PhD Oral Exam - Mohammad Reza Daneshvar Garmroodi, Mechanical Engineering

When studying for a doctoral degree (PhD), candidates submit a thesis that provides a critical review of the current state of knowledge of the thesis subject as well as the student’s own contributions to the subject. The distinguishing criterion of doctoral graduate research is a significant and original contribution to knowledge.

Once accepted, the candidate presents the thesis orally. This oral exam is open to the public.

Abstract

Mixing is a common process in many natural and industrial applications, such as food processing, pharmaceuticals, oil extraction, and more. Despite its ubiquity, mixing remains one of the most challenging paradigms in engineering to define, analyze, and understand systematically. In many of these applications, the working fluid exhibits a yield stress behavior.

Traditionally, mixing has been extensively studied under the assumption of homogeneity, i.e., the influence of heterogeneous fluid properties on the development of mixing is neglected. Therefore, empirical relationships are often used to estimate the mixing time and energy consumption. However, heterogeneity can play a crucial role in mixing dynamics, which is not captured by the current empirical relationships. Moreover, the effect of yield stress on mixing has often been examined qualitatively, with studies typically reporting that yield stress leads to mixing localization. Despite these observations, a mechanistic framework to describe the relationship between flow dynamics and mixing development in yield stress fluids remains lacking. In this thesis, we study the flow dynamics and mixing development in yield stress fluids.

To demonstrate the potential impact of heterogeneity on mixing dynamics and efficiency, we explore the homogenization of an additive in a cylindrical tank stirred by a disk. Two cases are considered: in the first (model problem T), both the fluid rheology and density depend on the additive concentration; in the second (model problem M), the additive is passive, meaning that the fluid rheology and density remain independent of the additive. We specifically examine the impact of neglecting buoyancy on mixing and flow dynamics. Our results show that, in model problem T, the mixing rate increases significantly in the presence of small buoyancy forces compared to model problem M. However, as buoyancy becomes large, the mixing rate decreases.

To establish a mechanistic framework linking fluid dynamics and mixing development, we develop a simplified model problem consisting of an infinite two-dimensional domain where a cylindrical stirrer moves along a circular path. First, we analyze the flow dynamics and mixing behavior for a Newtonian fluid at various stirring rates to identify different mixing mechanisms in the absence of a yield stress. We propose four distinct flow regimes based on the flow and mixing development at different stirring rates: (i) no shedding, (ii) weak shedding, (iii) trapped vortices, and (iv) escaped vortices. We further show that mixing is independent of the stirring speed when mixing is confined near the stirrer.

Finally, we explore stirring a Bingham fluid in the same setup to characterize the influence of yield stress and localization mechanisms. We demonstrate that introducing yield stress leads to mixing localization through three distinct mechanisms: (i) escaped shedding, (ii) trapped shedding, and (iii) suppressed shedding. We propose a classification of mixing regimes based on the identified localization mechanisms. We show that these regimes can be distinguished using spectral analysis of kinetic energy oscillations, revealing critical transition criteria.