Theoretical analysis for the optical deformation of emulsion droplets

TL;DR

This paper develops a theoretical model to predict the three-dimensional shapes of optically deformed emulsion droplets, accounting for optical forces and interfacial tension, and introduces a dimensionless number for shape transition analysis.

Contribution

It provides the first quantitative framework for 3D droplet shape prediction under optical deformation, including a shape transition criterion.

Findings

Numerical solutions reveal diverse droplet shapes based on optical and physical parameters.

A dimensionless number around 1.0 indicates the transition from ellipsoidal to dumbbell shapes.

The model explains the ambiguity in 2D silhouette observations by predicting 3D geometries.

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 $\approx 1.0$, obtained by balancing interfacial tension and laser forces, substantiated using a data collapse.