A study on the nonlinear stress of complex fluids under large amplitude oscillatoy shear (LAOS) flow in the perspective of symmetry and energy

Abstract

Large amplitude oscillatory shear (LAOS) test is widely applied to characterize complex fluids. Various analysis methods for LAOS stress in time domain or strain and strain rate domain had been suggested. However, their interpretation or physical meaning was not fully understood. For example, one of the analysis methods, stress decomposition, is under disputes due to the discordance in stress profile and structural characteristics. One of the purposes of this thesis is to explore the proper interpretation of stress decomposition analysis. Stress decomposition is an analysis method that decomposes total oscillatory stress into elastic and viscous stress by using mathematical symmetry of oscillation. In this thesis, stress decomposition is applied to oscillatory stress, which is calculated by Brownian dynamics (BD) simulation for both hard and soft sphere systems. Double peaks, which are experimentally observed only in the elastic stress of hard sphere systems, are observed only in the hard sphere systems in accordance with experiments. To find out the structural origin of double peaks, the structure of the particulate system is analyzed in terms of the softness of the particles and strain amplitude, which determine the presence of double peaks. In hard and soft sphere comparison, there is a significant difference in structure between two systems. However, the structures do not have the one-to-one match with the elastic stresses for hard spheres. The intensive investigation leads to the conclusion that it is necessary to consider the structures and the elastic stress in the whole cycle rather than them at each time step. We also suggest structural characteristics which make double peaks in the simulation. The other purpose of this thesis is to suggest a new method for analyzing oscillatory shear stress. To achieve this goal, the concept of work and stored energy, which has rarely been considered in the past, is adopted. The inner area in the strain-stress Lissajous curve throughout one cycle is known to be related to work or viscous characteristic of the material, and that of the strain rate-stress Lissajous with stored energy or elastic characteristic of the material. These relationships also work on nonlinear stress, and only areas throughout one full cycle are spotlighted until now. However, to precisely analyze the nonlinear stress, it helps to consider work and energy not only throughout a complete cycle but also during the cycle. We trace the work and energy during the oscillation. Firstly, we apply this concept to perfectly elastic solid and purely viscous liquid with different rheological behaviors. They are classified by tracing work and energy variation in the subdivided sections. This concept is also applied to viscoelastic fluid and Bingham fluid. The symmetry of work and energy with respect to flow reversal point disappears in these fluids, which leads to the conclusion that the extent of asymmetry needs to be considered. The oscillatory stress from Brownian dynamics simulation is also analyzed. Work is correlated to rheological property, oscillatory stress, and particle structure in this analysis. By these approaches, the possibility is shown that the systems with different rheological properties can be characterized by work or energy during the cycle. This thesis provides a new insight on the analysis of nonlinear oscillatory shear stress. This study is expected to provide an extendable framework for further understanding of the nonlinear oscillatory shear stress in the perspective of symmetry and energy.