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  • Liquid Particles Tracing in Three-dimensional Buoyancy-driven Flows
  • Abstract Buoyancy-driven convective flows are numerically analyzed in a cubic enclosure, containing a liquid subjected to a temperature difference between opposite lateral walls; all other walls are thermally insulated. The stationary gravity vector is perpendicular to the applied temperature gradient. The steady flow patterns are investigated within the framework of a liquid particles tracing technique. Three tracing techniques are compared: the first, based on a trilinear interpolation of the liquid velocity defined on the computational grid and an eighth order in time Runge-Kutta method; the second and the third, using a resampling the velocity field on a new approximately twice finer…
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  • Review: Possible strategies for the control and stabilization of Marangoni flow in laterally heated floating zones
  • Abstract The paper presents a comparative and critical analysis of some theoretical/experimental/numerical arguments concerning the possible stabilization of the surface-tension-driven (Marangoni) flow in the Floating Zone technique and in various related fluid-dynamic models. It is conceived as a natural extension of the focused overview published in Cryst. Res. Tech. 40(6), 531, (2005) where much room was devoted to discuss the intrinsic physical mechanisms responsible for three-dimensional and oscillatory flows in a variety of technological processes. Here, a significant effort is provided to illustrate the genesis of possible control strategies (many of which are still in a very embryonic condition), the underlying…
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  • Locomotion of a Viscous Drop, Induced by the Internal Secretion of Surfactant: Boundary Effects
  • Abstract We have studied the motion of a drop, induced by the internal secretion of a surface-active substance, in the vicinity of solid walls or non-deformable liquid-liquid interface under micro-gravity conditions. The secreted substance renders a non-uniform distribution of surfactant along the outer surface that, in turn, results in interfacial stress variation that ultimately leads to a surface motion and to locomotion of the drop. Cases of plane and spherical boundaries have been considered as well as cases of linear and non-linear dependence of the interfacial tension on concentration of surfactant. The dependence of the drop migration velocity on the location…
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  • Implementation of the level set method for continuum mechanics based tumor growth models
  • Abstract A computational framework for simulating growth and transport in biological materials based on continuum models is proposed. The advantages of the finite difference methodology employed are generality and relative simplicity of implementation. The Cartesian mesh/level set method developed here provides a computational tool for the investigation of a host of transport-based tissue/tumor growth models, that are posed as free or moving boundary problems and may exhibit complicated boundary evolution including topological changes. The methodology is tested here on a widely studied "incompressible flow" type tumor growth model with a numerical implementation in two dimensions; comparisons with results obtained from a…
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  • A Computational Study of Bubble Motion in Newtonian and Viscoelastic Fluids
  • Abstract The aim of this paper is to utilize a numerical model to compute bubble motion in quiescent Newtonian and viscoelastic liquids. For our numerical method, we use a coupled level set and volume-of-fluid method with a second order treatment for the jump conditions related to surface tension. We investigate axisymmetric gas-liquid systems with large density and viscosity ratios as well as buoyancy-driven flows with complex changes in topology. We present comparisons to previous computational results as well as experimental results.
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  • Thermocapillary Flow and Phase Change in Some Widespread Materials Processes
  • Abstract A few issues in materials science are reviewed with regard to the importance of fluid flows. The effect of convection on generic solidification problems is discussed. One relevant class of flows in melts is those driven by surface tension gradients. In welding this thermo- or solutocapillary flow will determine the penetration depth, and will depend very sensitively on the composition of the material, through the dependence of surface tension on temperature, presence of surfactants, etc. In crystal growth the convective motion in the melt may cause instabilities that are often undesired in practical processes. The unsteady flow structure can cause…
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  • Phase Distribution of Bubbly Flows under Terrestrial and Microgravity Conditions
  • Abstract We use direct numerical simulations to study phase distribution of bubbles under terrestrial and microgravity conditions. The full Navier-Stokes and energy equations, for the flows inside and outside the bubbles, are solved using a front tracking/finite difference technique. Both nearly spherical and deformable bubbles are considered. For buoyancy-driven flows, spherical bubbles at Re = O(10) and deformable ones at Re = O(100) exhibit a uniform spatial distribution at quasi steady-state conditions, while nearly spherical bubbles at Re = O(100) form horizontal rafts. Bubbles, driven by thermocapillary effects in microgravity, also form horizontal rafts, but due to an entirely different mechanism.…
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  • Numerical Simulation of CZ Crystal Growth of Oxide
  • Abstract In this paper, our recent numerical studies on the Czochralski (CZ) crystal growth of oxide are surveyed. In the first part of the analysis, a "global" heat transfer model for an inductively heated CZ furnace is introduced and depicted in detail. It is emphasized that accounting for the internal radiation within the crystal and/or melt is of crucial importance since they are often semitransparent to infrared radiation. Results coming from such a "global" approach suggest that the melt/crystal interface shape is strongly affected by the optical properties of the crystal, of the melt and by the melt convection. The second…
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