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

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. ... 
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 ... 
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 ... 
Exactsolution for Coneplate Viscometry
(201708)The viscosity of a Newtonian fluid is often measured by confining the fluid to the gap between a rotating cone that is perpendicular to a fixed disk. We call this experiment coneplate viscometry. When the cone angle ... 
Fluid Elasticity in Plastic Pipe Extrusion: Loads on Die Barrel
(201707)In large thick plastic pipe extrusion, the residence in the cooling chamber is long, and the melt inside the pipe sags under its own weight, causing the product to thicken on the bottom (and to thin on the top). To compensate ... 
Elastomers in LargeAmplitude Oscillatory Uniaxial Extension Revisited
(201707)In this work, we subject elastomers to a fixed prestretch in uniaxial extension, ε p , upon which a largeamplitude, ε 0 , oscillatory uniaxial extensional (LAOE) deformation is superposed. We find that if both ε p and ε ... 
Elastomers in Oscillatory Uniaxial Extension
(201602)In this work, we subject elastomers to a fixed prestretch in uniaxial extension, ε p , upon which a largeamplitude, ε 0 , oscillatory uniaxial extensional (LAOE) deformation is superposed. We find that if both ε p and ε ... 
Normal Stress Differences from Oldroyd 8Constant Framework: Exact Analytical Solution for LargeAmplitude Oscillatory Shear Flow
(201703)The Oldroyd 8constant framework for continuum constitutive theory contains a rich diversity of popular special cases for polymeric liquids. In this paper, we use part of our exact solution for shear stress to arrive at ... 
Exact Analytical Solution for LargeAmplitude Oscillatory Shear Flow from Oldroyd 8Constant Framework: Shear Stress
(201701)The Oldroyd 8constant model is a continuum framework containing, as special cases, many important constitutive equations for elastic liquids. When polymeric liquids undergo largeamplitude oscillatory shear flow, the shear ... 
Polymer Processing Partitioning Approach: Extruding Plastic Pipe
(201601)The proposed thesis research aims at deepening our understanding of the flow of polymer melts through eccentric plastic pipe extrusion dies. Specifically, the proposed thesis research will explore how viscoelasticity affects ... 
Knuckle Formation From Melt Elasticity in Plastic Pipe Extrusion
(201607)When plastic pipe is solidified, it proceeds through a long cooling chamber. Inside the chamber, inside the extrudate, the plastic is molten, and this inner surface solidifies last. Sag then happens inside this cooling ... 
Complex Polymer Orientation
(201507)Previously, we explored the dynamics of a dilute suspension of rigid dumbbells as a model for polymeric liquids in largeamplitude oscillatory shear (LAOS) flow. We derived the expression for the polymer orientation ... 
Plastic Pipe Solidification: Exact Solutions in Cylindrical Coordinates
(201512)For polymer melt solidification in plastic pipe extrusion, we perform an energy balance on the pipe extrudate in cylindrical coordinates to arrive at exact solutions for the temperature, and for the solidification rate. ...