Theoretical analysis for the optical deformation of emulsion droplets

Tapp, D.; Taylor, J.M.; Lubansky, A.S.; Bain, C.D.; Chakrabarti, B.

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.

Citation

Tapp, D., Taylor, J., Lubansky, A., Bain, C., & Chakrabarti, B. (2014). Theoretical analysis for the optical deformation of emulsion droplets. Optics Express, 22(4), 4523-4538. https://doi.org/10.1364/oe.22.004523

• Journal Article Type: Article
• Publication Date: Feb 24, 2014
• Deposit Date: Jan 14, 2015
• Publicly Available Date: Jan 20, 2015
• Journal: Optics Express
• Electronic ISSN: 1094-4087
• Publisher: Optica
• Peer Reviewed: Peer Reviewed
• Volume: 22
• Issue: 4
• Pages: 4523-4538
• DOI: https://doi.org/10.1364/oe.22.004523
• Public URL: https://durham-repository.worktribe.com/output/1414457