## 4 Numerical Model
### Modeling on Sturry and PIV Tracers  
By using the CFD-DEM solver _SediFoam_, the particles of the slurry and the tracers used in the PIV test were described by DEM, while the pore water was governed by the CFD method. The three-dimensional model incorporating the slurry, the tracers, and the PVD membrane is shown in Figure 6a tighter with illustrations on the model structure given in Figure 6b. The model was of cuboid shape with a height of 400 \(\upmu\)m and square bottom of side length of 100 \(\upmu\)m. As shown in Figure 6b, along the model height, the computational domain can be functionally divided into three regions, i.e., the particle-fluid mixed region ranging from 100 to 400 \(\upmu\)m, the membrane region ranging from 95 to 100 \(\upmu\)m and the pure water region ranging from 0 to 95 \(\upmu\)m.  
Figure 4: Structure of a PVD membrane of woven fabric.  
Figure 5: Numerical modeling on PVD membrane: (**a**) DEM modeling on PVD membrane, (**b**) schematic plan view on the membrane.  
In order to save computational cost as well as to simplify the calculation of particle interaction forces, the slurry particles were idealized into spheres, which were randomly scattered in the mixed region and not allowed to overlap with each other, as shown in Figure 6a. The number of the spheres was determined according to the initial void ratio of the slurry. The tracers were also modeled as spheres. However, they were evenly scattered only to the right boundary region of the model, as shown in Figure 6a, which was different from the slurry particles that were randomly distributed within the entire computational domain. Those tracer particles were tangential to the right boundary of the model, which mimics the situation that the tracer particles were scattered onto the inside surface of the observation window in the actual PIV test. As for the membrane, the constituting particles were fixed in space throughout the simulation. The pure water region merely serves to provide extra space for the continuous movement of particles that have passed through the membrane.  
The particle size distribution of the actual slurry that was sampled from Wenzhou of eastern China is shown in Figure 7. It was observed that the particle size generally confines to the range of 2-50 \(\upmu\)m with the median size \(d_{\text{S0}}\approx 20\)\(\upmu\)m. To make a reasonable representation of the actual slurry and also to reasonably simplify the modeling work, uniformly-sized spherical particles of diameter \(d=10\)\(\upmu\)m were adopted here to model the slurry. It was noted that \(d=10\)\(\upmu\)m was less than \(D=20\)\(\upmu\)m, which means the slurry particles were able to pass the membrane. Two concentrations of slurry particles that can be equivalently expressed as the initial void ratio \(e_{0}=2\) and 3 were considered for the slurry.  
Figure 6: Diagram of the numerical model: (**a**) three-dimensional model, (**b**) model structure.  
Figure 7: Particle size distribution of dredged slurry sampled from Wenzhou.  
One of the commonly used tracers is dark carbon powder that has a minimum diameter of about 16 \(\upmu\)m. Correspondingly, tracers of three diameters were considered in the model, i.e., \(d_{\text{t}}=16\), 18, and 25 \(\upmu\)m. Additionally, two mass densities \(\rho_{\text{t}}=2000\) and 2650 kg/m\({}^{3}\) were specified for the tracer to consider the tracers of different material origin, e.g., carbon powders and sand grains. Under the different combinations of the initial void ratio \(e_{0}\) of the slurry, the diameter \(d_{\text{t}}\) and the mass density \(\rho_{\text{t}}\) of the tracer, 8 modeling cases were considered in the present paper, which is summarized in Table 4, together with the geometry and material parameters of the solid and fluid phases. The different cases can cover a wide spectrum of the PIV model tests on the dredged slurry.