Chemical Engineering, Department of
http://hdl.handle.net/1974/769
2017-11-20T02:25:16ZExact-solution for Cone-plate Viscometry
http://hdl.handle.net/1974/23652
Exact-solution for Cone-plate Viscometry
Giacomin, A. Jeffrey; Gilbert, Peter H.
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 cone-plate viscometry. When the cone angle approaches π /2 , the viscometer gap is called narrow. The shear stress in the fluid, throughout a narrow gap, hardly departs from the shear stress exerted on the plate, and we thus call cone-plate flow nearly homogeneous. In this paper, we derive an exact solution for this slight heterogeneity, and from this we derive the correction factors for the shear rate on the cone and plate, for the torque, and thus, for the measured Newtonian viscosity. These factors thus allow the cone-plate viscometer to be used more accurately, and with cone-angles well below π /2 . We find cone-plate flow field heterogeneity to be far slighter than previously thought. We next use our exact solution for the velocity to arrive at the exact solution for the temperature rise, due to viscous dissipation, in cone-plate flow subject to isothermal boundaries. Since Newtonian viscosity is a strong function of temperature, we expect our new exact solution for the temperature rise be useful to those measuring Newtonian viscosity, and especially so, to those using wide gaps. We include two worked examples to teach practitioners how to use our main results.
2017-08-01T00:00:00ZFluid Elasticity in Plastic Pipe Extrusion: Loads on Die Barrel
http://hdl.handle.net/1974/23651
Fluid Elasticity in Plastic Pipe Extrusion: Loads on Die Barrel
Saengow, Chaimongkol; Giacomin, A. Jeffrey
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 for sag, engineers normally shift the die centerpiece downward. This paper focuses on how this decentering triggers unintended consequences for elastic polymer melts. We employ eccentric cylindrical coordinates, to capture exactly the geometry of our problem, the flow between eccentric cylinders. Specifically, we arrive at an exact analytical expression for the axial and lateral forces on the die barrel using the polymer process partitioning approach, designed for elastic liquids. We choose the Oldroyd 8-constant framework due to its rich diversity of constitutive special cases. Since our main results are in a form of simple algebraic expression along with two sets of curves, they can thus be used not only by engineers, but any practitioner. We close our paper with detailed dimensional worked examples to help practitioners with their pipe die designs.
2017-07-01T00:00:00ZElastomers in Large-Amplitude Oscillatory Uniaxial Extension Revisited
http://hdl.handle.net/1974/23017
Elastomers in Large-Amplitude Oscillatory Uniaxial Extension Revisited
Dessi, Claudia; Vlassopoulos, Dimitris; Giacomin, A. Jeffrey; Saengow, Chaimongkol
In this work, we subject elastomers to a fixed pre-stretch in uniaxial extension, ε p , upon which a large-amplitude, ε 0 , oscillatory uniaxial extensional (LAOE) deformation is superposed. We find that if both ε p and ε 0 are large enough, the stress responds with a rich set of higher harmonics, both even and odd. We further find the Lissajous-Bowditch plots of our measured stress responses versus uniaxial strain to be without two-fold symmetry, and specifically, to be shaped like convex bananas. Our new continuum model for this behavior combines a new nonlinear spring, in parallel with a Newtonian dashpot, and we call this the Voigt model with strain-hardening. We consider this three-parameter (Young’s modulus, viscosity and strain-hardening coefficient) model to be the simplest relevant one for the observed convex bananas. We fit the parameters to our both LAOE measurements, and then to our uniaxial elongation measurements at constant extension rate. We develop analytical expressions for the Fourier components of the stress response, parts both in-phase and out-of-phase with the extensional strain, for the zeroth, first, second and third harmonics. We find that the part of the second harmonic that is out-of-phase with the strain must be negative for proper banana convexity.
2017-07-01T00:00:00ZElastomers in Oscillatory Uniaxial Extension
http://hdl.handle.net/1974/23016
Elastomers in Oscillatory Uniaxial Extension
Dessi, Claudia; Vlassopoulos, Dimitris; Giacomin, A. Jeffrey; Saengow, Chaimongkol
In this work, we subject elastomers to a fixed pre-stretch in uniaxial extension, ε p , upon which a large-amplitude, ε 0 , oscillatory uniaxial extensional (LAOE) deformation is superposed. We find that if both ε p and ε 0 are large enough, the stress responds with a rich set of higher harmonics, both even and odd. We further find the Lissajous-Bowditch plots of our measured stress responses versus uniaxial strain to be without two-fold symmetry, and specifically, to be shaped like convex bananas. Our new continuum uniaxial model for this behavior combines a new nonlinear spring, in parallel with a Newtonian dashpot, and we call this the Voigt model with strain-hardening. We consider this three-parameter (Young’s modulus, viscosity and strain-hardening coefficient) model to be the simplest relevant one for the observed convex bananas. We fit the parameters to our both uniaxial elongation measurements at constant extension rate, and then to our LAOE measurements. We develop analytical expressions for the Fourier components of the stress response, parts both in-phase and out-of-phase with the extensional strain, for the zeroth, first, second and third harmonics. We find that the part of the second harmonic that is out-of-phase with the strain must be negative for proper banana convexity.
2016-02-01T00:00:00Z