Polymers Research Group Technical Report Series
This series includes technical reports prepared by faculty, students and staff who are affiliated with the Polymers Research Group in the Department of Chemical Engineering at Queen’s University. These reports are intended to furnish rapid communication to persons who have an active interest in the subject matter and to stimulate comment, including corrections of possible errors.
Recent Submissions

Startup Steady Shear Flow from the Oldroyd 8Constant Framework
(201901)One good way to explore fluid microstructure, experimentally, is to suddenly subject the fluid to a large steady shearing deformation, and to then observe the evolving stress response. If the steady shear rate is high ... 
Hydrodynamic Interaction for Rigid Dumbbell Suspensions in Steady Shear Flow
(201812)From kinetic molecular theory, we can attribute the rheological behaviors of polymeric liquids to macromolecular orientation. The simplest model to capture the orientation of macromolecules is the rigid dumbbell. For a ... 
Molecular Continua for Polymeric Liquids in LargeAmplitude Oscillatory Shear Flow
(201705)In this paper, we connect a molecular description of the rheology of a polymeric liquid to a continuum description, and then test this connection for largeamplitude oscillatory shear flow (LAOS). Specifically, for the ... 
Simple Accurate Expressions for Shear Stress in LargeAmplitude Oscillatory Shear Flow
(201705)Analytical solutions for shear stress in largeamplitude oscillatory shear flow (LAOS), for continuum or molecular models, often take the form of the first few terms of a power series in the shear rate amplitude. For ... 
Padé Approximant for Normal Stress Differences in LargeAmplitude Oscillatory Shear Flow
(201711)Analytical solutions for the normal stress differences in largeamplitude oscillatory shear flow (LAOS), for continuum or molecular models, normally take the form of the first few terms of a series expansion in the shear ... 
Nonlinear Core Deflection in Injection Molding
(201802)Injection molding of thin slender parts is often complicated by core deflection. This deflection is caused by molten plastics race tracking through the slit between the core and the rigid cavity wall. The pressure of this ... 
Ethermodynamic Instability of Polymeric Liquids in LargeAmplitude Oscillatory Shear Flow from Corotational Maxwell Fluid
(201804)When polymeric liquids are subjected to oscillatory shear flow, if the amplitude of the shear rate is high enough, the shear stress response will become aperiodic. This has been variously attributed to fracture, common ... 
Power Series for Shear Stress of Polymeric Liquid in LargeAmplitude Oscillatory Shear Flow
(201804)xact solutions for shear stress in a polymeric liquid subjected to largeamplitude oscillatory shear flow (LAOS) contain many Bessel functions. For the simplest of these, for instance, the corotational Maxwell fluid, in ... 
Macromolecular Tumbling and Wobbling in LargeAmplitude Oscillatory Shear Flow
(201811)For a suspension of rigid dumbbells, in any simple shear flow, we recently solved for the diffusion equation for the orientation distribution function by a power series expansion in the shear rate magnitude. In this paper, ... 
Order in Oscillatory Shear Flow
(201812)We examine the second order orientation tensor for the simplest molecular model relevant to a polymeric liquid in largeamplitude oscillatory shear flow (LAOS), the rigid dumbbell suspension. For this we use an approximate ... 
Exact Analytical Interconversion between Durometer Hardness Scales
(201702)Previous work has related Young’s modulus to durometer hardness for any standardized scale. In this paper, we build on this work to solve explicitly and exactly for the hardness in any one standardized durometer hardness ... 
Power Series for Normal Stress Differences of Polymeric Liquids in LargeAmplitude Oscillator Shear Flow
(201804)Exact solutions for normal stress differences in polymeric liquids subjected to largeamplitude oscillatory shear flow (LAOS) contain many Bessel functions, each appearing in infinite sums. For the simplest relevant model ... 
Series Expansion for Shear Stress in LargeAmplitude Oscillatory Shear Flow From Oldroyd 8Constant Framework
(201806)When polymeric liquids undergo largeamplitude oscillatory shear flow (LAOS), the shear stress responds as a Fourier series, the higher harmonics of which are caused by the fluid nonlinearity, and the first harmonic of ... 
Exact Coefficients for Rigid Dumbbell Suspensions for Steady Shear Flow Material Function Expansions
(200807)From kinetic molecular theory, we can attribute the elasticity of polymeric liquids to macromolecular orientation. For a suspension of rigid dumbbells, subject to a particular flow field, we must first solve the diffusion ... 
Degradation in ParallelDisk Rheometry
(201808)We analyze quantitatively the oxidative degradation of a sample in a paralleldisk rheometer, as oxygen diffuses inward, radially, from the free boundary. We examine rheometer error mitigation by means of nitrogen blanketing, ... 
Orientation Distribution Function Pattern for Rigid Dumbell Suspensions In Any Simply Shear Flow
(201809)For rigid dumbbells suspended in a Newtonian solvent, the viscoelastic response depends exclusively on the dynamics of dumbbell orientation. The orientation distribution function ψ (θ ,φ ,t) represents the probability of ... 
Polymer Orientation Contributions in LargeAmplitude Oscillatory Shear Flow
(201701)Previously, we used a dilute suspension of rigid dumbbells as a model for the dynamics for polymeric liquids in largeamplitude oscillatory shear (LAOS) flow. We then use dumbbell orientation to explain fluid elasticity. ... 
Review of Nonlinear Oscillatory Shear Flow Notations and Presentations: Polymeric Liquids
(201812)We review notations for, along with ways of presenting, the shear stress responses to largeamplitude oscillatory shear flow (LAOS). We find that the Fourier loss and storage viscosities to be the simplest primal notations ... 
Degradation in ConePlate Rheometry
(201807)We analyze quantitatively the oxidative degradation of a sample in a coneplate rheometer, as oxygen diffuses inward, radially, from the free boundary. We examine rheometer error mitigation by means of nitrogen blanketing, ... 
Exact Solutions for Oscillatory Shear Sweep Behaviors of Complex Fluids from the Oldroyd 8constant Framework
(201705)Largeamplitude oscillatory shear flow (LAOS) is a popular for studying the nonlinear physics of complex fluids. Specifically, the strain rate sweep (also called the strain sweep) is used routinely to identify the onset ...