Scholarly Contributions
http://hdl.handle.net/1974/16003
This community includes Queenâ€™s peer-reviewed research publications, including journal articles, book chapters, conference proceedings, and more.2019-03-21T16:17:11ZPower Series for Normal Stress Differences of Polymeric Liquids in Large-Amplitude Oscillator Shear Flow
http://hdl.handle.net/1974/26041
Power Series for Normal Stress Differences of Polymeric Liquids in Large-Amplitude Oscillator Shear Flow
Poungthong, P.; Giacomin, A. Jeffrey; Saengow, Chaimongkol; Kolitawong, Chanyut
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 of a polymeric liquid, the corotational Maxwell fluid in LAOS, Bessel functions appear 38 times in the exact solution. By relevant, we mean that higher harmonics are predicted in LAOS. By contrast, approximate analytical solutions for normal stress differences in LAOS often take the form of the first few terms of a power series in the shear rate amplitude, and without any Bessel functions at all. Perhaps the best example of this, from continuum theory, is the Goddard integral expansion (GIE) that is arrived at laboriously. There is thus practical interest in extending the GIE, to an arbitrary number of terms. However, each term in the GIE requires much more work than its predecessor. For the corotational Maxwell fluid, for instance, the GIE for the normal stress differences has yet to be taken beyond the fifth power of the shear rate amplitude. In this paper, we begin with the exact solution for normal stress difference responses in corotational Maxwell fluids, and then perform an expansion by symbolic computation to confirm up to the fifth power, and to then continue the GIE. In this paper for example, we continue the GIE to the 41st power of the shear rate amplitude. We use Ewoldt grids to show our main result to be highly accurate. We also show, except in its zero-frequency limit, the radius of convergence of the GIE to be infinite. We derive the pattern for the common denominators of the GIE coefficients, and also for every numerator for the zeroth harmonic coefficients. We also find that the numerators of the other harmonics appear to be patternless.
2018-04-01T00:00:00ZSeries Expansion for Shear Stress in Large-Amplitude Oscillatory Shear Flow From Oldroyd 8-Constant Framework
http://hdl.handle.net/1974/26040
Series Expansion for Shear Stress in Large-Amplitude Oscillatory Shear Flow From Oldroyd 8-Constant Framework
Poungthong, P.; Giacomin, A. Jeffrey; Saengow, Chaimongkol; Kolitawong, Chanyut
When polymeric liquids undergo large-amplitude 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 which is a nonlinear function of both the frequency and the shear rate amplitude. The Oldroyd 8-constant framework for continuum constitutive theory contains a rich diversity of popular special cases for polymeric liquids. The shear stress response for the Oldroyd 8-constant framework has recently yielded to exact analytical solution. However, in its closed form, Bessel functions appear 24 times, each within summations to infinity. In this paper, to simplify the exact solution, we expand it in a Taylor series of the dimensionless shear rate amplitude. We truncate the power series expansion after the 16th power of the shear rate amplitude. We find our main result reduces to the well-known expression for the special cases of the corotational Jeffreys and corotational Maxwell fluids. Whereas these special cases yielded to the Goddard integral expansion (GIE), the more general Oldroyd 8-constant framework does not. We use Ewoldt grids to show our main result to be highly accurate, for the corotational Jeffreys and corotational Maxwell fluids. Our solutions agree closely with the exact solutions so long as Wi/De < 7/2 , for the special cases of the corotational Jeffreys and corotational Maxwell fluids. We apply our main result for the special case of the Johnson-Segalman fluid, to describe the measured frequency sweep and shear rate amplitude sweep responses of molten atactic polystyrene. For this, we use the Spriggs relations to generalize our main result to multimode, which then agrees closely with the measured responses.
2018-06-01T00:00:00ZExact Coefficients for Rigid Dumbbell Suspensions for Steady Shear Flow Material Function Expansions
http://hdl.handle.net/1974/26039
Exact Coefficients for Rigid Dumbbell Suspensions for Steady Shear Flow Material Function Expansions
Piette, Jourdain H.; Jbara, Layal; Saengow, Chaimongkol; Giacomin, A. Jeffrey
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 equation for the orientation distribution function. From this distribution, we then calculate physical properties such as the steady shear flow material functions. We thus arrive at power series expansions in the shear rate for both the orientation distribution function and for the steady shear flow material functions. Analytical work on many viscoelastic material functions must be checked for consistency, in their steady shear flow limits, against these power series. For instance, for large amplitude oscillatory shear flow, we recover the coefficients of these expansions in the limits of low test frequency. The coefficients of the steady shear viscosity and the first normal stress coefficient functions are not known exactly beyond the fourth power. In this work, for both of these functions, we arrive at exact expressions for the first 20 coefficients. We close with five worked examples illustrating uses for our new coefficients.
2008-07-01T00:00:00ZDegradation in Parallel-Disk Rheometry
http://hdl.handle.net/1974/26038
Degradation in Parallel-Disk Rheometry
Giacomin, A. Jeffrey; Pasquino, R.; Saengow, Chaimongkol; Gilbert, Peter H.
We analyze quantitatively the oxidative degradation of a sample in a parallel-disk rheometer, as oxygen diffuses inward, radially, from the free boundary. We examine rheometer error mitigation by means of nitrogen blanketing, and also, of parallel-disk partitioning. We arrive at exact analytical expressions for the oxygen concentration, and thus, for the degradation rate. We then integrate this rate over time to get the amount of oxygen reacted as a function of radial position and time in the degrading sample. To illustrate the usefulness of our analytical expressions, we provide two worked examples investigating the effect of nitrogen blanketing and parallel-disk partitioning. We find that, though nitrogen blanketing always produces less degradation, its benefits are limited for short times. Additionally, parallel-disk partitioning provides a simpler solution and allows samples to be run for longer times without degradation compromising measurement, even in samples initially saturated with oxygen. We also consider the effect of antioxidants. We also consider an important special case, without chemical reaction, where the sample dries by evaporation from its free surface. We close by comparing the roles played by polymer degradation in parallel-disk flow versus cone-plate flow.
2018-08-01T00:00:00Z