Dripping-onto-substrate (DoS): Dos and don’ts

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 observations of the rate of filament thinning, as well as model-based bounds on calculating a viscosity η and extensional relaxation time τE of a liquid using DoS. Dilute solutions of polyethylene oxide and polyacrylamide are used to probe the lower limit of measurable τE, 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≥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 filament capture rate, a “figure of merit” (expressed in s−1) that can be used to quantify the number of data points within the elastocapillary regime that are available for extraction of τE. Finally, model-agnostic bounds for reliable measurements of the transient extensional viscosity ηE+ using DoS rheometry are derived. These bounds prescribe experimental limitations due to inertia, gravity, and measurement resolution (spatial and temporal) that can assist rheologists in the design and interpretation of extensional viscosity measurements using DoS. Collectively, these results provide a quantitative roadmap for reliable DoS rheometry and affirm its use for measuring the transient extensional viscosity of liquid-like materials.