Error analysis for reducing noisy wide‐gap concentric cylinder rheometric data for nonlinear fluids: Theory and applications

This work discusses the propagation of errors for the recovery of the shear rate from wide‐gap concentric cylinder viscometric measurements of non‐Newtonian fluids. A least‐square regression of stress on angular velocity data to a system of arbitrary functions is used to propagate the errors for the series solution to the viscometric flow developed by Krieger and Elrod and Pawlowski, and for the first term of the series developed by Krieger (‘‘power‐law’’ approximation). A numerical experiment shows that, for measurements affected by significant errors, the first term of the Krieger–Elrod–Pawlowski series (‘‘infinite radius’’ approximation) and the power‐law approximation may recover the shear rate with equal accuracy as the full Krieger–Elrod–Pawlowski solution. An experiment on a clay slurry indicates that the clay has a larger yield stress at rest then during shearing, and that, for the range of shear rates investigated, a four‐parameter constitutive equation approximates reasonably well its rheology. The error analysis presented is useful for studying the rheology of fluids such as particle suspensions, slurries, foams, and magma. The viscometric measurements of these fluids are usually affected by significant errors that are introduced by ‘‘non‐Couette’’ flow in the viscometer and by temperature, time, and shear rate dependence of the rheological parameters.