Measuring yield stress: a new, practical, and precise technique derived from detailed penetrometry analysis

The displacement of an object through a yield stress is a complex process which involves the continuous deformation and transition of new regions from the solid to the liquid regime. We studied the force vs depth variations during the progressive penetration of a plate or a cylinder in a bath of simple yield stress fluids with negligible thixotropic character (Carbopol solutions, emulsions, and foams). Three regimes could be distinguished: elastic deformation, penetration (partially immersed object), and displacement through the fluid (fully immersed object). A detailed analysis of the force vs depth curves makes it possible to show that in the partially immersed regime the force is the sum of the critical force before penetration and a term associated with a uniform shear stress along the main plate surface, which is independent on the object geometry (plate dimensions and cylinder radius). This understanding can be used to precisely determine the yield stress as the critical shear stress along the plate at vanishing velocities. We also show that it is possible to measure accurately the yield stress from relaxation tests (stress vs time curve for motion stoppage): it indeed appears that the additional force term associated with penetration is negligible in that case so that the asymptotic average shear stress after stoppage is equal to the yield stress.