Continuous Droplet-Based Viscometer

Continuous viscosity measurements have a wide range of applications from industrial chemical production to medical diagnosis. In this work, we have developed a simple droplet-based (i.e., water-in-oil) continuous viscometer capable of measuring viscosity changes in less than 10 seconds and consuming a total sample volume of less than 1 µl per hour. The viscometer employs a flow-focusing geometry and generates droplets under constant pressure. The length of the droplets (L_d) is highly correlated to the aqueous-phase viscosity (µ_aq) at high ratios of aqueous-inlet to oil-inlet pressure (AIP/OIP), yielding a linear relationship between µ_aq and 1/(L_d – L_c) where L_cis the minimal obtainable droplet length.

Theoretical analysis was conducted to predict the droplet size and verify the experimentally found linear relationship. The theoretical analysis is based on the mechanism for flow-rate controlled breakup proposed by Garstecki et al. in a T-junction geometry. They found that the droplet length is linearly proportional to the ratio of the dispersed-phase to continuous-phase flow rate. We combined this relationship with a pressure balance between the applied pressure and the pressure drop from the inlet to the outlet of the device to derive the flow rate ratio. The resulting equations can successfully predict droplet lengths and verify the linear relationship between µ_aq and 1/(L_d – L_c). The equations can also be applied to optimize the device geometry (i.e., channel widths, depths and lengths).