Exploring How the Surface-Area-to-Volume Ratio Influences the Partitioning of Surfactants to the Air–Water Interface in Levitated Microdroplets

Abstract

Quantitative characterization of the surface of microdroplets is important to understanding and predicting numerous chemical and physical processes, such as cloud droplet formation and accelerated chemistry in microdroplets. However, it is increasingly appreciated that the surface compositions of microdroplets do not necessarily match those of macroscale solution due to their large surface-area-to-volume (SA−V) ratios and confined volumes. In this work, we explore how both droplet size and composition affect the surface composition of microdroplets by measuring the equilibrium surface tensions of levitated microdroplets containing a single surfactant. We measure the critical micelle concentrations (CMCs) for surfactants of various strengths (macroscale CMC values ranging from 0.02 to 10 mM) in microdroplets with radii ranging from 5 to 25 μm. We accurately model the surface tensions of microdroplets using an equilibrium partitioning model that only requires droplet size and adsorption parameters from macroscale measurements as inputs. Our model predicts that surfactants have an "effective CMC" in microdroplets that is always larger in value than the corresponding macroscale CMC. In some instances, the effective CMC of a surfactant in microdroplets is several orders of magnitude larger than both its macroscale CMC and its macroscale solubility limit. We present a simple expression for the effective CMC in microdroplets that depends on both the macroscale CMC of a surfactant and the SA−V ratio of the microdroplet. Ultimately, our experimental results and model can be used broadly to predict microdroplet surface compositions when investigating surface-driven accelerated chemistry in microdroplets or estimating cloud droplet activation.