Sign switch of Gaussian bending modulus for microemulsions; a self-consistent field analysis exploring scale invariant curvature energies

Bending rigidities of tensionless balanced liquid-liquid interfaces as occurring in microemulsions are predicted using self-consistent field theory for molecularly inhomogeneous systems. Considering geometries with scale invariant curvature energies gives unambiguous bending rigidities for systems with fixed chemical potentials: The minimal surface Im3m cubic phase is used to find the Gaussian bending rigidity, $\bar{\kappa}$, and a torus with Willmore energy $W=2 \pi^2$ allows for direct evaluation of the mean bending modulus, $\kappa$. Consistent with this, the spherical droplet gives access to $2 \kappa + \bar{\kappa}$. We observe that $\bar{\kappa}$ tends to be negative for strong segregation and positive for weak segregation; a finding which is instrumental for understanding phase transitions from a lamellar to a sponge-like microemulsion. Invariably, $\kappa$ remains positive and increases with increasing strength of segregation.Comment: 7 pages, 5 figure

A one-parameter model for microemulsions

Oil and water do not mix. Oil molecules like each other and so does water molecules. Oil molecules however do not like water molecules as much as their own. Thus, there exists a effective repulsive force between oil and water molecules. Imagine pouring a glass of water into a container that has oil. Eventually, the oil will phase separate and reach the top of the container. This happens as a result of the repulsive force often referred to as the hydrophobic nature of oil. Indeed gravity dictates their position, but, interaction drives the separation. As a thought experiment, imagine oil likes water. Do you think that if we repeat the same experiment in the presence of gravity, will oil come to the top of the container? I will leave this as an open question. When oil separates from water, an interface will form between the oil-rich and water-rich regions. However, there are enormous scenarios where we would like the oil to mix completely with water. It would be extremely beneficial if we can achieve this without providing mechanical work. Such stable mixtures of oil and water can be achieved by adding a surfactant. These surfactants have both oil-loving and water-loving parts and hence assemble at the interface between oil and water. Such assembly promotes thermodynamically stable mixtures (no mechanical work required) with an enormous interfacial area. Such thermodynamically stable mixtures of oil, water and surfactant are defined as microemulsions. To understand microemulsions. This is all this thesis is about. Our target is to generate a generic yet simplistic model to the whole class of microemulsions with accuracy at the molecular level. Firstly, we will provide a brief review of microemulsions. Later, we will present various applications of microemulsions in different fields. Finally, we will discuss existing models and conclude with an outline of the thesis

The physics of microemulsions extracted from modeling balanced tensionless surfactant-loaded liquid-liquid interfaces

Microemulsions are explored using the self-consistent field approach. We consider a balanced model that features two solvents of similar size and a symmetric surfactant. Interaction parameter χ and surfactant concentration φsb complement the model definition. The phase diagram in χ-φsb coordinates is known to feature two lines of critical points, the Scott and Leibler lines. Only upon imposing a finite distance between the interfaces, we observe that the Scott line meets the Leibler line. We refer to this as a Lifshitz point (LP) for real systems. We add regions that are relevant for microemulsions to this phase diagram by considering the saturation line, which connects (χ, φsb)-points for which the interface becomes tensionless. Crossing this line implies a first-order phase transition as internal interfaces develop, characteristic for one-phase microemulsions. The saturation line ends at the so-called microemulsion point (MP). The MP is shown to connect with the LP by a line of MP-like critical points, found by searching for a "MP" while the distance between interfaces is fixed. A pair of binodal lines that envelop the three-phase (Winsor III) microemulsion region is shown to connect to the MP. The cohesiveness of the middle phase in Winsor III is related to non-monotonic, inverse DLVO-type interaction curves between the surfactant-loaded tensionless interfaces. The mean and Gaussian bending modulus, relevant for the shape fluctuations and the topology of interfaces, respectively, are evaluated along the saturation line. Near the MP, both rigidities are positive and vanish in a power-law fashion with coefficient unity at the MP. Overseeing these results proves that the MP has a pivoting role in the physics of microemulsions.</p

Elastic properties of symmetric liquid-liquid interfaces

The mean (κ) and Gaussian (κ) bending rigidities of liquid-liquid interfaces, of importance for shape fluctuations and topology of interfaces, respectively, are not yet established: Even their signs are debated. Using the Scheutjens Fleer variant of the self-consistent field theory, we implemented a model for a symmetric L-L interface and obtained high-precision (mean-field) results in the grand-canonical (μ,V,T) ensemble. We report positive values for both moduli when the system is close to critical where the rigidities show the same scaling behavior as the interfacial tension γ. At strong segregation, when the interfacial width becomes of the order of the segment size, κ turns negative. The length scale λκ/γ remains of the order of segment size for all strengths of interaction; yet the 1/N chain length correction reduces λ significantly when the chain length N is small.</p

On jet instability modes of a subsonic Hartmann whistle

Numerical experiments to understand the resonant acoustic response of a subsonic jet impinging on the mouth of a tube, known as the Hartmann whistle configuration, were performed as large-eddy simulations. The tube length was chosen so that its fundamental duct mode, for one end closed and one end open, would match the dominant mode in the exciting jet. When the tube mouth was placed in the path of a regular stream of vortex rings, formed by the instability of the jet’s bounding shear layer, a strong resonant, tonal response (whistling) was obtained. At three diameters from the jet, OASPL was 150–160 dB. A tube with a thicker lip generated a louder response. When the tube was held closer to the nozzle exit, the impinging unsteady shear layer could not provoke any significant resonance. The simulations reveal that the tonal response of a Hartmann whistle operating in subsonic mode is significant.</p