The characterisation of irregularly-shaped particles A re-consideration of finite-sized, "porous" and "fractal" grains

Context. A porous and/or fractal description can generally be applied where particles have undergone coagulation into aggregates. Aims. To characterise finite-sized, "porous" and "fractal" particles and to understand the possible limitations of these descriptions. Methods. We use simple structure, lattice and network considerations to determine the structural properties of irregular particles. Results. We find that, for finite-sized aggregates, the terms porosity and fractal dimension may be of limited usefulness and show with some critical and limiting assumptions, that "highly-porous" aggregates (porosity greater than or similar to 80%) may not be "constructable". We also investigate their effective cross-sections using a simple "cubic" model. Conclusions. In place of the terms porosity and fractal dimension, for finite-sized aggregates, we propose the readily-determinable quantities of inflation, I (a measure of the solid filling factor and size), and dimensionality, D (a measure of the shape). These terms can be applied to characterise any form of particle, be it an irregular, homogeneous solid or a highly-extended aggregate.