A Phase Field Modeling Study of the Rayleigh-Taylor Instability Subject to a Horizontal Electric Field

2013 ◽  
Author(s):  
Qingzhen Yang ◽  
Zhengtuo Zhao ◽  
Ben Q. Li ◽  
Yucheng Ding
Keyword(s):  
Electric Field ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Taylor Instability ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Dielectric Fluids ◽  
Fortran Code ◽  
Rayleigh Taylor Instability

A numerical phase field model is developed to investigate the Rayleigh-Taylor instability (RTI) subject to a horizontal electric field. The model entails the simultaneous solution of the electric field equation and the Navier-Stokes equation for fluid flow coupled with the phase field model for the evolution of the fluid-fluid interface deformation and morphology. The in-house Fortran code was developed to enable the computing. Results show that, for pure dielectric fluids, the presence of the horizontal electric field induces polarization charges and produces a Korteweg-Helmholtz force which acts to suppress the RTI. For poorly conducting liquids, for which a leaky dielectric description is more appropriate. In this model, both polarization and free charges present. The effect of the free charge in this case depends on the specific values of λε and λσ. For the fluids of λε >1, it aggravates RTI if λσ<λε, and suppresses that when λσ>λε.

Phase Field Modeling of Nonequilibrium Patterns on the Surface of a Liquid Film Under Lateral Oscillations at the Substrate

2014 ◽  
Vol 24 (09) ◽  
pp. 1450110 ◽  
Author(s):  
Rodica Borcia ◽  
Michael Bestehorn
Keyword(s):  
Liquid Film ◽  
Phase Field ◽  
Field Model ◽  
Phase Field Model ◽  
Solid Substrate ◽  
Navier Stokes ◽  
Bottom Plate ◽  
Navier Stokes Equation ◽  
Harmonic Vibrations ◽  
Spatial Dimensions

We use a phase field model which couples the generalized Navier–Stokes equation (including the Korteweg stress tensor) with the continuity equation for studying nonlinear pattern formation on the surface of a liquid film under (linear and circular) lateral harmonic vibrations at the solid substrate. First, we prove the thermodynamic consistency of our phase field model. Next, we present computer simulations in three spatial dimensions. We illustrate nonequilibrium patterns at the instability onset, confirming in this way the results recently reported in Phys. Rev. E 88, 023025 (2013). The lateral profiles of the deflected surface are compared with those reported in J. Fluid Mech. 686, 409 (2011) for Faraday instability excited by vertical harmonic vibrations at the bottom plate.

scholarly journals Phase-field model for the Rayleigh–Taylor instability of immiscible fluids

2009 ◽  
Vol 622 ◽  
pp. 115-134 ◽  
Author(s):  
ANTONIO CELANI ◽  
ANDREA MAZZINO ◽  
PAOLO MURATORE-GINANNESCHI ◽  
LARA VOZELLA
Keyword(s):  
Phase Field ◽  
Field Model ◽  
Stokes Equations ◽  
Phase Field Model ◽  
Terminal Velocity ◽  
Immiscible Fluids ◽  
Taylor Instability ◽  
Upper And Lower Bounds ◽  
Weakly Nonlinear ◽  
Rayleigh Taylor Instability

The Rayleigh–Taylor instability of two immiscible fluids in the limit of small Atwood numbers is studied by means of a phase-field description. In this method, the sharp fluid interface is replaced by a thin, yet finite, transition layer where the interfacial forces vary smoothly. This is achieved by introducing an order parameter (the phase-field) continuously varying across the interfacial layers and uniform in the bulk region. The phase-field model obeys a Cahn–Hilliard equation and is two-way coupled to the standard Navier–Stokes equations. Starting from this system of equations we have first performed a linear analysis from which we have analytically rederived the known gravity–capillary dispersion relation in the limit of vanishing mixing energy density and capillary width. We have performed numerical simulations and identified a region of parameters in which the known properties of the linear phase (both stable and unstable) are reproduced in a very accurate way. This has been done both in the case of negligible viscosity and in the case of non-zero viscosity. In the latter situation, only upper and lower bounds for the perturbation growth rate are known. Finally, we have also investigated the weakly nonlinear stage of the perturbation evolution and identified a regime characterized by a constant terminal velocity of bubbles/spikes. The measured value of the terminal velocity is in agreement with available theoretical prediction. The phase-field approach thus appears to be a valuable technique for the dynamical description of the stages where hydrodynamic turbulence and wave-turbulence come into play.

scholarly journals Experimental and numerical modeling for flattening and rapid solidification with crystallization behavior of supersonic ceramic droplets

2020 ◽  
Author(s):  
Y. Wang ◽  
Y Bai ◽  
K Wu ◽  
J Zhou ◽  
M G Shen ◽  
...  
Keyword(s):  
Rapid Solidification ◽  
Phase Field ◽  
Crystallization Behavior ◽  
Field Model ◽  
Solidification Rate ◽  
Phase Field Model ◽  
Oriented Attachment ◽  
Navier Stokes ◽  
Columnar Grains ◽  
And Migration

Abstract Successive impingement of supersonic droplets after refining in plasma jet usually forms a fine-lamellar structured coating with high mechanical properties. However, the comprehensive process (such as flattening, rapid solidification and crystallization) of high-velocity impact of refined droplets is difficult to understand. In this study, an experimental study showed that the content of refinement droplets reached to 90 % and displayed the multi-scale equiaxed grains morphology at extremely rapid solidification rate. Phase-field model revealed a hybrid coalescence growth of oriented attachment and migration of grains boundary under the dynamic temperature gradient. Furthermore, an optimized numerical model that consisted of the Navier-Stokes and energy balance equations coupled with the Cahn-Hilliard and phase-field model for growth orientation of grains was developed to accurately reproduce the comprehensive process of refined supersonic droplets. The size distribution and crystallographic orientation of columnar grains for single or two flattened droplets were in a good agreement with the experimental results. The interface between two-flattened droplets exhibited an epitaxial growth of columnar grains. This optimized model can be an effective method in predicting the flattening and solidification with crystallization behavior of droplets during plasma spraying.

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