Thermodynamic stability of nanosized multicomponent bubbles/droplets: The square gradient theory and the capillary approach

Formation of nanosized droplets/bubbles from a metastable bulk phase is connected to many unresolved scientific questions. We analyze the properties and stability of multicomponent droplets and bubbles in the canonical ensemble, and compare with single-component systems. The bubbles/droplets are described on the mesoscopic level by square gradient theory. Furthermore, we compare the results to a capillary model which gives a macroscopic description. Remarkably, the solutions of the square gradient model, representing bubbles and droplets, are accurately reproduced by the capillary model except in the vicinity of the spinodals. The solutions of the square gradient model form closed loops, which shows the inherent symmetry and connected nature of bubbles and droplets. A thermodynamic stability analysis is carried out, where the second variation of the square gradient description is compared to the eigenvalues of the Hessian matrix in the capillary description. The analysis shows that it is impossible to stabilize arbitrarily small bubbles or droplets in closed systems and gives insight into metastable regions close to the minimum bubble/droplet radii. Despite the large difference in complexity, the square gradient and the capillary model predict the same finite threshold sizes and very similar stability limits for bubbles and droplets, both for single-component and two-component systems.

Effect of compressibility in bubble formation in closed systems

We analyze the stability of small bubbles in a closed system with fixed volume, temperature, and number of molecules. We show that there exists a minimum stable size of a bubble. Thus there exists a range of densities where no stable bubbles are allowed and the system has a homogeneous density which is lower than the coexistence density of the liquid. This becomes possible due to the finite liquid compressibility. Capillary analysis within the developed"modified bubble" model illustrates that the existence of the minimum bubble size is associated to the compressibility and it is not possible when the liquid is strictly incompressible. This finding is expected to have very important implications in cavitation and boiling.

Approximate solution to the speed of spreading viruses

Recently, it has been shown that the speed of virus infections can be explained by time-delayed reactiondiffusion [J. Fort and V. Me´ndez, Phys. Rev. Lett. 89, 178101 (2002)], but no analytical solutions were found. Here we derive formulas for the front speed, valid in appropriate limits. We also integrate numerically the evolution equations of the system. There is good agreement with both numerical and experimental speeds