How to characterize drying liquids

Paints, inks, and liquid bandages are just three types of colloidal suspensions that rely on the evaporation of a solvent to leave behind a functional material. As the suspension dries, it shrinks. And as it shrinks, its viscosity, elasticity, and other rheological properties change.

Thibaut Divoux of the University of Lyon in France and his collaborators set themselves the previously unmet challenge of measuring those changes directly as they happen. Their tool of choice was a shear rheometer, which relies on confining a liquid between two closely separated circular plates. The rotation of one plate in relation to the other is influenced in a measurable way by the liquid’s rheological properties.

The layers of interest are so thin that the liquid can readily maintain contact with both plates even as it dries. That condition might seem an advantage. It isn’t. If the gap between the two plates remains the same during evaporation, two effects introduce systematic errors into the rheological measurements.

First, as the sample’s volume shrinks, the curvature radius of the liquid meniscus decreases at the periphery of the lower plate. Consequently, capillary forces pull the upper plate down, thereby introducing a normal force whose origin lies not in the liquid’s properties but in its geometry. Second, as the evaporating liquid retreats to the center, its contact area decreases. Again, the rheometer ends up measuring a change due to geometry.

Divoux and his collaborators circumvented those effects by ensuring that the normal force on the liquid is maintained at zero. As the liquid evaporates, the gap between the plates is allowed to decrease. The zero normal force (ZNF) protocol not only avoids introducing a misleading force, it also ensures that the liquid extends to the edge of the plates throughout the measurement.

Using the ZNF protocol, the researchers conducted two types of measurement: continuous shear and oscillatory shear. They performed those measurements on a range of liquids, including a simple mixture of water and glycerol. In the water–glycerol experiment, the researchers determined the mixture’s viscosity continuously for four hours as the water evaporated and the concentration of glycerol increased.

So long as the concentration of glycerol remained uniform, the instantaneously measured values of the mixture’s viscosity matched those derived and tabulated for fixed water–glycerol ratios using standard rheological techniques. The ZNF protocol can indeed measure the rheological properties of drying mixtures in situ directly and in real time.

At the longest durations, a radial gradient developed. The gradient’s onset occurred earlier under oscillatory shear than with continuous shear, which gave the mixture more time to homogenize. By assuming a linear gradient, Divoux and his collaborators could theoretically reproduce the viscosity measured with the the ZNF protocol at high glycerol concentrations and under both continuous and oscillatory shear.

The results from the water–glycerol experiment and others reported in the researchers’ paper validate the ZNF protocol. They also open its use as a tool for investigating the rheological properties of the wide class of liquids, like paints and inks, whose importance and usefulness derive from the evaporation of their solvents. (P. Lehéricey et al., J. Rheol. 65, 427, 2021 .)