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Quasi-static simulation of droplet morphologies using a smoothed particle hydrodynamics multiphase model

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Abstract

Numerical simulation of the morphology of a droplet deposited on a solid surface requires an efficient description of the three-phase contact line. In this study, a simple method of implementing the contact angle is proposed, combined with a robust smoothed particle hydrodynamics multiphase algorithm (Zhang 2015). The first step of the method is the creation of the virtual liquid–gas interface across the solid surface by means of dummy particles, thus the calculated surface tension near the triple point serves to automatically modulate the dynamic contact line towards the equilibrium state. We simulate the evolution process of initially square liquid lumps on flat and curved surfaces. The predictions of droplet profiles are in good agreement with the analytical solutions provided that the macroscopic contact angle is accurately implemented. Compared to the normal correction method, the present method is straightforward without the need to manually alter the normal vectors. This study presents a robust algorithm capable of capturing the physics of the static wetting. It may hold great potentials in bio-inspired superhydrophobic surfaces, oil displacement, microfluidics, ore floatation, etc.

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Acknowledgements

The work was supported by the National Natural Science Foundation of China (Grants 11672335 and 11611530541), China Postdoctoral Science Foundation (Grant 2017M622307), Shandong Natural Science Foundation (Grant ZR201709210320), Fundamental Research Funds for the Central Universities (Grant 18CX02153A), and the Endeavour Australia Cheung Kong Research Fellowship Scholarship from the Australian government.

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Authors and Affiliations

  1. Department of Engineering Mechanics, College of Pipeline and Civil Engineering, China University of Petroleum (East China), Qingdao, 266580, China

    Xiangwei Dong, Jianlin Liu & Sai Liu

  2. College of Mechanical and Electronic Engineering, China University of Petroleum (East China), Qingdao, 266580, China

    Xiangwei Dong & Zengliang Li

Authors
  1. Xiangwei Dong
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  2. Jianlin Liu
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Correspondence to Jianlin Liu.

Appendix

Appendix

1.1 Detection of the triple contact points

Another critical step is the detection of the triple contact points. We propose the following procedures (see Fig. 13):

Fig. 13
figure 13

Detection of the triple contact points using an accurate method

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  1. 1.

    Search for boundary particles belonging to the liquid and gas phases.

  2. 2.

    Identify the lowest boundary particle close to the solid surface for both the gas and liquid phases, labeled as particles g and l.

  3. 3.

    Determine mean coordinates for particles g and l as those for an intermediate point p. The projection of point p on the solid surface is then regarded as the triple contact point.

Following the method proposed by Dilts [35], the boundary particles can be detected by scanning the 3h radius (3h is the radius of the support domain) circle around an SPH particle. If the circle of the SPH particle is not completely covered by the circles of its neighbors, this particle is labeled as a boundary particle. Otherwise, it is an inner particle. By using this procedure, the position of the triple contact point can be accurately identified. However, it is relatively complex to implement, especially for three-dimensional cases. A simplified procedure can be realized through summarizing the fluid particles near the triple line, as shown in Fig. 14a.

Fig. 14
figure 14

Detection of the triple contact points using a simplified method. a illustration of triple contact point, b comparison between accurate method and simplified method

Full size image

We first calculate the averaged location of these particles, then project the point on the solid surface, and the projected point is identified as the triple contact point. We compare the results of the accurate method and simplified method, as shown in Fig. 14b. It shows that the results obtained by the simplified method match well with the accurate results. The simplified procedure is easy to implement and may be more workable for three-dimensional (3D) application.

Note that the position of the three-phase contact point is not constant and changes with the movement of the droplet, so the procedure must be carried out at each time step. The proposed method is implemented with no need of changing the original flow chart of the simulation.

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Dong, X., Liu, J., Liu, S. et al. Quasi-static simulation of droplet morphologies using a smoothed particle hydrodynamics multiphase model. Acta Mech. Sin. 35, 32–44 (2019). https://doi.org/10.1007/s10409-018-0812-x

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