Date: Tuesday 6th of December 2016, 13:30.
Location: MC3107 (Media, Humanities & Technology Building).

‘Curvature dependence of the heat and mass transfer resistances of the surface of nano bubbles and droplets’

by Dick Bedeaux,
Department of Chemistry, Norwegian University of Science and Technology, 7491 Trondheim, Norway.

Abstract:

We analyse 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 [8] we are then able to calculate these resistances for a hexane-cyclohexane mixture [12], argon [13, 14] and for water [15]. It is found that the resistances change considerably in the nanoscale range. This agrees with molecular dynamics results [9]. In earlier work we studied the stability of nanoscale droplets and bubbles [10, 11]. Furthermore we calculated the Tolman length and the rigidities for argon and water [16, 17].
[1] 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.
[2] 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.
[3] 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
[4] 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.
[5] 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
[6] 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
[7] 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
[8] 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
[9] 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
[10] K. S. Glavatskiy, D. Reguera, and D. Bedeaux, Effect of compressibility in bubble formation in closed systems, J. Chem. Phys. 138 (2013) 204708-6
[11] 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
[12] Ø Wilhelmsen, D Bedeaux and S Kjelstrup, Heat and mass transfer through interfaces of nanosized bubbles/droplets: the influence of interface curvature. Phys. Chem. Chem. Phys. 16 (2014) 10573-10586.
[13] Ø Wilhelmsen, TT Trinh, S Kjelstrup, TS van Erp and D Bedeaux, Heat and Mass Transfer across Interfaces in Complex Nano-Geometries, Phys. Rev. Letters 114 (2015) 065901.
[14] Ø Wilhelmsen, TT Trinh, S Kjelstrup and D Bedeaux, Influence of Curvature on the Transfer Coefficients for Evaporation and Condensation of Lennard-Jones Fluid from Square-Gradient Theory and Nonequilibrium Molecular Dynamics, J. Phys. Chem. C 119 (2015) 8160-8173.
[15] Ø Wilhelmsen, TT. Trinh, A Lervik, VK Badam, S Kjelstrup, and D Bedeaux, Coherent description of transport across the water interface: From nanodroplets to climate models, Phys. Rev. E, Accepted 8 Febr. 2016
[16] Ø Wilhelmsen,  D Bedeaux and D Reguera, Tolman length and rigidity constants of the Lennard-Jones fluid, J. Chem. Phys. 142 (2015) 064706 (11).
[17] Ø Wilhelmsen,  D Bedeaux and D Reguera, Communication: Tolman length and rigidity constants of water and their role in nucleation, J. Chem. Phys. 142 (2015) 171103 (5).