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).

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