Recent experiments on the foamability of liquid particle suspensions (with a particle size varying from nanometers to micrometers in diameter and in the absence of any surfactants) have shown that the foamability correlates well with the degree of particle coverage at the air-liquid surface. Furthermore, these experiments have also revealed foam inhibition due to the aggregation or clustering of particles in the bulk at high particle concentrations. The present study is aimed at theoretically modeling the observed phenomena. Theoretical analyses based on Monte Carlo simulations and the integral equations of statistical mechanics are used to model the particle aggregation phenomena in the bulk. The radial distribution functions, which show the particle packing density, are analyzed to obtain the effective energy of interaction between the particles. The maximum in foaminess due to the adsorption of particles on the air-liquid surface and clustering of particles in the bulk is explained. The modeling results are in good agreement with the experimental observations on foaminess with small particles.