Some inverse problems in rheology leading to integral equations

Abstract

Two inverse problems of the integral type, which are of the general importance to rheology, are discussed. The first of them is the possibility of calculating the molecular weight distribution (MWD) from the flow curve and the second one is the interrelation between creep and relaxation functions. It was shown that the first problem is incorrect and any solution is unstable in respect to minor experimental errors. It means that the general solution of this problem is impossible in principle and only estimations of the width of unimodal MWD can be received from the curvature of the flow curve. The possibility of the correct calculation of the creep function exists in case the relaxation curve being approximated by the sum of exponential members. But the approximation of the relaxation curve within the experimental accuracy is the necessary, but not sufficient condition for the correct solution of this integral inverse problem, because not every mode of approximation leads to the satisfactory prediction of creep function.