Multi-scale modeling of particulate systems by incorporating particle roughness

Nyah Victoria Zarate, Purdue University

Abstract

This thesis investigates multi-scale modeling approaches for particulate systems by incorporating particle roughness as it relates to particle adhesion. Particle adhesion plays a fundamental role in many industrial processes, such as granulation and transport of powders. Regardless of the application, there is a general need to control and understand the interactions at the particle-substrate and particle-particle interfaces at micro- to nano-meter scales in order to predict powder behavior and increase efficiency during the industrial processes of solids. In this thesis, a random rough surface model has been developed and experimentally validated for adhesion force calculation of particles-surfaces interactions. The model is able to represent particle-surface interactions accurately and with greater robustness by accounting for surface roughness. In this work, the surface model is based on two main assumptions; first, the height distribution of the surface profile is Gaussian in nature; and second, the autocorrelation function of the surface can be fitted with a linear function. A single line scan of the roughness profile data is used to generate a randomly rough surface. The Randomly Rough Surface (RRS) model is validated by comparison with AFM colloidal probe measurements of roughness of the surfaces of eight different colloidal particles (fused silica spheres, aluminum oxide, aluminum oxide coated with nano-scale hydrophilic spheroidal silica aluminum oxide coated with nano-scale hydrophobic spheroidal silica spheres and silicon nitride AFM probe) and two surfaces (unpolished and polished silicon). The RRS model is then incorporated into the Simulated-Particle Adhesion (SPA) model to compute adhesion force distributions. SPA predicted distributions are compared to the adhesion force distribution obtained by colloidal probe AFM for all particle-surface combinations. The two distributions were compared by using mean adhesion force data, where the model had a maximum error of 22% compared to the experimental measurements. In all cases, the adhesion force spectrum encompassed the entire experimental adhesion force distributions. In most case, however, the range of the predicted adhesion distribution was larger than in the experimental case. This is attributed to the model including extreme configurations which have a very low probability of occurrence. The mean adhesion forces produced using the RRS model and prior Beaudoin group Gold Standard (GS) models were compared with the experimental results. The errors between GS model and experimental results were 4-8% and the errors between the RRS model and experimental were 10-22%. It can be seen that the error when using the GS model was lower than the RRS model. This difference can be attributed to the fact that the GS model uses multiple surface scanned data to describe the interacting surface roughness. However, in the RRS, only a single line scan is used to generate the surface. Therefore, there is an obvious tradeoff between using the two models. The GS model can provide relatively better surface representation when compared to the RRS model. However, the time, equipment and labor needed to gather the appropriate data is dramatically increased. A sensitivity analysis of the RRS model was performed using several different particle radii, particle roughness and surface roughness with constant auto correlation length. Results showed that using a random rough surface with Gaussian height distribution produced a log-normal adhesion force distribution. In addition, the peak curvature probability distribution of the asperities on the surface also followed a log-normal distribution. Hence, another unique contribution of this work is that the peak-curvature distribution of random rough surfaces explains the log-normal adhesion force distributions observed in this study and in the literature. This is the first study to relate statistical functions of surface roughness to an in-depth examination of particle adhesion force distributions for elastic micron-sized randomly rough particulate systems. The results have significant impact on multi-scale modeling approaches, emphasizing the effect of particle surface topography on adhesion force can impact the assembly of particles, and showing it is not sufficient to model particles as ideal spheres with single point adhesion forces. Using simple statistical functions to describe the effect of roughness on adhesion can open up the possibility of including such details in macroscopic particle assembly models.

Degree

Ph.D.

Advisors

Beaudoin, Purdue University.

Subject Area

Chemical engineering

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