Polymers Research Group Technical Report Series
http://hdl.handle.net/1974/8680
2019-06-26T10:16:13ZStartup Steady Shear Flow from the Oldroyd 8-Constant Framework
http://hdl.handle.net/1974/26303
Startup Steady Shear Flow from the Oldroyd 8-Constant Framework
Saengow, Chaimongkol; Giacomin, A. Jeffrey; Grizutti, Nino; Pasquino, R.
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 enough, the shear stress and also the normal stress differences can, overshoot, and then, they can even undershoot. We call such responses nonlinear, and this experiment shear stress growth. This paper is devoted to providing exact analytical solutions for interpreting measured nonlinear shear stress growth responses. Specifically, we arrive at the exact solutions for the Oldroyd 8-constant constitutive framework. We test our exact solution against the measured behaviours of two wormlike micellar solutions. At high shear rates, these solutions overshoot in stress growth without subsequent undershoot. The micellar solutions present linear behavior at low shear rate, and otherwise, nonlinear. Our framework provides slightly early underpredictions of the overshoots at high shear rate. The effect of salt concentration on the nonlinear parameters is explored.
2019-01-01T00:00:00ZHydrodynamic Interaction for Rigid Dumbbell Suspensions in Steady Shear Flow
http://hdl.handle.net/1974/26273
Hydrodynamic Interaction for Rigid Dumbbell Suspensions in Steady Shear Flow
Piette, Jourdain H.; Saengow, Chaimongkol; Giacomin, A. Jeffrey
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 suspension of rigid dumbbells, subject to any shear flow, for instance, we must first solve the diffusion equation for the orientation distribution function. From this distribution, we then calculate the first and second normal stress differences. To get reasonable results for the normal stress differences in steady shear flow, one must account for hydrodynamic interaction between the dumbbell beads. However, for the power series expansions for these normal stress differences, three series arise. The coefficients for two of these series, (ck,dk), are not known, not even approximately, beyond the second power of the shear rate. Analytical work on many viscoelastic material functions in shear flow must be checked for consistency, in their steady shear flow limits, against these normal stress differences power series expansions. For instance, for large-amplitude oscillatory shear flow (LAOS), we must recover the power series expansions in the limits of low frequency. In this work, for (ck,dk), we arrive at exact expressions for the first 18 coefficients.
2018-12-01T00:00:00ZMacromolecular Tumbling and Wobbling in Large-Amplitude Oscillatory Shear Flow
http://hdl.handle.net/1974/26088
Macromolecular Tumbling and Wobbling in Large-Amplitude Oscillatory Shear Flow
Jbara, Layal M.; Giacomin, A. Jeffrey
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, we focus specifically on large-amplitude oscillatory shear flow (LAOS), for which we extend the orientation distribution function to the 6th power of the shear rate amplitude. We arrive at the Fourier solution for each harmonic contribution to the total orientation distribution function, separating each harmonic into its coefficients in and out-of-phase with cosnωt , ψ ′n and ψ ′′ n , respectively. We plot, for the first time, the evolving normalized alternant macromolecular orientation. Moreover, to deepen our understanding of the macromolecular motions, we distinguish and study the two types of possible rotations, tumbling and wobbling.
2018-11-01T00:00:00ZOrder in Oscillatory Shear Flow
http://hdl.handle.net/1974/26087
Order in Oscillatory Shear Flow
Kanso, Mona A.; Giacomin, A. Jeffrey; Saengow, Chaimongkol; Gilbert, Peter H.
We examine the second order orientation tensor for the simplest molecular model relevant to a polymeric liquid in large-amplitude oscillatory shear flow (LAOS), the rigid dumbbell suspension. For this we use an approximate solution to the diffusion equation for rigid dumbbells, an expansion for the orientation distribution function truncated after the fourth power of the shear rate amplitude. We then calculate the second order orientation tensor, and then use this to calculate the order parameter tensor. We next examine the invariants of both the second order orientation tensor and the order parameter tensor. From the second invariant of the order parameter tensor, we calculate the scalar, the nematic order, and examine its evolution for a polymeric liquid in LAOS. We find this nematic order, our main result, to be even. We use Lissajous figures to illustrate the roles of the Weissenberg and Deborah numbers on the evolving order in LAOS. We use the low frequency limit of our main result to arrive at an expression for the nematic order in steady shear flow. Our work gives a first glimpse into macromolecular order in LAOS. Our work also provides analytical benchmarks for numerical solutions to the diffusion equation for both oscillatory and steady shear flows.
2018-12-01T00:00:00Z