A close examination of table three in [31] and table four in [38] reveals that the ASK inhibitor agreement between experiment and theory in our case is reasonable considering the complexity of the solution. Figure 7 Dynamic contact angle of TiO 2 -DI water nanofluid, comparison of experiment and theory. Table 2 Coefficient of contact line friction ζ , theoretical equilibrium
contact angle , and error of comparison Staurosporine in vivo between theory and experiment Nanoparticle concentration ζ[Pa·s] Error 2% 32 52.1 1.1 1% 99 48.2 1 0.5% 464 46.4 0.65 0.1% 483 45.3 0.54 0.05% 486 44.8 0.34 Table 2 shows values of ζ for various nanoparticle volume concentrations. From solution concentration of 0.05% to 0.5% ζ only changes by 5%; however, it drops rapidly for denser
solutions. It is possible that the relative higher hydrophobicity at the three-phase contact line for denser solutions lowers the affinity JAK inhibitor of surface molecules to water molecules, thereby lowering the friction. At dense concentrations, the presence of large amount of nanoparticles in the wedge film varies the flow field structure. Without nanoparticles, it has been stated that there are two flow patterns in the wedge film: rolling and lubricating patterns [5]. Nanoparticles in the wedge film can change these flow patterns and result in more complex flow structures. As a result of these interparticle interactions, dissipation is more pronounced in the wedge film. Equation 19 gives better results at lower nanoparticle concentrations next since complex interparticle interactions are less frequent in dilute
solutions (see Table 2). Other sources of disagreement between experiment and theory can be local variations in the concentration of the nanoparticles in the nanofluid [21], pinning of the contact line, and variations in solid–liquid interfacial tension (σ sl) [18, 21]. It is not possible to model all these effects in theory, and only simple models which can accommodate some of these effects can be developed. Also shown in Table 2 are the theoretical equilibrium contact angles, , which are in reasonable agreement with the experimental equilibrium contact angles, (see Table 1). Conclusions Due to a wide range of industrial applications, studying capillary flow of liquids laden with metallic and metal oxide nanoparticles is important. Metal oxide TiO2 nanoparticles are especially interesting in enhanced heat removal applications. Agglomeration of nanoparticles results in clusters that have larger effective diameter than the actual particle size. These clusters can deposit on the surface of solid substrates and form a heterogeneous surface condition inside the droplet away from the three-phase contact line that increases the equilibrium contact angle.