Summary
This theory is derived to model the behavior of a dilute suspension of deformable, incompressible elastic spheres within an incompressible Newtonian fluid. It is shown that a full range of viscoelastic effects are evidenced by this type of heterogeneous media. The (isothermal) constitutive relation which governs the macroscopic behavior of the fluid is found to be that of the Coleman-Noll second order theory of incompressible viscoelastic fluids with the related relaxation functions being specified through analytical expressions involving the coefficient, of viscosity of the carrier fluid, the shear modulus of the elastic inclusions and their volume concentration. The relationship of the present work to previous similar analyses is discussed. Also the relationship of the effects seen with the present special theory to some observed effects in the testing of homogeneous polymeric fluids is considered.
Zusammenfassung
Diese theorie wird zur Beschreibung des Verhaltens einer schwachen Suspension von deformierbaren inkompressiblen elastischen Kugeln in einer inkompressiblen Newtonschen Flüssigkeit hergeleitet. Es wird gezeigt, daß eine Vielzahl von viskoelastischen Erscheinungen bei diesem heterogenen Werkstoff auftreten. Es zeigt sich, daß die das makroskopische Verhalten der Suspension beschreibende isotherme Werkstoffgleichung vom Typ der inkompressiblen viskoelastischen Flüssigkeit zweiter Ordnung ist, wobei die Relaxationsfunktion durch einen, den Koeffizienten der inneren Reibung der Trägerflüssigkeit, den Schubmodul, und die Volumskonzentration der elastischen Anteile enthaltenden analytischen Ausdruck gegeben ist. Der Zusammenhang dieser Arbeit mit ähnlichen Untersuchungen wird diskutier und die durch diese Theorie beschriebenen Erscheinungen mit bei der Prüfung homogener Polymere beobachteten verglichen.
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Christensen, R.M. A special theory of viscoelastic fluids for application to suspensions. Acta Mechanica 16, 183–198 (1973). https://doi.org/10.1007/BF01179989
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DOI: https://doi.org/10.1007/BF01179989