Rheological properties, stochastic characteristics, and second law violations of atomic fluids in Couette flow

Fluids treated as a discrete collection of particles rather than as a continuum, exhibit exotic properties under shear at sub-continuum scales. For instance, at a critical strain-rate, the fluid becomes non-Newtonian owing to an ordering transition and the thermodynamic entropy production can be negative on small length and time scales due to the probabilistic nature of the system observables. Therefore, a complete characterization and study of fluid behavior is accomplished through the interplay between statistical and continuum mechanics. Molecular dynamics (MD) is naturally suited to provide insight into the behavior of such systems. It has been widely used to probe the behavior of a wide variety of systems on very small length and time scales. This research focuses on understanding the rheological nature, in particular, shear-thinning of atomic fluids to obtain a general constitutive relationship between shear-stress and strain-rate. We studied the statistical characteristics of the fluid properties to gain insight into the structural features that result in non-Newtonian behavior, the system’s tendency to violate the second law of thermodynamics, and the latter’s consequences for continuum theories. Using non-equilibrium molecular dynamics (NEMD) simulations, we study the shear-stress under steady-state conditions and its dependency on fluid properties (temperature and density) and applied shear-strain rate. The term strain-rate, more common in the physics literature, is used here in place of deformation rate. We propose a rheological equation of state that fits observed system responses exceptionally well and captures the extreme shear-thinning effect. This model arises naturally from the Boltzmann equation and kinetic theory and gives rise to a viscosity model similar to the well-established Cross model, but absent empirical parameters. The model possesses an inherent scaling parameter that unifies the rheological properties of the Lennard-Jones (LJ) fluid. Additionally, the probabilistic nature of the shear stress and the system’s tendency to violate the second law of thermodynamics is investigated by observing negative shear-stress increments. We draw conclusions on the implications these phenomena have on continuum theories adapted to atomic fluids such as flow stability. Building on these models, we aim to understand the transitions to turbulence and flow instability in atomic fluids. Via the Poincaré inequality, we generalize a classical continuum methodology to atomic fluids and obtain a fluid dependent lower bound on the critical Reynolds number.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Theoretical & Applied Mechanics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2021

Author dc:creator

• Raghavan, Bharath Venkatesh

Contributors dc:contributor

• Ostoja-Starzewski, Martin
• Schleife, Andre
• Patricio Chamorro Chavez, Leonardo
• Liebenberg, Leon

• rheology
• molecular dynamics
• stochastic
• shear-thinning
• second law of thermodynamics
• fluid dynamics
• fluid mechanics

Statement dc:rights

• Copyright 2020 Bharath Venkatesh Raghavan

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/109348

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/109348