Numerical simulation of incompressible two‐phase flows with a Boussinesq–Scriven interface stress tensor

We consider the numerical simulation of a three‐dimensional two‐phase incompressible flow with a viscous interface. The simulation is based on a sharp interface Navier–Stokes model and the Boussinesq–Scriven constitutive law for the interface viscous stress tensor. In the recent paper [Soft Matter 7, 7797–7804, 2011], a model problem with a spherical droplet in a Stokes Poiseuille flow with a Boussinesq–Scriven law for the surface viscosity has been analyzed. In that paper, relations for the droplet migration velocity are derived. We relate the results obtained with our numerical solver for the two‐phase Navier–Stokes model to these theoretical relations. Copyright © 2013 John Wiley & Sons, Ltd.     

The derivation of thermal relaxation time between two-phase bubbly flow

Thermal relaxation time constant is derived analytically for the relaxed model with unequal phase-temperatures of a vapour bubble at saturation temperature and a non-steady temperature field around the growing vapour bubble. The energy and state equation are solved between two finite boundary conditions. Thermal relaxation time perform a good agreement with Mohammadein (in Doctoral thesis, PAN, Gdansk, 1994) and Moby Dick experiment in terms of non-equilibrium homogeneous model (Bilicki et al. in Proc R Soc Lond A428:379–397, 1990) for lower values of initial void fraction. Thermal relaxation is affected by Jacob number, superheating, initial bubble radius and thermal diffusivity.     

Temperature distribution in a mixture surrounding a growing vapour bubble

The paper presents temperature distribution of superheated liquid during the growth of spherical vapour bubble between two-phase temperatures. The heat equation is resolved by the modification of similarity parameter method of Screven [Chem Engng Sci 10:1-13(1959)] between two finite boundaries. Under these conditions, the growth of vapour bubble and temperature are obtained analytically in an implicit form which are different than that obtained before. The growth rate is obtained as a generalized formula compared with Plesset amd Zwick and Scriven et al. theories [J Appl Phys 25:493-500(1954);Chem Engng Sci 10:1-13(1959)]. The growth and temperature field affected by the initial superheating and thermal diffusivity.