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Abstract
Impressive improvements in the ability of microfluidic devices to reliably fabricate a wide variety of droplet, capsule, and particle architectures necessitate comparable improvements in techniques to measure and characterize these materials in line. Measurement and control of droplet surface tension are needed to ensure droplet stability while minimizing excess use of surfactants. Standard techniques to measure surface tension typically measure one droplet at a time. Fluidics can be leveraged to measure surface tension in-line with droplet formation. Typically, this requires channel geometries that enable extensional flow. Transient relaxation of deformed droplets is then measured at the exit of a constriction. We propose an alternative approach, in which a single value of steady deformation within a constriction is used to measure surface tension. We flow aqueous droplets in mineral oil through a series of increasingly narrow constrictions and measure steady deformation. In a subset of experiments, droplets contain varying concentrations of polyethylene glycol diacrylate, a common blank-slate hydrogel polymer. We calculate surface tension using Taylor’s small deformation theory, which describes the relationship between steady deformation in shear flows and the Capillary number, the ratio of the applied viscous stress to restoring surface tension stress. We measure surface tension over a wide range of surfactant concentration. Validation using both the transient deformation fluidic approach and pendant droplet measurements demonstrates the viability of our approach. Importantly, our results suggest that steady state measurements of deformation in pressure driven flows provide accurate assessments of surface tension, even when droplets are slightly confined. The use of multiple constrictions allows measurement of hundreds of droplets at several distinct shear rates without the need to vary control parameters. This steady deformation approach represents a readily-accessible option for measuring surface tension of micro-scale droplets in pressure driven flow through rectangular channels.
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. Table S3 provides viscosities for PEGDA solutions. Fig. S7 depicts surface tension as a function of PEGDA concentration for span 80 mole fraction of 0.001. The last section Fig. S8 depicts surface tension as a function of droplet size normalized with the channel height.
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