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We study the variation of the adhesion forces between wet TiO2 nanoparticles as a function of their size and the ambient relative humidity. Combining all-atom molecular dynamics and capillary simulations we demonstrate that the linear scaling of the interparticle forces with the particle diameter, well established for microscopic and macroscopic particles, can be extended down to diameters of a few nm. At this size scale, however, the molecular nature of the water adsorbates dictates the adhesion forces both via solvation effects and influencing parameters of analytical capillary models such as the equilibrium particle–particle separation distance and the water/particle contact angle. Moreover, the water surface tension becomes considerably larger than the macroscopic bulk value due to combined effects of thin-film confinement and tight curvature, in a way that strongly depends on humidity and particle size. Taking these effects into proper account, classical capillary equations can be used to predict the...

Capillary forces are very important considering the handling of powders as they, in general, exceed other adhesion forces. These capillary forces are dependent on several different parameters. Especially the distance between the particles is an important parameter. For example, in moving bulk solids a large variety of distances between particles will occur. Therefore, the distance-dependence of capillary bridges was investigated with a numerical simulation method, assuming thermodynamic equilibrium which is attained very fast for small particles. This method uses the Kelvin equation and the Young-Laplace equation to calculate numerically the shape of the capillary bridge without any assumption regarding the shape. The force is eventually derived from the meniscus shape. The distance becomes extremely important when the capillary liquid bridge between two surfaces is only determined by capillary condensation depending on relative humidity. Only a slight increase of the distance within the fraction of a nanometer changes the behaviour of the capillary force significantly. Furthermore, the influence of the force on the separation of particles will be presented. The force decreases almost linearly with increasing distance for a wide range of distances and consequently, a contact stiffness for capillary bridges could be derived. These results may e.g. be used in DEM models. Also, the maximum separation distance of capillary bridges in thermodynamic equilibrium and the correlation with the according bridge volume was investigated. As two limiting cases for capillary bridges at varying distances one can assume either a constant curvature, i.e. infinitely fast attainment of equilibrium, or a constant volume, i.e. infinitely slow attainment of equilibrium. Therefore, a comparison of these two possibilities will be presented and discussed as well.

Since, in the presence of humidity the inter-particle processes are dominated by capillary forces, a fundamental understanding of the water adsorption and the capillary bridge formation is very important. However, the adsorbed water structure and thus the capillary bridge formation is influenced by various parameters like the particle morphology (e.g. particle size, roughness) as well as the surface chemistry (surface energy, adsorbate structure) and therefore needs to be analyzed on a submicroscopic or even molecular basis. A multi-scale approach ranging from experiments on an individual particle level (AFM and liquid bridge simulation) and investigations on small particle ensembles (combined QCM-D/FTIR) up to macroscopic description of bulk behavior is presented in this chapter. In this context, the combined in situ QCM-D/FTIR experiments are bridging the gap between experiments on an individual particle level and macroscopic bulk behavior. Variation of surface chemistry by means of adsorption of functional organic molecules allows for the correlation of macroscopic particle behavior to nanoscopic effects like the presence and structure of adsorbate layers as well as the formation of capillary bridges while keeping the disperse properties constant. Besides extensive experimental work, simulations of capillary bridges formed by condensation from humid air are presented. It is clearly shown that well known approximations which have been introduced for micron-sized particles are not valid any more for nano-scaled particles. The forces between nanoparticles by static liquid bridges and their dependency on particle size, contact angle, humidity and interparticle distance are discussed in detail. Furthermore, capillary forces during separation of particles are studied thoroughly and a constitutive law based on a contact stiffness allows the transfer to DEM simulations of wet powders. Finally, it is demonstrated by comparison to Molecular Dynamics simulations, that the used continuum approach to simulate capillary bridges might even be used down to particle sizes of a few nanometers, if some additional effects are considered correctly.

Capillary forces between particles often dominate other adhesion forces. However, the calculation of the shape of capillary bridges and the resulting force is complex, so often assumptions and approximations are used. These assumptions are not useful for nanoscale particles. Therefore, a simulation method was established to calculate numerically the shape of the meniscus and derive the corresponding capillary bridge force. The main focus are nanoscaled particles with liquid bridges formed by condensing air humidity. The dependence of the capillary force on various parameters such as particle sizes, contact angle and humidity was investigated and it is demonstrated that often-used assumptions cannot be used for nanoscaled particles without remarkable mistake.

Capillary forces are very important as they exceed in general other adhesion forces. But at the same time the exact calculation of these forces is very complex, so often assumptions and approximations are used. Previous research was done with regard to micrometer sized particles, but the behavior of nanoscale particles is different. Hence, the results for micrometer sized particles cannot be directly transferred when considering nanoscale particles. Therefore, a simulation method was developed to calculate numerically the shape of a rotationally symmetrical capillary bridge between two spherical particles or a particle and a plate. The capillary bridge in the gap between the particles is formed due to capillary condensation and is in thermodynamic equilibrium with the gas phase. Hence the Kelvin equation and the Young-Laplace equation can be used to calculate the profile of the capillary bridge, depending on the relative humidity of the surrounding air. The bridge profile consists of several elements that are determined consecutively and interpolated linearly. After the shape is determined, the volume and force, divided into capillary pressure force and surface tension force, can be calculated. The validation of this numerical model will be shown by comparison with several different analytical calculations for micrometer-sized particles. Furthermore, it is demonstrated that two often used approximations, (1) the toroidal approximation and (2) the use of an effective radius, cannot be used for nanoscale particles without remarkable mistake. It will be discussed how the capillary force and its components depend on different parameters, like particle size, relative humidity, contact angle, and distance, respectively. The rupture of a capillary bridge due to particle separation will also be presented.