Statistical theory of parcticle size distributions in emulsions and suspensions

Abstract

The particle size distributions in emulsions and suspensions are mostly empirical. Here a rigorous statistical theory of the problem is given, leading to the logarithmic-normal distribution for the sizes of the particle. On the simple physical basis that the disruption of the interface and the evolution of the particle sizes during emulsification are random turbulent processes, the log-normal law is derived by considering the process as a Markoff chain. An alternate simpler derivation is also presented. The nature of the simplifying assumption involved in the theory is clearly brought out. Some properties of the log-normal curve are given. The statistical analysis in fitting the log-normal distribution to the experimental data with special reference to the distortion of the fractile diagram and the advantages of a theoretical distribution over an empirical one are discussed in detail with suitable examples.