cohesion model lubrication

Purpose

Modelling lubrication as proposed by Zhang et al. and Tomac and Gutierrez.

Syntax

cohesion lubrication

Associated material properties

Global scalars 

dynamicFluidViscosity ( $\mu$ ): dynamic viscosity of the fluid [pressure*time]

Description

The model computes the lubrication force between two particles or between a particle and a wall according to the formula:

$F_L = -6 \pi \mu {r^*}^2 \frac{v_n}{h},$

where $h$ is the surface distance, $v_n$ is the normal component of the relative velocity, and $r^*$ is the effective radius given by

$1/r^* = 1/r_i + 1/r_j,$

with $r_i$ and $r_j$ being the respective particle radii.

The lubrication force is only computed if the surface distance $h$ is within the interval $0.001 (2r^*) < h < 2r^*$ .

Literature

[1] Zhang, W., Noda, R., & Horio, M. (2005). Evaluation of lubrication force on colliding particles for DEM simulation of fluidized beds. Powder technology, 158(1-3), 92-101.

[2] Tomac, I., & Gutierrez, M. (2013). Discrete element modeling of non-linear submerged particle collisions. Granular matter, 15(6), 759-769.