Binding potential and wetting behavior of binary liquid mixtures on surfaces.

We present a theory for the interfacial wetting phase behavior of binary liquid mixtures on rigid solid substrates, applicable to both miscible and immiscible mixtures. In particular, we calculate the binding potential as a function of the adsorptions, i.e., the excess amounts of each of the two liquids at the substrate. The binding potential fully describes the corresponding interfacial thermodynamics. Our approach is based on classical density functional theory. Binary liquid mixtures can exhibit complex bulk phase behavior, including both liquid-liquid and vapor-liquid phase separation, depending on the nature of the interactions among all the particles of the two different liquids, the temperature, and the chemical potentials. Here we show that the interplay between the bulk phase behavior of the mixture and the properties of the interactions with the substrate gives rise to a wide variety of interfacial phase behaviors, including mixing and demixing situations. We find situations where the final state is a coexistence of up to three different phases. We determine how the liquid density profiles close to the substrate change as the interaction parameters are varied and how these determine the form of the binding potential, which in certain cases can be a multivalued function of the adsorptions. We also present profiles for sessile droplets of both miscible and immiscible binary liquids.

Foam-Based Electrophoretic Separation of Charged Dyes.

Electrophoretic separation of a fluorescent dye mixture, containing rhodamine B (RB) and fluorescein, in liquid foams stabilized by anionic, cationic, or non-ionic surfactants in water-glycerol mixtures was studied in a custom-designed foam separation device. The effects of the external electric field applied across the foam and the initial pH of the solution on the effectiveness of separation were also studied. The fluid motion due to electroosmosis and the resulting back pressure within the foam and local pH changes were found to be complex and affected the separation. Fluorescein dye molecules, which have a positive or negative charge depending on the solution pH, aggregated in the vicinity of an electrode, leaving a pure band of neutral dye RB. The effectiveness of the separation was quantified by the percentage width of the pure RB band, which was found to be between 29 and 42%. This study demonstrates the potential of liquid foam as a platform for electrophoretic separation.

Stability of Two-Dimensional Liquid Foams under Externally Applied Electric Fields.

Liquid foams are highly complex systems consisting of gas bubbles trapped within a solution of surfactant. Electroosmotic effects may be employed to induce fluid flows within the foam structure and impact its stability. The impact of external electric fields on the stability of a horizontally oriented monolayer of foam (2D foam) composed of anionic, cationic, non-ionic, and zwitterionic surfactants was investigated, probing the effects of changing the gas-liquid and solid-liquid interfaces. Time-lapse recordings were analyzed to investigate the evolution of foam over time subject to varying electric field strengths. Numerical simulations of electroosmotic flow of the same system were performed using the finite element method. Foam stability was affected by the presence of an external electric field in all cases and depended on the surfactant type, strength of the electric field, and the solid material used to construct the foam cell. For the myristyltrimethylammonium bromide (MTAB) foam in a glass cell, the time to collapse 50% of the foam was increased from ∼25 min under no electric field to ∼85 min under an electric field strength of 2000 V/m. In comparison, all other surfactants trialed exhibited faster foam collapse under external electric fields. Numerical simulations provided insight as to how different zeta potentials at the gas-liquid and solid-liquid interfaces affect fluid flow in different elements of the foam structure under external electric fields, leading to a more stable or unstable foam.

Discrete Self-Similarity in Interfacial Hydrodynamics and the Formation of Iterated Structures.

The formation of iterated structures, such as satellite and subsatellite drops, filaments, and bubbles, is a common feature in interfacial hydrodynamics. Here we undertake a computational and theoretical study of their origin in the case of thin films of viscous fluids that are destabilized by long-range molecular or other forces. We demonstrate that iterated structures appear as a consequence of discrete self-similarity, where certain patterns repeat themselves, subject to rescaling, periodically in a logarithmic time scale. The result is an infinite sequence of ridges and filaments with similarity properties. The character of these discretely self-similar solutions as the result of a Hopf bifurcation from ordinarily self-similar solutions is also described.