Abstract:
Fluids have fascinated many generations of scientists and engineers. Although a considerable
amount of research has been devoted to the study of
uids of low molecular weight (well
described by the Navier-Stokes equations), many challenging problems in both theory and applications
still remain. But, even more challenging are non-Newtonian
uids, whose motions
cannot be described by the Navier-Stokes equations. The present work would be of fundamental
importance to the dynamics of fast
ows of a class of such
uids (dilute polymeric solutions).
Here, we consider a well-known theoretical model (Oldroyd-B
uid) in order to represent, in the
simplest possible manner, the polymer-solvent coupling in a dilute polymer solution, and study
how the resulting non-Newtonian rheology a ects the known structure of the continuous spectrum
in the inviscid limit. In general, the equation governing the evolution of small-amplitude
perturbations to inviscid shearing
ows, the Rayleigh equation, is singular, and the continuous
spectra associated with the Rayleigh equation owe their origin to such singular points. Additional
continuous spectra exist with the introduction of elasticity, and it has already been shown,
in the inertialess limit, that the nature of the continuous spectrum is sensitive to the base-state
velocity pro le and the particular constitutive model used (UCM v/s Oldroyd-B; Wilson et al.
(1999)). The viscoelastic continuous spectra owe their origin to the `simple
uid' assumption underlying
almost all constitutive equations used in polymer rheology. The fact that the polymeric
stress only depends on the evolution of the polymer conformation along a particular streamline,
and is not in
uenced by the polymer molecules convected by streamlines in the immediate
vicinity, supports the existence of continuous spectra in elastic liquids, and this is independent
of the Reynolds number. In this thesis, we study the nature of the elastic continuous spectrum
at large Reynolds number which serves as a complement to the aforementioned study of Wilson
et al. (1999) in the absence of inertia.
