Regularization of First Kind Integral Equations with Application to Couette Viscometry

Abstract

The recovery of flow curves for non-Newtonian fluids from Couette rheometry measurements involves the solution of a quite simple first kind Volterra integral equation with a discontinuous kernel. In this paper, a new implementation of regularization is proposed. It involves the direct regularization of the observational equations through the construction of basis functions that exploit the mathematical structure in the integral equation. The proposed implementation is first derived for a general first kind integral equation and then applied to the Couette rheometer equation. For the regularization of this problem, the basis functions take on a form similar to that for B-splines.