Toward a molecular-level understanding of homogeneous bubble and droplet nucleation in simple fluids

Mark Jacob Uline, Purdue University

Abstract

Homogeneous nucleation is the activated process by which the new phase (vapor, liquid or solid) is formed from a bulk metastable fluid (superheated liquid, super-cooled vapor or liquid) in the absence of impurities or solid surfaces. In order to generate new insights into the molecular-level mechanisms for nucleation, an adaption of density-functional theory (DFT) is used to calculate the free energy surface, or W( n, v), of both homogeneous bubble formation within the pure-component superheated Lennard-Jones (LJ) liquid and homogeneous droplet formation within the pure-component supercooled LJ vapor. The DFT calculations, which constrain n, the number of particles located inside the bubble, for a fixed volume, v, indicate that W(n, v ) for either a bubble or a droplet is quite different from what is predicted from classical nucleation theory (CNT). For example, DFT reveals that liquid-to-vapor nucleation is more appropriately described by an “activated instability”. As the free energy barrier is surmounted, W( n, v) abruptly ends along a locus of instabilities. Further growth of the post-critical bubbles must necessarily proceed via a mechanism appropriate for an unstable system. DFT also suggests that there are a multitude of plausible transition pathways for the pre-critical bubble to cross the activation barrier, which is in contrast to the CNT prediction of a well-defined saddle point providing the only likely transition pathway. Some of these conclusions also apply to vapor-to-liquid nucleation, though key differences between both free energy surfaces are noted. In contrast to the bubble surface, W(n, v) for droplet formation does not abruptly end after the ridge is surmounted. Nevertheless, limits of stability do appear when the liquid clusters become too dense, such that the surrounding supercooled vapor can no longer maintain its vapor-like density. In the end, the DFT analysis of vapor-to-liquid nucleation serves to highlight the important differences between droplet and bubble nucleation, indicating that any future descriptions of bubble formation cannot solely rely on ideas that have emerged from the study of droplet formation. Furthermore, several key features of W(n, v) were found to collapse onto a single curve in a nearly temperature-independent fashion when plotted against a scaling parameter quantifying the location of the state point in the metastable region. We find that the ridge of unstable equilibrium points scales in both bubble and droplet nucleation. We also find that the radius of the stability limits scale for bubble nucleation; however, the work at the stability limit does not scale. Finally, a surface thermodynamic analysis relevant to the adapted DFT is derived. The surface tension and Tolman length of an embryo is determined as a function of v and n and compared to previous results.

Degree

Ph.D.

Advisors

Corti, Purdue University.

Subject Area

Chemical engineering

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