Abrupt phase transitions

This chapter studies abrupt phase transitions, familiar from boiling water, raindrops, snowflake formation, and frost. At these transitions, the properties change abruptly -- the ice cube and the water in which it floats are at the same temperature and pressure, but have quite different densities and rigidities. The chapter studies the coexistence between two phases by matching their free energies, and discover the Maxwell equal-area construction. It examines the barriers to raindrop formation and discovers nucleation and critical droplet theory. It examines how the transition proceeds after nucleation, and discovers coarsening (familiar from the segregation of oil and water in well-shaken salad dressing), dendrites (snowflakes and frost patterns), and martensitic structures (important in steel). Exercises explore nucleation of dislocations, of cracks, and of droplets in the Ising model; complex free energies and nucleation rates; dendrites in surface growth and snowflakes; and martensites, minimizing sequences, and origami.

WETTING AND PREWETTING PHENOMENA IN NEMATIC LIQUID CRYSTAL DISK-LIKE DROPLET

We present a theoretical investigation of wetting and prewetting phenomena in a nematic-disk like droplet under a concentric anchoring configuration. Our theoretical model is based on Landau–de Gennes free energy together with a quadratic surface energy. By using the Maxwell construction, we numerically solve the Euler–Lagrange differential equation. The occurrence of boundary layer transition is summarized in the phase diagram scanned by temperature and surface potential. We find that prewetting phenomenon disappear below a critical droplet size and critical temperature.

Effect of protein type, concentration and oil droplet size on the formation of repulsively jammed elastic nanoemulsion gels

Sodium caseinate (SC)-stabilized 40% oil-in-water nanoemulsions (NEs) could be transformed into elastic gels below a critical droplet size due to increase in ϕeff by a thicker steric barrier of SC, while whey protein (WPI)-stabilized NEs remained liquid due to thinner steric barrier of WPI.

Comment on Kokkola et al. (2008) – Comparisons with analytical solutions from Khvorostyanov and Curry (2007) on the critical droplet radii and supersaturations of CCN with insoluble fractions

Analytical solutions for the critical radii rcr and supersaturations scr of the cloud condensation nuclei with insoluble fractions were derived by Khvorostyanov and Curry (2007, hereafter KC07). Similar solutions were found later by Kokkola et al. (2008, hereafter Kok08); however, Kok08 used the approximation of an ideal dilute solution, while KC07 used more accurate assumptions that account for nonideality of solutions. Kok08 found a large discrepancy with KC07 in the critical supersaturations. Various possible reasons of this are analyzed. It is shown that the major discrepancy was caused by a simple mistake in Kok08 in the equation for the critical supersaturation: erroneous ''plus'' sign between the Kelvin and Raoult terms instead of correct ''minus'' sign. If this mistake is corrected, the equations from Kok08 mostly repeat the equations from KC07, except that Kok08 use the dilute solution approximation. If the mistake in Kok08 is corrected, then the differences in the critical radii and supersaturations do not exceed 16–18%, which characterizes the possible errors of an ideal diluted solution approximation. If the Kok08 scheme is corrected and applied to a nonideal solution, then the difference with KC07 does not exceed 0.4–1%.