Assumed periodicity and dynamic shear stress transduction in rheometry

• Published in: Journal of rheology (New York : 1978) 2010-07, Vol.54 (4), p.835-858
• Main Authors: Kolitawong, Chanyut, Giacomin, A. Jeffrey, Johnson, Leann M.
• Format: Article
• Language: English
• Subjects: Assumed periodicity; Cross-disciplinary physics: materials science; rheology; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Physics; Rheological measurements; Rheology; Shear stress transducer; Sliding plate rheometer; Solid mechanics; Step shear; Structural and continuum mechanics; Techniques and apparatus; Transducer dynamic response; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
• ISSN: 0148-6055; 1520-8516
• DOI: 10.1122/1.3439774

In viscoelastic property measurements, material is subjected to time unsteady deformations using a rheometer. In step shear strain experiments, for example, the shear strain suddenly jumps to a steady value. In this paper, we develop a method to study the dynamic response of a shear stress transducer in a sliding plate rheometer for any time unsteady rheological test. This general method is developed by first considering a special case of step shear strain for a fluid sample with material ingress in the annular transducer gap. Both the fluid sample and its ingress obey the generalized Maxwell model. Our main mathematical trick is assumed periodicity where a single step in shear strain is treated as the first step in a reciprocating square wave. After solving the problem in the frequency domain, we recover our single step by taking the limit as the period goes to infinity. The transducer eccentricity following step shear is then determined analytically by solving the force balance on the transducer active face using bipolar cylindrical coordinates. Dimensionless graphs are provided for estimating transducer dynamic response in step shear strain. Finally, a worked example illustrates the application of these results.