Problems with one-sided constraints for Navier-Stokes equations and the dynamic contact angle

1990 ◽  
Vol 31 (2) ◽  
pp. 185-197 ◽  
Author(s):  
C. Baiocci ◽  
V. V. Pukhnachev
Keyword(s):  
Contact Angle ◽  
Stokes Equations ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Navier Stokes ◽  
Navier Stokes Equations

Level Set Based Modeling of Electrowetting on Dielectrics Droplet

2012 ◽  
Vol 461 ◽  
pp. 138-141
Author(s):  
Yin Xia Chang ◽  
Si Xiang Zhang ◽  
Wei Zhou ◽  
Bao Liu
Keyword(s):  
Surface Tension ◽  
Contact Angle ◽  
Level Set ◽  
Stokes Equations ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Navier Stokes ◽  
Electric Force ◽  
Electrowetting On Dielectric ◽  
Static Contact

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.

scholarly journals Study of Fluids Motion in a Microchannel under Heat Source

2020 ◽  
Vol 2 (SI2) ◽  
pp. First
Author(s):  
Long Thanh Le
Keyword(s):  
Contact Angle ◽  
Heat Source ◽  
Water Droplet ◽  
Stokes Equations ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Immiscible Fluids ◽  
Navier Stokes ◽  
Two Phase ◽  
Receding Contact Angle

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.

Numerical Study of a Small Droplet Movement in a Microchannel under Heat Source

2019 ◽  
Vol 894 ◽  
pp. 104-111
Author(s):  
Thanh Long Le ◽  
Jyh Chen Chen ◽  
Huy Bich Nguyen
Keyword(s):  
Contact Angle ◽  
Heat Source ◽  
Water Droplet ◽  
Stokes Equations ◽  
Numerical Study ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Initial Position ◽  
Immiscible Fluids ◽  
Two Phase

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.

scholarly journals Numerical investigation of the thermocapillary migration of a water droplet in a microchannel by applying a heat source

2020 ◽  
Vol 3 (SI1) ◽  
pp. First
Author(s):  
Le Thanh Long ◽  
Jyh Chen Chen ◽  
Nguyen Huy Bich
Keyword(s):  
Contact Angle ◽  
Heat Source ◽  
Water Droplet ◽  
Stokes Equations ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Initial Position ◽  
Immiscible Fluids ◽  
Two Phase ◽  
Thermocapillary Migration

The migration of a small droplet has been developed during the last two decades due to its applications in industry and high technology such as MEMS and NEMS devices, Lap-On-a- chip, transportation of fluids and so on. There have many studies on this topic in which the energy source as a driving force for the moving of a droplet is quite a difference like heating, magnetics, pressure, electric, laser, and so on. In this study, the numerical computation is used to investigate the transient thermocapillary migration of a water droplet in a micro-channel under the effect of heating source. 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 and continuity equation coupled with the energy equation. Both the upper wall and the bottom wall of the microchannel are set to be ambient temperature. 40mW heat source is placed at a 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. Furthermore, the results also indicate that 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 the actuation process.

scholarly journals Directional Water Wicking on a Metal Surface Patterned by Microchannels

Materials ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 490
Author(s):  
Nima Abbaspour ◽  
Philippe Beltrame ◽  
Marie-Christine Néel ◽  
Volker P. Schulz
Keyword(s):  
Contact Angle ◽  
Stokes Equations ◽  
Industrial Applications ◽  
Type Structure ◽  
Navier Stokes ◽  
Small Space ◽  
Dimensionless Numbers ◽  
Navier Stokes Equations ◽  
Static Contact ◽  
Insight Into

This work focuses on the simulation and experimental study of directional wicking of water on a surface structured by open microchannels. Stainless steel was chosen as the material for the structure motivated by industrial applications as fuel cells. Inspired by nature and literature, we designed a fin type structure. Using Selective Laser Melting (SLM) the fin type structure was manufactured additively with a resolution down to about 30 μm. The geometry was manufactured with three different scalings and both the experiments and the simulation show that the efficiency of the water transport depends on dimensionless numbers such as Reynolds and Capillary numbers. Full 3D numerical simulations of the multiphase Navier-Stokes equations using Volume of Fluid (VOF) and Lattice-Boltzmann (LBM) methods reproduce qualitatively the experimental results and provide new insight into the details of dynamics at small space and time scales. The influence of the static contact angle on the directional wicking was also studied. The simulation enabled estimation of the contact angle threshold beyond which transport vanishes in addition to the optimal contact angle for transport.

Numerical Study of Liquid Slug Stability During Adiabatic Two Phase Flow Inside a Minichannel

2007 ◽  
Author(s):  
A. Mukherjee ◽  
J. S. Allen
Keyword(s):  
Contact Angle ◽  
Continuity Equation ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Phase Flow ◽  
Liquid Slug ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Liquid Plug

The present study is performed to analyze stability of a liquid meniscus inside a microchannel. A liquid plug is placed inside a microchannel and the shape and stability of upstream and downstream interfaces have been studied for different airflow rates. The thickness of the liquid plug and the contact angle has been varied systematically. In the numerical model the complete Navier-Stokes equations along with continuity equation are solved using the SIMPLER method. The liquid vapor interface is captured using the level set technique. The liquid plug is seen to move downstream along with the air and surface instabilities are noted at the upstream and downstream interfaces. At low contact angle, water is found to accumulate at the channel corners due to capillary forces causing the slug to disintegrate. The numerical results are found to be qualitatively similar to experimental data.

scholarly journals On a two-point boundary value problem for the 2-D Navier-Stokes equations arising from capillary effect

2020 ◽  
Vol 15 ◽  
pp. 17
Author(s):  
Bhagya Athukorallage ◽  
Ram Iyer
Keyword(s):  
Contact Angle ◽  
Boundary Value Problem ◽  
Liquid Surface ◽  
Stokes Equations ◽  
Contact Angle Hysteresis ◽  
Boundary Value ◽  
Navier Stokes ◽  
Classical Solutions ◽  
Point Boundary ◽  
Navier Stokes Equations

In this article, we consider the motion of a liquid surface between two parallel surfaces. Both surfaces are non-ideal, and hence, subject to contact angle hysteresis effect. Due to this effect, the angle of contact between a capillary surface and a solid surface takes values in a closed interval. Furthermore, the evolution of the contact angle as a function of the contact area exhibits hysteresis. We study the two-point boundary value problem in time whereby a liquid surface with one contact angle at t = 0 is deformed to another with a different contact angle at t = ∞ while the volume remains constant, with the goal of determining the energy loss due to viscosity. The fluid flow is modeled by the Navier-Stokes equations, while the Young-Laplace equation models the initial and final capillary surfaces. It is well-known even for ordinary differential equations that two-point boundary value problems may not have solutions. We show existence of classical solutions that are non-unique, develop an algorithm for their computation, and prove convergence for initial and final surfaces that lie in a certain set. Finally, we compute the energy lost due to viscous friction by the central solution of the two-point boundary value problem.

scholarly journals Numerical Investigation of Different Dynamic Contact Angle Models for a Droplet Impacting a Surface in OpenFOAM

2019 ◽  
Vol 3 (1) ◽  
pp. 9-17
Author(s):  
Ndivhuwo Musehane ◽  
Rhameez Herbst
Keyword(s):  
Surface Tension ◽  
Contact Angle ◽  
Contact Line ◽  
Dynamic Contact Angle ◽  
Dynamic Contact ◽  
Navier Stokes ◽  
Spreading Process ◽  
Moving Contact Line ◽  
Continuity Equations ◽  
Moving Contact

Computational Fluid Dynamics (CFD) is used to study the spreading process of a water droplet with a radius of 0.00275mm impacting a wax surface at a velocity of 1.18ms−1 . This type of flow is considered to be Multiphase, incompressible, laminar, surface tension dominated and is governed by the Navier stokes and continuity equations. To accurately model the spreading process 3 different contact angle models are investigated, two of which take into account the moving contact line. The governing equations are solved using the open source C++ library OpenFOAM, which uses a Finite Volume Method (FVM) of discretization and a Volume Of Fluid (VOF) interface capturing method. The VOF method is known to produce unphysical velocities when high pressure gradients exist between the two phases, thus a numerical improvement is implemented to reduce the magnitudes of the unphysical velocities. The improvement reduces the magnitudes of the unphysical velocities and as shown in literature their magnitudes increase with an increase in surface tension dominance. The improvement is implemented together with different contact angle models and results obtained show that contact angle models that take into account the moving contact line gives a good correlation of the spreading diameter obtained numerically with the one obtained experimentally.

Sign in / Sign up

Export Citation Format

Share Document