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.

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.

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.

On a SAV-MAC scheme for the Cahn–Hilliard–Navier–Stokes phase-field model and its error analysis for the corresponding Cahn–Hilliard–Stokes case

2020 ◽  
Vol 30 (12) ◽  
pp. 2263-2297
Author(s):  
Xiaoli Li ◽  
Jie Shen
Keyword(s):  
Error Analysis ◽  
Phase Field ◽  
Field Model ◽  
Chemical Potential ◽  
Phase Field Model ◽  
Auxiliary Variable ◽  
Field Variable ◽  
Second Order ◽  
Navier Stokes ◽  
Order Error

We construct a numerical scheme based on the scalar auxiliary variable (SAV) approach in time and the MAC discretization in space for the Cahn–Hilliard–Navier–Stokes phase- field model, prove its energy stability, and carry out error analysis for the corresponding Cahn–Hilliard–Stokes model only. The scheme is linear, second-order, unconditionally energy stable and can be implemented very efficiently. We establish second-order error estimates both in time and space for phase-field variable, chemical potential, velocity and pressure in different discrete norms for the Cahn–Hilliard–Stokes phase-field model. We also provide numerical experiments to verify our theoretical results and demonstrate the robustness and accuracy of our scheme.

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