Department of Mathematics

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Browsing Department of Mathematics by Department "Chemical Engineering"

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    Obtaining reliable transient rheological data on concentrated short fiber suspensions using a rotational rheometer
    Eberle, A. P. R.; Baird, Donald G.; Wapperom, Peter; Velez-Garcia, G. M. (AIP Publishing, 2009-09-01)
    The conventional method for obtaining transient rheological data on short glass fiber-filled polymeric fluids is to use the parallel disk (PP) geometry in a rotational rheometer. Using the PP geometry large transient stress overshoot behavior was observed during the startup of flow measurements on a 30 wt% short glass fiber-filled polybutylene terephthalate. A contributing factor to this behavior is believed to be induced fiber collisions caused by the inhomogeneous velocity field (radial varying velocity gradient). A novel approach was taken in which a "donut" shaped sample was used in a cone-and-plate device (CP-D) to maintain a sufficient gap to fiber length ratio. The magnitude of the first normal stress difference was reduced by 70%, and the time to reach steady state was reduced by 100 strain units. The Lipscomb model coupled with the Folgar-Tucker model for the evolution of fiber orientation was fit to the stress growth behavior measured using both the PP geometry and CP-D resulting in different parameters. In addition, the fitted model parameters were found to depend on the initial fiber orientation. It is believed that the CP-D allows for an accurate determination of the stress growth behavior and eventually will allow one to obtain unambiguous model parameters. (C) 2009 The Society of Rheology. [DOI: 10.1122/1.3177348]
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    Using startup of steady shear flow in a sliding plate rheometer to determine material parameters for the purpose of predicting long fiber orientation
    Ortman, Kevin; Baird, Donald G.; Wapperom, Peter; Whittington, Abby R. (AIP Publishing, 2012-07-01)
    The properties of long glass fiber reinforced parts, such as those manufactured by means of injection molding and compression molding, are highly dependent on the fiber orientation generated during processing. A sliding plate rheometer was used to understand the transient stress and orientation development of concentrated long glass fibers during the startup of steady shear flow. An orientation model and stress tensor combination, based on semiflexible fibers, was assessed in its ability to predict fiber orientation when using model parameters obtained from the fits of the stress responses. Specifically, samples of different initial fiber orientations was subjected to the startup of steady shear flow, and an orientation model based on bead and rod theory was coupled with a derived stress tensor that accounts for the semiflexibility of the fibers to obtain the corresponding model parameters. The results showed the semiflexible orientation model and stress tensor combination, overall, provided improved rheological results as compared to the Folgar-Tucker model when coupled with the stress tensor of Lipscomb et al. [J. Non-Newtonian Fluid Mech. 26, 297-325 (1988)]. Furthermore, it was found that both stress tensors required empirical modification to accurately fit the measured data. Finally, orientation models provided encouraging results when predicting the transient fiber orientation for all initial fiber orientations explored. (C) 2012 The Society of Rheology. [http://dx.doi.org/10.1122/1.4717496]
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    Using transient shear rheology to determine material parameters in fiber suspension theory
    Eberle, A. P. R.; Baird, Donald G.; Wapperom, Peter; Velez-Garcia, G. M. (AIP Publishing, 2009-05-01)
    Fiber suspension theory model parameters for use in the simulation of fiber orientation in complex flows are, in general, either calculated from theory or fit to experimentally determined fiber orientation generated in processing flows. Transient stress growth measurements in startup of shear flow and flow reversal in the shear rate range, (gamma)over dot = 1-10 s(-1), were performed on a commercially available short glass fiber-filled polybutylene terephthalate using a novel "donut-shaped" sample in a cone-and-plate geometry. Predictions using the Folgar-Tucker model for fiber orientation, with a "slip" factor, combined with the Lipscomb model for stress were fit to the transient stresses at the startup of shear flow. Model parameters determined by fitting at (gamma)over dot = 6 s(-1) allowed for reasonable predictions of the transient stresses in flow reversal experiments at all the shear rates tested. Furthermore, fiber orientation model parameters determined by fitting the transient stresses were compared to the experimentally determined evolution of fiber orientation in startup of flow. The results suggested that fitting model predictions to the stress response in well-defined flows could lead to unambiguous model parameters provided the fiber orientation as a function of time or strain at some shear rate was known. (C)2009 The Society of Rheology. [DOI: 10.1122/1.3099314]