Instant yield stress measurement from falling drop size: The “syringe test”

We analyze different flow regimes of a filament formed by extrusion of a material through a cylindrical die. We deduce that the elongational yield stress of a simple yield stress fluid (i.e., with negligible thixotropy effects) can be determined from the mass of the droplet after filament breakage and an estimation of the critical radius at pinch-off at the solid-liquid regime transition. We demonstrate that such a simple characterization is relevant in a relatively wide range of extrusion velocities, i.e., this velocity slightly affects the drop mass in this range. For the simple yield stress fluids used, Carbopol gel, clay-water paste at different concentrations, and emulsion, covering a large range of yield stress values (50–1000 Pa), the elongational yield stress appears to be equal to the simple shear yield stress times a factor equal to about $1.53$⁠. As a consequence, this simple test may be used to obtain, almost instantaneously and without sophisticated apparatus (a syringe and a balance are sufficient), a good estimate of the shear yield stress of simple yield stress fluids. In that case, the main source of uncertainty (up to about 20%) is the value of the critical radius at the solid-liquid transition. Finally, we review the operating conditions (material properties and extrusion characteristics) for which we can expect this approach to be valid.