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A DEM-based Euler–Lagrange model for motion of particle–fluid two-phase mixtures

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Abstract

The effects of interstitial fluid on the behaviors of two approaching particles play an important role in the rheology of granular–fluid mixtures. In this paper, an Euler–Lagrange model is developed to study the effects of interstitial fluid on the frictional behaviors of particle contacts which is resolved by the discrete element method (DEM). A formulation of the friction coefficient for immersed particle contacts, involving the effects of interstitial fluid viscosity and pressure, is proposed based on the results of a laboratory experiment. The enhancement effect of the porosity of granular materials on the inter-particle friction coefficient is taken into account. For the inter-particle normal contact force, an existing empirical formula of the coefficient of restitution for immersed particle collisions is adopted. The model is verified in the laboratory experiment of collisions between a single particle and a solid wall in both air and water. The model is further validated by simulating subaerial granular landslides into water down an inclined slope. Without the effects of interstitial fluid on the inter-particle friction coefficient, the propagation velocity of subaerial landslides intruding into the water and the generated tsunami wave is underestimated. Moreover, if the enhancement effect of the landslide porosity is excluded, the propagation velocity of the landslide and the generated wave are overestimated.

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Data Availability

The data that support the findings of this study are available upon reasonable request to the authors.

Abbreviations

\(C_{{\text{D}}}\) :

Drag coefficient

\(d\) :

Particle diameter

\(e\) :

Coefficient of restitution

\(E\) :

Young’s modulus

\({\mathbf{F}}\) :

Force

\({\mathbf{g}}\) :

Gravitational acceleration

\(i,j\) :

Particle index

\(I\) :

Moment of inertia

\(m\) :

Mass

\({\mathbf{M}}\) :

Torque

\({\mathbf{n}}\) :

Unit normal vector

\(N\) :

Neighboring particle number

\({\mathbf{r}}\) :

Force arm

\(\gamma_{ij} ,\gamma^{\prime}_{ij}\) :

Damping viscosity subjected to the normal and tangential contact force

\(\mu\) :

Friction coefficient

\(R\) :

Particle radius

\({\text{Re}}\) :

Reynolds number

\({\text{St}}\) :

Particle Stokes number

\(t\) :

Time

\({\mathbf{u}}\) :

Velocity

\(V\) :

Particle volume

\(\alpha\) :

Volume fraction

\({{\varvec{\upvarepsilon}}}\) :

Relative displacement

\({{\varvec{\upomega}}}\) :

Angular velocity

\(\rho\) :

Density

\(\upsilon\) :

Poisson’s ratio

\(\nu\) :

Kinetic viscosity

\(\Delta t\) :

Time step

\(k_{ij} ,k^{\prime}_{ij}\) :

Spring stiffness subjected to the normal and tangential contact force

\(\mu^{\prime}\) :

Coefficient of rolling friction

\({\text{N,T}}\) :

Normal and tangential components of contact parameters

\({\text{f,p}}\) :

The continuous phase and the granular particles

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Funding

This research is jointly supported by the National Natural Science Foundation of China (NSFC) under grant Nos. 41961144014 and 12102493, and the Science and Technology Development Fund, Macau SAR (File No. 0090/2020/A2, 0050/2020/AMJ).

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Authors and Affiliations

  1. Department of Ocean Science and Engineering, Southern University of Science and Technology, Shenzhen, China

    Wenxin Li

  2. State Key Laboratory of Internet of Things for Smart City and Department of Ocean Science and Technology, University of Macau, Taipa, Macao, China

    Huabin Shi

  3. Department of Ocean Science and Engineering, Southern University of Science and Technology, Shenzhen, China

    Xiping Yu

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  1. Wenxin Li
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Correspondence to Xiping Yu.

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Li, W., Shi, H. & Yu, X. A DEM-based Euler–Lagrange model for motion of particle–fluid two-phase mixtures. Acta Geotech. 19, 971–989 (2024). https://doi.org/10.1007/s11440-023-02054-5

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