Development of Surface Tension Model for Particle Method

Abstract

Surface tension is a dominant force in gas-liquid flows within micro/nano spaces, such as gas-liquid flows of micro-electro-mechanical systems, nano-in-print processes, and resin coating processes. We developed a surface tension model for a particle method to simulate gas-liquid flows within micro/nano spaces; the inter-particle force between particles was defined to simulate interactions at gas-liquid and liquid-solid interfaces. The inter-particle force was given by the derivation of potential energy and was related to the surface tension by Bakker's equation. The surface tension was modeled as volume force in the Navier-Stokes equation, and the volume force was changed in proportion to the curvatures of interfaces. The surface tension model was verified for pressure in a drop, oscillation of a square drop, and wall adhesion. The predicted pressure in a drop quantitatively agreed well with those given by the Young-Laplace equation. The oscillation of a square drop was qualitatively simulated. In the wall-adhesion verification, effects of different contact angles on drop deformations were quantitatively simulated. We clarified that our new surface tension model was useful for simulating gas-liquid interfaces.

Particle based droplet simulation in liquid-liquid two-phase flow

“…The previous research used the interfacial tension model that considered only the volume force or intermolecular potential force of a single fluid, and then the droplet formed in the simulation was not detached from the catheter or the droplet did not contact with the tip of the catheter even in the case that it was detached. Then, we employ the interfacial tension model proposed by Ishii et al (Ishii and Sugii 2012), which considers the influence by the pressure gradient on the interface boundary between two different materials, and this paper proposes a new interfacial model that can be applied to liquid-liquid two-phase flow. The model developed by Ishii et al (Ishii and Sugii 2012) is based on the method (Kondo et al 2007), and employs the potential model shown in the following equation.…”

“…Then, we employ the interfacial tension model proposed by Ishii et al (Ishii and Sugii 2012), which considers the influence by the pressure gradient on the interface boundary between two different materials, and this paper proposes a new interfacial model that can be applied to liquid-liquid two-phase flow. The model developed by Ishii et al (Ishii and Sugii 2012) is based on the method (Kondo et al 2007), and employs the potential model shown in the following equation.…”

“…The potential force is calculated by the potential function as follows. 4where, and are the initial distance between particles and the radius of influence for interfacial tension, which is 3.1 times of the initial particle distance (Ishii and Sugii 2012). The normal pressure at particle is calculated with the following equation.…”

Numerical Calculation of Three Phase Flow (Gas – Solid – Liquid) of Thermal Spray Process

“…In the surface tension model, the calculation is performed only by the particle position, so it is not necessary to calculate the curvature of the interface and it can be calculated stably without suddenly entering a large value. Due to this condition, the Ishii method which eliminated parameter adjustment and improved internal pressure of droplet was adopted in present study [19]. The normal force Fp, and the shear force Fs are applied on the interface between the gas and the particles.…”

Numerical simulation of droplet behavior on an inclined plate using the Moving Particle Semi-implicit method

“…Zhang et al (2015) and Matsunaga et al (2018) improved the polygon wall model of Harada et al (2008). Studies of wettability on the polygon wall without using wall particles have been performed by Murozono et al (2009), Ishii and Sugii (2012), and Hattori et al (2016); these researchers successfully reproduced static wettability in the equilibrium state by using the MPS method. The models of Kondo et al (2007aKondo et al ( , 2007b and Harada et al (2008) are also described in the reference of Koshizuka et al (2018).…”