Experimental and Theoretical Validation of System Variables That Control the Position of Particles at the Interface of Immiscible Liquids.

We construct a mathematical model describing the equilibrium flotation height of a spherical particle at the interface of immiscible liquids. The behavior of such a system depends on several experimentally measurable parameters, which include surface tensions, densities of all phases, and system scale. These parameters can be absorbed into three quantities that entirely determine the equilibrium position of the particle: the contact angle between the interface and particle, the Bond number, and the ratio of particle buoyant density to liquid phase densities-a new, dimensionless number that we introduce here. This experimentally convenient treatment allows us to make predictions that apply generally to the large parameter space of interesting systems. We find the model is in good agreement with experiments for particle size and interfacial tension spanning 3 orders of magnitude. We also consider the low interfacial tension case of aqueous two-phase systems (ATPSs) theoretically and experimentally. Such systems are more sensitive to changes in density than higher-tension aqueous/organic two-phase systems; we experimentally demonstrate that a millimeter-sized bead in an ATPS can be controllably positioned with between 5.9 and 95.1% of its surface area exposed to the bottom phase, whereas the same bead in an aqueous/organic system is limited to a range of 18.2-61.6%. Finally, we discuss the potential for wettability-based control for micron length-scale particles, which are not sensitive to changes in density. Our results can be used to simply define the experimentally controllable parameters that affect the equilibrium position and the length scales of a particle over which such parameters can be effectively tuned. A complete understanding of these properties is important for a number of applications including colloidal self-assembly and chemical patterning (e.g., formation of desymmetrized or Janus particles). By considering ATPSs, we broaden the potential uses to biological applications such as cell separation and interfacial tissue assembly.