DoS Dos and Don'ts

Abstract: Dripping-onto-Substrate (DoS) rheometry is a well-established method for measuring the extensional rheology of low-viscosity liquids. However, clear guidelines on the capabilities and limitations of the technique are lacking. In the present work, we define operational limits for measuring a transient extensional viscosity directly from observation of the rate of filament thinning, as well as model-based bounds on calculating a viscosity $η$ and extensional relaxation time $τ_E$ of a liquid using DoS. Dilute solutions of polyethylene oxide (PEO) and polyacrylamide (PAM) are used to probe the lower limit of measurable $τ_E$, demonstrating that values as low as 0.1 ms can be resolved, provided (a) the intrinsic Deborah number (based on the ratio of the relaxation time and the Rayleigh breakup time scale) is $De \geq \mathcal{O}(0.1)$ and (b) an instrumental constraint related to spatial and temporal resolution is satisfied. This instrumental constraint is quantified through a new metric we define as the \textit{filament capture rate}, a ``figure of merit'' (expressed in Hz) that can be used to quantify the number of data points within the elasto-capillary regime that are available for extraction of $τ_E$. We also investigate the sensitivity to other experimental parameters including variations in nozzle radius and Bond number ($Bo$). Across the tested range ($0.2 < Bo < 0.7$), extensional relaxation times for the same fluid vary by less than $\pm16$ \%; however, experiments with low viscosity fluids at $Bo > 0.5$ exhibit damped gravitational oscillations that affect early-time dynamics. Collectively, these results provide a quantitative roadmap for reliable DoS rheometry and affirm its use for measuring sub-millisecond relaxation times in weakly elastic fluids.