Identification of rheological parameters of Herschel–Bulkley fluids from free surface data

Abstract

An inverse analysis for simultaneous identification of three rheological parameters of non-Newtonian Herschel-Bulkley fluids from free surface data is presented. The three-dimensional gravity-driven thin film of the Herschel-Bulkley fluid flowed down an inclined plane is modeled using the lubrication approximation. The governing equation is solved by an explicit finite difference method to obtain the fluid thickness. Based on a defined least square objective function and a gradient-based minimization method (here steepest-descent method), linearly-independent explicit expressions are derived for sensitivity coefficients which enable us to estimate simultaneously three rheological parameters of Herschel-Bulkley fluids accurately using the transient readings at only one point (sensor). Three test cases are considered to reveal the accuracy and efficiency of the proposed inverse analysis.

Keywords

• Gravity-driven flow
• Lubrication approximation
• Herschel-Bulkley fluid
• Inverse problem
• Parameter estimation
• Sensitivity analysis