title: Theoretical analysis for the optical deformation of emulsion droplets.
abstract: We propose a theoretical framework to predict the three-dimensional shapes of optically deformed micron-sized emulsion droplets with ultra-low interfacial tension. The resulting shape and size of the droplet arises out of a balance between the interfacial tension and optical forces. Using an approximation of the laser field as a Gaussian beam, working within the Rayleigh-Gans regime and assuming isotropic surface energy at the oil-water interface, we numerically solve the resulting shape equations to elucidate the three-dimensional droplet geometry. We obtain a plethora of shapes as a function of the number of optical tweezers, their laser powers and positions, surface tension, initial droplet size and geometry. Experimentally, two-dimensional droplet silhouettes have been imaged from above, but their full side-on view has not been observed and reported for current optical configurations. This experimental limitation points to ambiguity in differentiating between droplets having the same two-dimensional projection but with disparate three-dimensional shapes. Our model elucidates and quantifies this difference for the first time. We also provide a dimensionless number that indicates the shape transformation (ellipsoidal to dumbbell) at a value ≈ 1.0, obtained by balancing interfacial tension and laser forces, substantiated using a data collapse.
authors.forename: David
authors.initials: D
authors.lastname: Tapp
authors.forename: Jonathan M
authors.initials: JM
authors.lastname: Taylor
authors.forename: Alex S
authors.initials: AS
authors.lastname: Lubansky
authors.forename: Colin D
authors.initials: CD
authors.lastname: Bain
authors.forename: Buddhapriya
authors.initials: B
authors.lastname: Chakrabarti