The surface tension of surfactant-containing, finite volume droplets

Abstract

Surface tension influences the fraction of atmospheric particles that become cloud droplets. Although surfactants are an important component of aerosol mass, the surface tension of activating aerosol particles is still unresolved, with most climate models assuming activating particles have a surface tension equal to that of water. By studying picoliter droplet coalescence, we demonstrate that surfactants can significantly reduce the surface tension of finite-sized droplets below the value for water, consistent with recent field measurements. Significantly, this surface tension reduction is droplet size-dependent and does not correspond exactly to the macroscopic solution value. A fully independent monolayer partitioning model confirms the observed finite-size-dependent surface tension arises from the high surface-to-volume ratio in finite-sized droplets and enables predictions of aerosol hygroscopic growth. This model, constrained by the laboratory measurements, is consistent with a reduction in critical supersaturation for activation, potentially substantially increasing cloud droplet number concentration and modifying radiative cooling relative to current estimates assuming a water surface tension. The results highlight the need for improved constraints on the identities, properties, and concentrations of atmospheric aerosol surfactants in multiple environments and are broadly applicable to any discipline where finite volume effects are operative, such as studies of the competition between reaction rates within the bulk and at the surface of confined volumes and explorations of the influence of surfactants on dried particle morphology from spray driers.

Keywords: aerosol; cloud condensation nuclei; cloud droplet number concentration; surface tension; surfactant.

Fig. 1.

Conceptual description of the experimental procedure. (A) Two droplets containing a primary solute (0.9 M glutaric acid or 0.5 M NaCl) and the soluble surfactant Triton X-100 were optically trapped and coalesced. (B) The dynamic shape oscillations characteristic of the coalescence event were monitored by time-dependent changes to the backscattered light intensity. (C) The composite droplet size and refractive index (RI) were obtained by comparison of the whispering gallery modes in the Raman spectrum of the droplet to a library of Mie theory calculations. Parameterizations of RI and concentration give the primary solute concentration. The surfactant concentration is determined by assuming the primary solute:surfactant ratio in the nebulized solution is conserved in the droplet. (D) Together these data allow surfactant concentration-dependent measurements of the surface tensions of picoliter droplets.

Fig. 2.

(A) Comparison of picoliter droplet (∼7- to 9-μm radius) surface tensions to macroscopic solution surface tensiometry measurements and monolayer partitioning model predictions at different droplet radii plotted as a function of [Triton X-100]_tot for droplets nebulized from an aqueous solution containing 0.9 M glutaric acid. Droplet measurements are averaged to 0.03 mM bins. Uncertainty bars represent the SD of the mean. (B) When monolayer partitioning model predictions are plotted as a function of [Triton X-100]_bulk (symbols), the results collapse onto macroscopic solution (flat surface) measurements (solid line), indicating that the model accurately considers surface-bulk partitioning in the droplets.

Fig. 3.

Size dependence of composite droplet surface tension for droplets produced by nebulization of an aqueous solution of 0.9 M glutaric acid and 0.42 mM Triton X-100. The solid line is the model prediction. A relative surface tension is plotted to superimpose the measured and modeled values. The relative value for γ_CMC, the macroscopic solution value of surface tension at this concentration, is provided by the dotted line. The upper axis gives the surface-to-volume ratio for the droplet radii on the bottom axis. Data were averaged to 0.5-μm bins. Uncertainty bars represent the SD of the mean.

Fig. 4.

Comparison of picoliter droplet (∼7- to 9-μm radius) surface tensions to values from macroscopic solution surface tensiometry measurements and monolayer partitioning model predictions at different droplet radii plotted as a function of [Triton X-100]_tot for droplets nebulized from an aqueous solution containing 0.5 M NaCl. In practice, model results for different radii overlap each other. Droplet measurements are averaged to 0.1 mM bins. Uncertainty bars represent the SD of the mean.

Fig. 5.

(A) Monolayer partitioning model predictions of the surface tension of a 0.05-μm-radius droplet as [Triton X-100]_tot is increased. (B) Surface tension predictions for droplets containing different initial [Triton X-100]_tot growing hygroscopically (i.e., by addition of water) from 0.05-μm to 10-μm radius. (C) Köhler curves describing cloud droplet activation for the same droplets. The different colored lines refer to droplets with initial compositions indicated by the colored circles in A. The predictions account for both dilution and the changing surface-to-volume ratio of the growing particle.