The work in this thesis is concerned with a theoretical and experimental investigation of certain time dependent simple flow situations on a controlled stress rheometer. We begin by carrying out a viscoelastic analysis of unidirectional combined steady and oscillatory shear flow, that is valid for large oscillatory shear amplitudes. The theory uses a corotational Goddard-Miller model to describe the non-linear relationship between the shear stress and shear rate in the fluid. Our main interest in this work is the description of the reduction in mean shear stress in the fluid due to the fluctuation of the shear rate about a non-zero mean. The effect of elasticity in this flow situation is examined by comparing mean shear stress reduction with that predicted by an inelastic model. A comparison is also made with data obtained on a controlled stress rheometer. A linear viscoelastic theory which is able to interpret the effect of fluid inertia on pure oscillatory complex viscosity data, is developed for the controlled stress instrument. The relevant equations of motion are solved by numerical methods. A first and second order perturbation technique is used to obtain theoretical expressions for the complex viscosity function for a number of geometries, commonly used-to measure dynamic data. The theory is then used to interpret the effect of fluid inertia on experimental dynamic data. Finally, we carry out a theoretical investigation of the dynamic behaviour of a 'yield stress' material. The generalised Maxwell model is modified, and then used to describe the non-linear viscoelastic dynamic behaviour of 'yield stress’ materials.

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