scholarly journals Investigation of behavior of the dynamic contact angle on the basis of the Oberbeck-Boussinesq approximation of the Navier-Stokes equations

2016 ◽  
Vol 84 ◽  
pp. 00014 ◽  
Author(s):  
Olga Goncharova ◽  
Alla Zakurdaeva ◽  
Jean-Claude Legros
2012 ◽  
Vol 461 ◽  
pp. 138-141
Author(s):  
Yin Xia Chang ◽  
Si Xiang Zhang ◽  
Wei Zhou ◽  
Bao Liu

This paper discusses the modeling of Electrowetting On Dielectric (EWOD) device that moves fluid droplets through surface tension effects and electric force. Instead of using a static contact angle as most papers did, we take the dynamic contact angle into count by using expression proposed by Voinov and Tanner. Firstly, the level set model and its initial values is present. Then the governing equations are discussed, and the diffused format is adopted for density and viscosity varies to smooth over the interface. The detailed expression for surface tension and electric force are also described for Navier–Stokes equations. After presenting the boundary conditions, the steps of numerical implementation are detailed.


Author(s):  
Long Thanh Le

In this study, the numerical computation is used to investigate the transient thermocapillary migration of a water droplet in a Microchannel. For tracking the evolution of the free interface between two immiscible fluids, we employed the finite element method with the two-phase level set technique to solve the Navier-Stokes equations coupled with the energy equation. Both the upper wall and the bottom wall of the microchannel are set to be an ambient temperature. The heat source is placed at the left side of a water droplet. When the heat source is turned on, a pair of asymmetric thermocapillary convection vortices is formed inside the droplet and the thermocapillary on the receding side is smaller than that on the advancing side. The temperature gradient inside the droplet increases quickly at the initial times and then decreases versus time. Therefore, the actuation velocity of the water droplet first increases significantly, and then decreases continuously. The dynamic contact angle is strongly affected by the oil flow motion and the net thermocapillary momentum inside the droplet. The advancing contact angle is always larger than the receding contact angle during actuation process.


2017 ◽  
Vol 12 (2) ◽  
pp. 111-118
Author(s):  
Vladimir Popov

Under study is the applicability of the high-frequency electromagnetic field impulse for metal heating and melting with a view to its subsequent alloying. The processes of heating, phase transition, heat and mass transfer in the molten metal, solidification of the melt are considered with the aid the proposed mathematical model. The substrate surface is covered with a layer of alloying substances. The distribution of the electromagnetic energy in the metal is described by empirical formulas. Melting and solidification of the metal is considered at the Stephan’s approximation. The flow in the liquid is described by the Navier – Stokes equations in the Boussinesq approximation. According to the results of numerical experiments, the flow structure in the melt and distribution of the alloying substances was evaluated versus the characteristics of induction heating


2019 ◽  
Vol 894 ◽  
pp. 104-111
Author(s):  
Thanh Long Le ◽  
Jyh Chen Chen ◽  
Huy Bich Nguyen

In this study, the numerical computation is used to investigate the transient movement of a water droplet in a microchannel. For tracking the evolution of the free interface between two immiscible fluids, we employed the finite element method with the two-phase level set technique to solve the Navier-Stokes equations coupled with the energy equation. Both the upper wall and the bottom wall of the microchannel are set to be an ambient temperature. 40mW heat source is placed at the distance of 1 mm from the initial position of a water droplet. When the heat source is turned on, a pair of asymmetric thermocapillary convection vortices is formed inside the droplet and the thermocapillary on the receding side is smaller than that on the advancing side. The temperature gradient inside the droplet increases quickly at the initial times and then decreases versus time. Therefore, the actuation velocity of the water droplet first increases significantly, and then decreases continuously. The dynamic contact angle is strongly affected by the oil flow motion and the net thermocapillary momentum inside the droplet. The advancing contact angle is always larger than the receding contact angle during actuation process.


2018 ◽  
Vol 855 ◽  
pp. 43-66 ◽  
Author(s):  
Ke Wu ◽  
Bruno D. Welfert ◽  
Juan M. Lopez

The dynamic response to shear of a fluid-filled square cavity with stable temperature stratification is investigated numerically. The shear is imposed by the constant translation of the top lid, and is quantified by the associated Reynolds number. The stratification, quantified by a Richardson number, is imposed by maintaining the temperature of the top lid at a higher constant temperature than that of the bottom, and the side walls are insulating. The Navier–Stokes equations under the Boussinesq approximation are solved, using a pseudospectral approximation, over a wide range of Reynolds and Richardson numbers. Particular attention is paid to the dynamical mechanisms associated with the onset of instability of steady state solutions, and to the complex and rich dynamics occurring beyond.


Author(s):  
V.N. Popov ◽  
A.N. Cherepanov

The purpose of the research was to numerically simulate the processes when melting drops fall on a substrate. The paper deals with the solidification on the metal surface of a binary aluminum alloy modified by activated refractory nanosized particles, which are the centers of crystalline phase nucleation. We formulated a mathematical model which describes the thermo- and hydrodynamic phenomena in the drop upon interaction with a solid substrate, heterogeneous nucleation during melt cooling, and subsequent crystallization. The flow in a liquid is described by the Navier --- Stokes equations in the Boussinesq approximation. The position of the free boundary of the melt is fixed by marker particles moving with the local liquid velocity. On the melt --- substrate contact surface, thermal resistance is taken into account. The hydrodynamic problem is considered under conditions of crystallization of molten metal. The temperature conditions and the kinetics of the growth of the solid phase in the solidifying aluminum alloy are described for various sizes of formed splats. Satisfactory agreement was found between the shape of the splat obtained by the results of numerical simulation and the available experimental data. The adequacy of the crystallization model in the presence of ultradisperse refractory particles in a binary alloy is confirmed. It was determined that, regardless of the size of the drop, bulk crystallization of the metal takes place. It was found that at a high rate of collision of a drop with a substrate during the melt spreading, a small fraction of the solid phase can be formed.


2020 ◽  
Vol 221 (2) ◽  
pp. 1264-1280
Author(s):  
Rene Gassmöller ◽  
Juliane Dannberg ◽  
Wolfgang Bangerth ◽  
Timo Heister ◽  
Robert Myhill

SUMMARY Mantle convection and long-term lithosphere dynamics in the Earth and other planets can be treated as the slow deformation of a highly viscous fluid, and as such can be described using the compressible Navier–Stokes equations. Since on Earth-sized planets the influence of compressibility is not a dominant effect, density deviations from a reference profile are at most on the order of a few percent and using the full governing equations poses numerical challenges, most modelling studies have simplified the governing equations. Common approximations assume a temporally constant, but depth-dependent reference profile for the density (the anelastic liquid approximation), or drop compressibility altogether and use a constant reference density (the Boussinesq approximation). In most previous studies of mantle convection and crustal dynamics, one can assume that the error introduced by these approximations was small compared to the errors that resulted from poorly constrained material behaviour and limited numerical accuracy. However, as model parametrizations have become more realistic, and model resolution has improved, this may no longer be the case and the error due to using simplified conservation equations might no longer be negligible: while such approximations may be reasonable for models of mantle plumes or slabs traversing the whole mantle, they may be unsatisfactory for layered materials experiencing phase transitions or materials undergoing significant heating or cooling. For example, at boundary layers or close to dynamically changing density gradients, the error arising from the use of the aforementioned compressibility approximations can be the dominant error source, and common approximations may fail to capture the physical behaviour of interest. In this paper, we discuss new formulations of the continuity equation that include dynamic density variations due to temperature, pressure and composition without using a reference profile for the density. We quantify the improvement in accuracy relative to existing formulations in a number of benchmark models and evaluate for which practical applications these effects are important. Finally, we consider numerical aspects of the new formulations. We implement and test these formulations in the freely available community software aspect, and use this code for our numerical experiments.


Sign in / Sign up

Export Citation Format

Share Document