Experimental and theoretical bulk phase diagram and interfacial tension of ouzo.

Ouzo is a well-known drink in Mediterranean countries, with ingredients water, alcohol and trans-anethole oil. The oil is insoluble in water, but completely soluble in alcohol, so when water is added to the spirit, the available alcohol is depleted and the mixture exhibits spontaneous emulsification. This process is commonly known as the louche or ouzo effect. Although the phase boundaries of this archetypal ternary mixture are well known, the properties of coexisting phases have not previously been studied. Here, we present a detailed experimental investigation into the phase behaviour, including tie-lines connecting coexisting phases, determination of the critical point (also called the plait point in ternary systems) and measurements of the surface tension and density for varying alcohol concentrations. Additionally, we present a theory for the thermodynamics and phase diagram of the system. With suitable selection of the interaction parameters, the theory captures nearly all features of the experimental work. This simple model can be used to determine both bulk and non-uniform (e.g. interfacial) properties, paving the way for a wide range of future applications of the model to ternary mixtures in general. We show how our accurate equilibrium phase diagram can be used to provide improved understanding of non-equilibrium phenomena.

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.

Dynamic density functional theory for sedimentation processes on complex domains: Modelling, spectral elements, and control problems.

Modelling of many real-world processes, such as drug delivery, wastewater treatment, and pharmaceutical production, requires accurate descriptions of the dynamics of hard particles confined in complicated domains. In particular, when modelling sedimentation processes or systems with driven flows, it is important to accurately capture volume exclusion effects. This work applies Dynamic Density Functional Theory to the evolution of a particle density under diffusion, external forces, particle-particle interaction, and volume exclusion. Using a spectral element framework, for the first time it is possible to include all of these effects in dynamic simulations on complex domains. Moreover, this allows one to apply complicated no-flux, and other non-local, non-linear, boundary conditions. The methodology is also extended to control problems, addressing questions of how to enhance production set-up in industrially-motivated processes. In this work the relevant models are introduced, numerical methods are discussed, and several example problems are solved to demonstrate the methods' versatility. It is shown that incorporating volume exclusion is crucial for simulation accuracy and we illustrate that the choice of boundary conditions significantly impacts the dynamics.

Nascent Transcript Folding Plays a Major Role in Determining RNA Polymerase Elongation Rates.

Transcription elongation rates influence RNA processing, but sequence-specific regulation is poorly understood. We addressed this in vivo, analyzing RNAPI in S. cerevisiae. Mapping RNAPI by Miller chromatin spreads or UV crosslinking revealed 5' enrichment and strikingly uneven local polymerase occupancy along the rDNA, indicating substantial variation in transcription speed. Two features of the nascent transcript correlated with RNAPI distribution: folding energy and GC content in the transcription bubble. In vitro experiments confirmed that strong RNA structures close to the polymerase promote forward translocation and limit backtracking, whereas high GC in the transcription bubble slows elongation. A mathematical model for RNAPI elongation confirmed the importance of nascent RNA folding in transcription. RNAPI from S. pombe was similarly sensitive to transcript folding, as were S. cerevisiae RNAPII and RNAPIII. For RNAPII, unstructured RNA, which favors slowed elongation, was associated with faster cotranscriptional splicing and proximal splice site use, indicating regulatory significance for transcript folding.

General dynamical density functional theory for classical fluids.

We study the dynamics of a colloidal fluid including inertia and hydrodynamic interactions, two effects which strongly influence the nonequilibrium properties of the system. We derive a general dynamical density functional theory which shows very good agreement with full Langevin dynamics. In suitable limits, we recover existing dynamical density functional theories and a Navier-Stokes-like equation with additional nonlocal terms.

Accurate prediction of nonadiabatic transitions through avoided crossings.

In the case of one nuclear degree of freedom, we derive an explicit formula for the nuclear wave function transmitted through an avoided crossing, and show that it agrees to high accuracy with precise numerical calculations.