Fractal approaches to characterize the structure of capillary suspensions using rheology and confocal microscopy

The rheological properties of a particle suspension can be substantially altered by adding a small amount of a secondary fluid that is immiscible with the bulk phase. The drastic change in the strength of these capillary suspensions arises due to the capillary forces, induced by the added liquid, leading to a percolating particle network. Using rheological scaling models, fractal dimensions are deduced from the yield stress and from oscillatory strain amplitude sweep data as function of the solid volume fraction. Exponents obtained using aluminum-oxide-based capillary suspensions, with a preferentially wetting secondary fluid, indicate an increase in the particle gel's fractal dimension with increasing particle size. This may be explained by a corresponding relative reduction in the capillary force compared to other forces. Confocal images using a glass model system show the microstructure to consist of compact particle flocs interconnected by a sparse backbone. Thus, using the rheological models two different fractal dimensionalities are distinguished - a lower network backbone dimension (D = 1.86-2.05) and an intrafloc dimension (D = 2.57-2.74). The latter is higher due to the higher local solid volume fraction inside of the flocs compared to the sparse backbone. Both of these dimensions are compared with values obtained by analysis of spatial particle positions from 3D confocal microscopy images, where dimensions between 2.43 and 2.63 are computed, lying between the two dimension ranges obtained from rheology. The fractal dimensions determined via this method corroborate the increase in structural compactness with increasing particle size.