A Quantitative Relationship between the Magnitude of Interparticle Forces and the Hausner Ratio

Interparticle forces (IPFs) significantly affect the performance of gas-solid fluidized beds with Geldart groups A and C powders. Different types of IPFs can be present in a gas-solid fluidized bed, including van der Waals, electrostatic, liquid bridge, and solid bridge or sintering forces. Models have been presented in literature to fundamentally describe and estimate these types of IPFs for micron-sized particles. A critical challenge in applying these models to bulk particulate systems is their dependence on many factors for an adequate estimation of the level of IPFs. These parameters include particle diameter and shape, surface properties, conductivity, Hamaker constant, operating conditions, humidity, etc. The measurement of some parameters in these models, e.g., the curvature of liquid bridge, are hardly possible and others, e.g., the surface roughness for fine irregular-shaped particles, are hardly reliable. Hausner ratio (HR) is defined as the ratio of tapped to loose bulk densities. It has long been employed for a qualitative evaluation of IPFs, i.e., a higher HR is generally translated to a higher degree of cohesivity. However, no equation has been proposed to relate these two quantitatively.

A simple model is presented in this work to describe the variation of the bed voidage and HR with the size of agglomerates for Geldart group C powders. The model suggests that the magnitude of IPFs, i.e., the ratio of IPFs and weight of a particle, is inversely proportional to the fourth power of solid phase fraction of the tapped bed. The proposed equation can quantify the magnitude of resultant IPFs acting on each particle irrespective of the type of IPFs under various conditions, including ambient and elevated operating conditions. The quantified IPFs by the proposed equation for several powders agreed with the results of other experimental approaches for estimating these forces.