Dick Bedeaux (Norwegian University of Science and Technology)
We analyze the curvature dependence of the heat and mass transfer resistances of the surface of nano bubbles and droplets. For this we use an extension [1-7] of the so-called square gradient model introduced by van der Waals to describe the density profile in a one-component fluid, and by Kahn and Hilliard for mixtures, to time dependent problems. This enables us to calculate equilibrium and non-equilibrium density profiles for the two phase state. Together with earlier derived integral relations  we are then able to calculate these resistances. It is found that the resistances change considerably in the nanoscale range. This agrees with molecular dynamics results . In earlier work we studied the stability of nanoscale droplets and bubbles [10,11].  D. Bedeaux, E. Johannessen and A. Røsjorde, The Nonequilibrium van der Waals Square Gradient Model I: The Model and its Numerical Solution, Physica A 330 (2003) 329-353.  E. Johannessen and D. Bedeaux, The Nonequilibrium van der Waals Square Gradient Model II: Local Equilibrium of the Gibbs Surface, Physica A 330 (2003) 354-372.  E. Johannessen and D. Bedeaux, The Nonequilibrium van der Waals Square Gradient Model III: Heat and Mass Transfer Coefficients, Physica A 336 (2004) 252-270.  K.S. Glavatskiy and D. Bedeaux, Non-equilibrium properties of a two-dimensional isotropic interface in a two-phase mixture as described by the square gradient model, Phys. Rev. E 77 (2008) 061101-17.  K.S. Glavatskiy and D. Bedeaux, Numerical solution and verification of local equilibrium for the flat interface in the two-phase binary mixture, Phys. Rev. E 79 (2009) 031608, 1-19.  K. S. Glavatskiy and D. Bedeaux, Transport of heat and mass in a two-phase mixture. From a continuous to a discontinuous description, J. Chem. Phys. 133 (2010) 144709-17.  K. S. Glavatskiy and D. Bedeaux, Resistances for heat and mass transfer through a liquid-vapor interface in a binary mixture, J. Chem. Phys. 133 (2010) 234501.  E. Johannessen and D. Bedeaux, Integral Relations for the Heat and Mass Transfer Resistivities of the Liquid-Vapor Interface, Physica A 370 (2006) 258-274.  A. Lervik, F. Bresme, S. Kjelstrup, D. Bedeaux and J.M. Rubi, Heat transfer in Protein-water interfaces, Phys. Chem. Chem. Phys. 12 (2010) 1610-1617.  K. S. Glavatskiy, D. Reguera, and D. Bedeaux, Effect of compressibility in bubble formation in closed systems, J. Chem. Phys. 138 (2013) 204708-6.  Ø. Wihelmsen, D. Bedeaux, S. Kjelstrup, D. Reguera, Thermodynamic stability of nanosized multicomponent bubbles/droplets: The square gradient theory and the capillary approach, J. Chem. Phys. 140 (2014) 024704-9.