## 1 Introduction
### Shear Induced Diffusion Based Segregation  
Nowadays, industries not only require and demand a high performance at low costs, but also look at the environmental impact of their processes. In this sense, making use of the principle of shear induced diffusion is an interesting option since it can be operated at much lower energy impact than e.g., microfiltration that in itself is already not that high in energy impact [9]. Shear induced diffusion (SID) is one of the natural migration mechanisms of particles and relies on collective particle behavior that directs particles away from a channel wall. Next to SID, there is Brownian diffusion and inertial lift [5]; see also Figure 1. Brownian diffusion includes the tendency of particles to move in a random direction, and inertial lift includes the effect of the fluid surrounding the particles, which directs individual particles away from the channel wall. To distinguish the different particle migration mechanisms, the dimensionless particle Reynolds number and Peclet number are used, which are indicative of the ratios between the different forces that are acting on the particles [10]. SID is dominant for particles in the range of 1 to 10 \(\upmu\)m, with a particle Reynolds number lower than one and a Peclet number that is higher than one (Figure 1). Considerable effort is put into understanding the principle of shear induced diffusion [12; 13; 14; 15; 16; 17; 18; 19; 20] that is especially relevant at high volume fractions and it causes particles to interact and move towards a region with low shear (i.e., the center of a channel) [21]. Depending on the size and volume fractions of small and large particles the former or latter will predominantly move towards the center of the channel when using particles of different sizes [19]. In a monodisperse suspension, the particles will  
Figure 1: Flux versus the particle diameter for different migration mechanisms (Graph is reprinted from Separation and Purification Technology, 174, [PERSON]; [PERSON] and [PERSON], Particle migration in laminar shear fields: A new basis for large scale separation technology?, 372–388, 2017, with permission from Elsevier, original is from Davis [11]). concentrate near the center, which is a lead for novel concentration processes based on shear-induced diffusion when removing the particle-free liquid that is close to the wall (Figure 2) [16; 17]. After the segregation of particles has taken place in a closed channel, a porous section can be considered to either concentrate particles, or separate different sized particles in case of a bidisperse or polydisperse suspension [21; 22]. Since the segregation already takes place inside the closed channel, the pores in the porous section do not need to have an exclusion effect and can therefore be larger than the size of the particles, unlike regular membrane filtration. The large pores have much lower tendency to block, and the formation of a cake layer is much less likely to occur, even while working with high particle volume fractions [21]. This allows for process intensification, and it will reduce cleaning costs, which in turn is expected to reduce the environmental impact of the process considerably [22]. The effect of SID has been experimentally investigated by [PERSON] and coworkers [21; 22; 23], and they found the high separation efficiency of a bidisperse suspension in a system consisting of a non-porous channel and a porous region, depending on the process conditions used. In order to facilitate process design, we have set up and validated a CFD model, which describes the effect of SID in a non-porous channel only, for a monodisperse suspension in earlier work [10]. In the current study, this CFD model will be used as a starting point for the description of the whole process that also consists of a porous section (Figure 3). The particle profile near the pore, and the re-constitution of the concentration profile after the pore are of core importance to this novel process; therefore, we focus on these aspects.