Solving the inverse problem of Couette viscometry by Tikhonov regularization

Most of the existing procedures for converting Couette viscometry data into a shear stress tau versus shear rate (gamma )over dot material function re ly on the small annular gap assumption or require the algebraic form of the tau-(gamma )over dot curve to be prespecified. Furthermore most of the exi sting procedures are not particularly suitable for fluids with yield stress . In this investigation the problem of converting Couette viscometry data i nto a tau-(gamma )over dot material function is formulated as a Volterra in tegral equation of the first kind. A method based on Tikhonov regularizatio n is then developed to solve this equation for the tau-(gamma )over dot cur ve. The method does not depend on the small gap assumption or require presp ecification of the algebraic form of the tau-(gamma )over dot relationship. It is equally applicable to fluids with and without yield stress. For flui ds with yield stress, provided the data include one or more points where th e fluid in the annular gap is partially sheared, the method will also extra ct the yield stress from the data. The performance of this general method i s demonstrated by applying it to synthetic Couette viscometry data with add ed random noise and to experimental data taken from the literature. (C) 200 0 The Society of Rheology. [S0148-6055(00)00206-6].