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Abstract
Advances in fluidic droplet generation necessitate accessible, high throughput methods to optimize formulations by measuring surface tension. One fluidic approach involves creating extensional flow using constrictions. Transient relaxation of deformed droplets is then measured at the constriction exit. We propose an alternative, arguably simpler approach: we use steady deformation within a constriction to measure surface tension. We calculate surface tension using Taylor's small deformation theory, which describes the relationship between droplet deformation and the Capillary number, or ratio of applied viscous stress to restoring surface tension stress. Taylor originally developed his theory for unconfined droplets in pure shear or pure extension. We apply Taylor’s theory to droplets in pressure driven flows. We generate and flow emulsion droplets through a series of increasingly narrow constrictions and use steady deformation to measure surface tension. We investigate both water-in-oil and oil-in-water droplets, stabilized by three different surfactants over a range of concentrations. In a subset of experiments, we vary the viscosity ratio by adding polyethylene glycol diacrylate to water droplets. Validation using both the transient deformation fluidic approach and pendant drop measurements on individual droplets demonstrates the viability of Taylor’s theory in regimes beyond those originally proposed. Importantly, our results suggest steady state deformation in pressure driven flows can be used to measure surface tension even when droplets are slightly confined. This steady droplet deformation approach to surface tension measurements represents a readily-accessible option for those using fluidic droplet generators to perform biomedical or other assays, or to investigate or optimize emulsion formulations.
Supplementary materials
Title
Supplementary Information: Droplet deformation in steady fluidic flows enables robust, accessible, high-throughput surface tension measurements
Description
Supplemental information includes additional contributions to the article, beginning with nomenclature. Fig. S1 depicts an example of device water sticking and Fig. S2 compares the 5X and 20X objective. Next, we describe the “transient” device analysis technique. Briefly, droplet contour change is measured along the x-axis, providing variables for Fig. S3. We then extract surface tension from the slope of Fig. S4. Section 4 provides measurement details for each experiment (Table S1). Fig. S5 plots velocity and deformation versus x-position and deformation versus viscous stress. The next section compares measurement methods to the current moment of inertia method (Fig. S6). Table S2 shows pendant droplet specifics. Fig. S7 depicts surface tension as a function of droplet size normalized with the channel height. The last section describes emulsion with tween with table S3 providing specifics.
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