong>of</strong> <strong>the</strong> surface (roughness , contamination, etc.). Theoretically, <strong>the</strong> Young-Dupré’ equation is correct, but as it is based on ideal surfaces (homogeneous, pure, smooth), it is experimentally difficult to obtain. Considering this, a range <strong>of</strong> contact angles is obtained, depending on <strong>the</strong> smoothness <strong>of</strong> <strong>the</strong> surface and with a maximum and minimum possible value. The difference between <strong>the</strong> maximum contact angle (θ A ) and <strong>the</strong> minimum or receding contact angle (θ R ) is referred as <strong>the</strong> contact angle hysteresis (Δθ= θ A − θ R ) [Possart and Kamusewitz, 2003]. 6.2.2.2 Model <strong>of</strong> Owens-Wendt : Two Components Theory Owens and Wendt [1969] considered that <strong>the</strong> surface energy is expressed in <strong>the</strong> form: S = γ S d + γ S p (3.18) with γ S d dispersive (or apolar) and γ S p polar (or non-dispersive) components. Following <strong>the</strong> work that Fowkes pioneered in 1962, [Fowkes, 1962] <strong>the</strong> different surface energy <strong>of</strong> solid (γ SV , γ SL and γ LV ) can be split into two components: polar and dispersive fractions. Based on <strong>the</strong> assumption that only <strong>the</strong> same type <strong>of</strong> interaction (polar and/or dispersive) can occur between both phases. Owens and Wendt [1969] proposed <strong>the</strong> following equation: d d 1/ 2 p p 1/ 2 12 1 2 2[( 1 . 2 ) ( 1 . 2 ) ] (3.19) - 81 -
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