Materials Chemistry

Gravitational settling of active droplets

Authors

Abstract

The gravitational settling of oil droplets solubilizing in an aqueous micellar solution contained in a capillary channel is investigated. The motion of these active droplets reflects a competition between gravitational and Marangoni forces, the latter due to interfacial tension gradients generated by differences in filled- micelle concentrations along the oil-water interface. This competition is studied by varying the surfactant concentration, the density difference between the droplet and the continuous phase, and the viscosity of the continuous phase. The Marangoni force enhances the settling speed of an active droplet when compared to the Hadamard-Rybczynski prediction for a (surfactant free) droplet settling in Stokes flow. The Marangoni force can also induce lateral droplet motion, suggesting that the Marangoni and gravitational forces are not always aligned. The decorrelation rate (𝛼) of the droplet motion, measured as the initial slope of the velocity autocorrelation and indicative of the extent to which the Marangoni and gravitational forces are aligned during settling, is examined as a function of the droplet size: correlated motion (small values of 𝛼) is observed at both small and large droplet radii, whereas significant decorrelation can occur between these limits. This behavior of active droplets settling in a capillary channel is in marked contrast to that observed in a dish, where the decorrelation rate increases with the droplet radius before saturating at large values of droplet radius. A simple relation for the crossover radius at which the maximal value of 𝛼 occurs for an active settling droplet is proposed.

Content

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Supplementary material

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Supplementary Material
Contains additional details on the experimental methods, data analysis techniques, and material properties of the various systems used in the main paper.
Thumbnail image of Video S1. Bromodecane in 3 wt% Triton X-100. Dish. R=41 µm drop.mp4
Video S1
Bromodecane droplet of R = 41 μm moving through a solution of 3 wt% Triton X-100 on a glass bottom dish.
Thumbnail image of Video S2. Bromodecane in 3 wt% Triton x-100. Dish. R=71 µm drop.mp4
Video S2
Bromodecane droplet of R = 71 μm moving through a solution of 3 wt% Triton X-100 on a glass bottom dish. Video taken at 20 fps on a Nikon Eclipse Ts2 microscope using an Imaging Source DFK 23UX249 color camera and IC Capture at 4x magnification (Nikon objective) (see experimental methods for details). Video shown in real time.
Thumbnail image of Video S3. Bromodecane settling in 3 wt% Triton X-100. R=41 micron drop.mp4
Video S3
Bromodecane droplet of R = 41 μm settling through a solution of 3 wt% Triton X-100. Video taken at 40 fps using a PCO Panda sCMOS camera and μManager software on a custom- built side-imaging microscope using a Nikon 2x objective (see experimental methods for details). Video shown in real time.
Thumbnail image of Video S4. Bromodecane settling in 3 wt% Triton X-100. R=73.mp4
Video S4
Video S4: Bromodecane droplet of R = 73 μm settling through a solution of 3 wt% Triton X-100. Video taken at 40 fps using a PCO Panda sCMOS camera and μManager software on a custom- built side-imaging microscope using a Nikon 2x objective (see experimental methods for details). Video shown in real time.
Thumbnail image of Video S5. Chaotic trail imaging.mp4
Video S5
Bromodecane droplet of R = 49 μm settling through a solution of 4.75 wt% Triton X- 100 with 5 wt% poly(ethylene glycol) (MW=20,000 g/mol). Video taken at 40 fps using a PCO Panda sCMOS camera and μManager software on a custom-built side-imaging microscope using a Nikon 10x objective (see experimental methods for details). Image brightness and contrast adjusted to better visualize droplet trail using ImageJ. Video shown in real time.
Thumbnail image of Video S6. axisymmetric trail imaging.mp4
Video S6
Bromodecane droplet of R = 69 μm settling through a solution of 4.75 wt% Triton X- 100 with 5 wt% poly(ethylene glycol) (MW=20,000 g/mol). Video taken at 40 fps using a PCO Panda sCMOS camera and μManager software on a custom-built side-imaging microscope using a Nikon 10x objective (see experimental methods for details). Image brightness and contrast adjusted to better visualize droplet trail using ImageJ. Video shown in real time.