Exploring How the\nSurface-Area-to-Volume Ratio Influences\nthe Partitioning of Surfactants to the Air–Water Interface\nin Levitated Microdroplets

Quantitative characterization of the surface of microdroplets\nis\nimportant to understanding and predicting numerous chemical and physical\nprocesses, such as cloud droplet formation and accelerated chemistry\nin microdroplets. However, it is increasingly appreciated that the\nsurface compositions of microdroplets do not necessarily match those\nof macroscale solution due to their large surface-area-to-volume (SA–V)\nratios and confined volumes. In this work, we explore how both droplet\nsize and composition affect the surface composition of microdroplets\nby measuring the equilibrium surface tensions of levitated microdroplets\ncontaining a single surfactant. We measure the critical micelle concentrations\n(CMCs) for surfactants of various strengths (macroscale CMC values\nranging from 0.02 to 10 mM) in microdroplets with radii ranging from\n5 to 25 μm. We accurately model the surface tensions of microdroplets\nusing an equilibrium partitioning model that only requires droplet\nsize and adsorption parameters from macroscale measurements as inputs.\nOur model predicts that surfactants have an “effective CMC”\nin microdroplets that is always larger in value than the corresponding\nmacroscale CMC. In some instances, the effective CMC of a surfactant\nin microdroplets is several orders of magnitude larger than both its\nmacroscale CMC and its macroscale solubility limit. We present a simple\nexpression for the effective CMC in microdroplets that depends on\nboth the macroscale CMC of a surfactant and the SA–V ratio\nof the microdroplet. Ultimately, our experimental results and model\ncan be used broadly to predict microdroplet surface compositions when\ninvestigating surface-driven accelerated chemistry in microdroplets\nor estimating cloud droplet activation.