Estimating the viscosity of a highly viscous liquid droplet through the relaxation time of a dry spot

We discuss in this paper a technique which enables the estimation of the viscosity of microscopic droplets, with application to particles suspended in the atmosphere. The principle of this technique is to deposit a droplet of material approximately 30-100 μm in diameter on a substrate and poke it with a sharp needle hence generating a hole. The amount of sample needed to perform such measurement allows the viscosity of small sample volumes (less than a microliter), such as those generated from atmospheric sampling, to be determined. We show here that the time required for the droplet to relax to its equilibrium shape can be related to the viscosity. We hereby present two mathematical models based on the lubrication approximation which are able to capture the droplet relaxation dynamics. One model is fully transient and resolves the dynamics of the wetting front using a disjoining pressure approach. The other is quasistatic and requires a relationship between the contact line velocity and the contact angle. Comparing the computed relaxation time to that measured experimentally enables the approximate evaluation of the viscosity. The mathematical models are first tested against data from the literature for the closure of a hole in a continuous thin film and then demonstrated for droplets of the polybutene oil N450000 (trade name Cannon Standard Oil), a high-viscosity standard, which serve as a benchmark sample since it is precisely characterized. We also present here viscosity estimates for droplets consisting of secondary organic material and water which are present over forested region yet remain very poorly understood for a lack of adequate characterization technique.