Development of Surface Tension Model Using Inter-Particle Force in Particle Method Based on Continuum Dynamics

2011 ◽  
Author(s):  
Eiji Ishii ◽  
Taisuke Sugii
Keyword(s):  
Surface Tension ◽  
Fluid Flow ◽  
Particle Method ◽  
Oscillation Period ◽  
Contact Angles ◽  
Particle Methods ◽  
Developed Surface ◽  
Particle Force ◽  
Continuum Dynamics ◽  
Surface Tension Model

The particle method is a useful approach to simulate fluid flows within micro/nano spaces such as micro-electromechanical systems, nano-in-print processes, and head-disk interfaces of hard disk drives. Particle methods are based on continuum dynamics, and some studies have recently extended the scope of these methods to approaches within micro/nano spaces. Surface tension is a dominant force in the fluid flow within micro/nano spaces. However, surface-tension models used in the particle methods need to be improved to achieve more stable and accurate simulation. In the present study, we developed a new surface tension model for the particle method using inter-particle force to improve the stability and accuracy of simulation; the inter-particle force was given by the derivation of potential energy in space. The developed surface tension model was verified using simple benchmark tests: pressure in a round droplet and oscillation period of a square liquid-droplet. The predicted pressure in a round droplet agreed well with that given by the Young-Laplace equation, and the predicted oscillation period of a square droplet agreed well with that given by Lamb’s theory. The wall-adhesion was also verified at various contact angles; heights of droplets on the wall agreed well with those given theoretically. We found that our new surface tension model was useful for simulating fluid flow within micro/nano spaces for particle method.

Spreading-Droplet Simulation With Surface Tension Model Using Inter-Particle Force in Particle Method

2013 ◽  
Author(s):  
Eiji Ishii ◽  
Taisuke Sugii
Keyword(s):  
Surface Tension ◽  
Contact Angle ◽  
Dynamic Contact Angle ◽  
Particle Method ◽  
Dynamic Contact ◽  
Contact Angles ◽  
Particle Methods ◽  
Static Contact ◽  
Particle Force ◽  
Surface Tension Model

Predicting the spreading behavior of droplets on a wall is important for designing micro/nano devices used for reagent dispensation in micro-electro-mechanical systems, printing processes of ink-jet printers, and condensation of droplets on a wall during spray forming in atomizers. Particle methods are useful for simulating the behavior of many droplets generated by micro/nano devices in practical computational time; the motion of each droplet is simulated using a group of particles, and no particles are assigned in the gas region if interactions between the droplets and gas are weak. Furthermore, liquid-gas interfaces obtained from the particle method remain sharp by using the Lagrangian description. However, conventional surface tension models used in the particle methods are used for predicting the static contact angle at a three-phase interface, not for predicting the dynamic contact angle. The dynamic contact angle defines the shape of a spreading droplet on a wall. We previously developed a surface tension model using inter-particle force in the particle method; the static contact angle of droplets on the wall was verified at various contact angles, and the heights of droplets agreed well with those obtained theoretically. In this study, we applied our surface tension model to the simulation of a spreading droplet on a wall. The simulated dynamic contact angles for some Weber numbers were compared with those measured by Šikalo et al, and they agreed well. Our surface tension model was useful for simulating droplet motion under static and dynamic conditions.

Surface Tension Model for Particle Method Using Inter-Particle Force Derived From Potential Energy

2012 ◽  
Author(s):  
Eiji Ishii ◽  
Taisuke Sugii
Keyword(s):  
Surface Tension ◽  
Fluid Flow ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Flow Simulation ◽  
Particle Method ◽  
Surface Force ◽  
Continuous Surface ◽  
Particle Force ◽  
Surface Tension Model

Fluid-flow simulation within micro/nano spaces is essential for designing micro/nano devices, such as those in micro-electro-mechanical systems and nanoimprint processes. Surface tension is a dominant force in the fluid flow within micro/nano spaces. Surface-tension models can be classified into two groups: models based on continuous surface force in immiscible phases, and models based on inter-particle force in miscible phases. The surface-tension model based on inter-particle force for modeling interactions between materials would fit fluid-flow simulation within micro/nano spaces better than the surface-tension model based on continuous surface force. We developed a surface tension model using inter-particle force for use with a particle method in a past study. However, workings of inter-particle forces in miscible phases were not verified. Furthermore, accuracy in three-dimensional simulation needed to be verified. These subjects were verified in this study using simple benchmark tests. First, cohesion based on potential energy was validated to qualitatively check the workings of inter-particle force. The phase separation from the mixed two-phase flow due to inter-particle force was simulated. Next, the inter-particle force at the gas-liquid interface was quantitatively verified using the theory of the Young-Laplace equation; the pressure in a droplet was compared in two- and three-dimensional simulations, and the predicted pressures in a droplet agreed well with this theory. The inter-particle force at the gas-liquid-solid interface for the wall adhesion of a droplet was also verified; the results for wall adhesion in three-dimensional space agreed much better than that in two-dimensional space. We found that our surface tension model was useful for simulating the fluid flow within micro/nano spaces.

A new algorithm for surface tension model in moving particle methods

2007 ◽  
Vol 55 (3) ◽  
pp. 225-240 ◽  
Author(s):  
Shuai Zhang ◽  
Koji Morita ◽  
Kenji Fukuda ◽  
Noriyuki Shirakawa
Keyword(s):  
Surface Tension ◽  
Particle Methods ◽  
Moving Particle ◽  
Surface Tension Model

scholarly journals 140 A development of surface tension model using inter-particle force

2006 ◽  
Vol 2006.19 (0) ◽  
pp. 337-338 ◽  
Author(s):  
Masahiro KONDO ◽  
Seiichi KOSHIZUKA ◽  
Koshiro SUZUKI
Keyword(s):  
Surface Tension ◽  
Particle Force ◽  
Surface Tension Model

Surface Tension Model Using Inter-Particle Force in Particle Method

2007 ◽  
Author(s):  
M. Kondo ◽  
S. Koshizuka ◽  
K. Suzuki ◽  
M. Takimoto
Keyword(s):  
Surface Tension ◽  
Contact Angle ◽  
Continuum Mechanics ◽  
Particle Methods ◽  
Small Scale ◽  
Normal Vector ◽  
Potential Force ◽  
Force Ratio ◽  
Particle Potential ◽  
Particle Force

Moving particle semi-implicit (MPS) method is widely used for the free surface flow analysis. In small scale problems, the surface tension is dominant. There are two approaches to calculate surface tension in particle methods. One is based on continuum mechanics governing equation which needs the normal vector and the curvature calculation. However, it requires complex formulation. The other is introducing inter-particle potential force. It is known that surface tension can be deduced from inter-molecular force. We propose inter-particle force whose potential is similar to the molecular potential. We reveal the inter-relation between this potential force and the surface tension coefficient used in continuum mechanics. The surface tension can be calculated using this inter-particle potential force. The oscillation cycle roughly agrees with the theoretical value. It is also important to introduce the contact angle to the solid wall, as well as the surface tension. The inter-particle force is also available to model the contact angle. The potential force ratio between fluid-fluid and fluid-wall can be derived from Young’s equation. Using this theoretical ratio of potential force, a larger contact angle appears, if we give a smaller potential force ratio.

A NUMERICALLY CONSISTENT MULTIPHASE POISEUILLE FLOW COMPUTATION BY A NEW PARTICLE METHOD

2015 ◽  
Vol 76 (8) ◽  
Author(s):  
K. C. Ng ◽  
Y. H. Hwang ◽  
T. W. H. Sheu ◽  
M. Z. Yusoff
Keyword(s):  
Fluid Flow ◽  
Poiseuille Flow ◽  
Particle Method ◽  
Numerical Approach ◽  
Particle Methods ◽  
Diffusion Term ◽  
Flow Solver ◽  
Mesh Free ◽  
Consistent Method ◽  
Moving Particle

Recently, there is a rising interest in simulating fluid flow by using particle methods, which are mesh-free. However, the viscous stresses (or diffusion term) appeared in fluid flow governing equations are commonly expressed as the second-order derivatives of flow velocities, which are usually discretized by an inconsistent numerical approach in a particle-based method. In this work, a consistent method in discretizing the diffusion term is implemented in our particle-based fluid flow solver (namely the Moving Particle Pressure Mesh (MPPM) method). The new solver is then used to solve a multiphase Poiseuille flow problem. The error is decreasing while the grid is refined, showing the consistency of our current numerical implementation.

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