Solving the inverse problem of Couette viscometry by Tikhonov regularization

Most of the existing procedures for converting Couette viscometry data into a shear stress τ versus shear rate γ material function rely on the small annular gap assumption or require the algebraic form of the τ–γ curve to be prespecified. Furthermore most of the existing procedures are not particularly suitable for fluids with yield stress. In this investigation the problem of converting Couette viscometry data into a τ–γ material function is formulated as a Volterra integral equation of the first kind. A method based on Tikhonov regularization is then developed to solve this equation for the τ–γ curve. The method does not depend on the small gap assumption or require prespecification of the algebraic form of the τ–γ relationship. It is equally applicable to fluids with and without yield stress. For fluids with yield stress, provided the data include one or more points where the fluid in the annular gap is partially sheared, the method will also extract the yield stress from the data. The performance of this general method is demonstrated by applying it to synthetic Couette viscometry data with added random noise and to experimental data taken from the literature.