Stress Development Due to Capillary Condensation in Powder Compacts: A Two‐Dimensional Model Study

A model experiment is presented to investigate the relationship between the humidity‐dependent liquid distribution and the macroscopic stress in a partially wet powder compact. Therefore, films of monosized spherical particles were cast on silicon substrates. Using environmental SEM the geometry of the liquid necks trapped between particles was imaged as a function of relative humidity. Simultaneously the macroscopic stress in the substrate adhered particle film was measured by capacitive deflection measurement. The experimentally found humidity dependence of the liquid neck size and the macroscopic film stress are compared with model predictions. The circle–circle approximation is used to predict the size of the liquid necks between touching particles as a function of the capillary pressure. Using the modified Kelvin relation between capillary pressure and relative humidity, we consider the effect of an additional solute which may be present in the capillary liquid. The results of the stress measurement are compared with the model predictions for a film of touching particles in hexagonal symmetry. The contribution of the capillary interaction to the adhesion force between neighboring particles is calculated using the integrated Laplace equation. The resulting film stress can be approximated relating this capillary force to an effective cross section per particle. The experimentally found humidity dependence of the liquid neck size is in good agreement with the model predictions for finite solute concentration. The film stress corresponds to the model predictions only for large relative humidities and shows an unexpected increase at small values. As is shown with an atomic force microscope, the real structure of the particle–particle contact area changes during the wet/dry cycle. A solution/reprecipitation process causes surface heterogeneities and solid bridging between the particles. It is claimed that the existence of a finite contact zone between the particles gives rise to the unexpected increase of the stress at small relative humidities.