10/10/2022
By Joanne Gagnon-Ketchen
Abstract:
The Young—Laplace, Kelvin, and Gibbs-Thomson equations form a cornerstone of colloidal and surface sciences and have found successful applications in many subfields of physics, chemistry, and biology. The Gibbs – Thomson effect for example predicts that small crystals are in equilibrium with their liquid melt at a lower temperature than large crystals and the positive interfacial energy increases the energy required to form small particles with a high curvature interface. In cases of liquids contained within porous media (confined geometry), the effect indicates decreasing the freezing / melting temperatures and the increment of the temperature is inversely proportional to the pore size. The Kelvin equation, on other hand, predicts a radius of a capillary condensed liquid meniscus that plays important role in adhesion, modulates kinetic friction and induces cloud formation. These phenomena can be reformulated for systems with arbitrarily curved surface boundaries and can be asked the following question: can one use the equations to predict the melting temperature for system phase transitions? The answer is no mainly because systems boundaries are not necessarily constant mean curvature shapes in general and the equations hold only for simple geometries (sphere, plane, or cylinder). We derived equations of motions for moving manifolds and consequently resolved generalization problems of the Young-Laplace, Kelvin, and Gibbs—Thomson equations for arbitrarily curved surfaces. Due to the generality of equations, we clarify that at appropriate internal/external pressure conditions systems, bounded by surfaces, may adopt any shape and thermal stability is strongly influenced by geometries of confined spaces. The equations are universally true for any surfaces: atomic, molecular, micro or macro scale, real or virtual, Riemannian or pseudo-Riemannian, active or passive and can be used to predict the temperature distribution in space-time if one assumes that it is arbitrarily curved hoper-surface.
Bio:
David Svintradze is the Research and Innovation Committee Professor and Professor of Biophysics at New Vision University in Tbilisi, Georgia. He received his PhD in Physics from the Tbilisi State University in Georgia in 2006 and did his postdoctoral fellowship at Virginia Commonwealth University in Richmond, VA. He served as Assistant Professor in the Department of Physics at Tbilisi State University from 2012 to 2017 and joined New Vision University in 2021. Svintradze’s research interests include new physics-inspired by biological processes such as the conformational motion of biological macromolecules and cell motility. He has authored more than 30 publications and given several invited international conference talks. He has also received funding from several sources including the National Science Foundation of Georgia.