## 2 Materials and Methods  
This research used an approach based on a combination of methods applied in prior published work conducting validated multiphysics simulations of VRB half-cells [16], 2D wedge full-cells [17] and then 3D cells with mixers [26]. A concise overview and key parameters are provided here, with further details of the model available in Appendix A of this paper. Previous simulations of wedge-shaped cells with increasing compression used 2D models for computational resource efficiency. This model, with variable porous electrode parameters,  
Figure 1: Single cell diagram showing mixers in a wedge-shaped cell with flow from left to right. Note there is a gap in the porous material in the mixer volume. was transferred into a 3D model in order to enable the assessment of geometries with mixers which cannot be defined in 2D. This model was then used to simulate three cases:  
* Case 1--conventional rectangular reference geometry uniformly compressed at 15% (3.4 mm thick), the average of the 0% to 30% compression used in the wedge geometries. * Case 2--wedge-shaped geometry with 0% compression (4 mm) at the inlet and 30% compression at the outlet (2.8 mm). * Case 3--wedge-shaped geometry with 0% to 30% compression with a blade-style mixer bounded by an 8 mm fluid domain. Based on the findings of previous research [26], 2-element mixers (Figure 2a) were placed at the halfway point in each half cell, which was shown to be the most effective out of the simulated variations. The present study used 400 cm\({}^{2}\) scale cells (200 mm length sections) rather than 900 cm\({}^{2}\) (300 mm length) for higher computational resource efficiency whilst remaining commercially relevant. Full-cell models (geometry with mixers, truncated for easy viewing, shown in Figure 2b) were used to assess the effect of the mixer on cell voltage. The active area of exposed membrane remains almost identical; however, 4% of the porous electrode is removed to accommodate the mixer. Symmetry boundary conditions were used on both sides of the unit-width geometry to minimize the computational domain. Meshing strategies resulting from previous refinement studies were used, which were found to achieve convergence for the minimum concentration values that are sensitive to both convective mass transfer and electrochemical processes. Mapped meshes with elements biased towards the outlet and current collector boundaries were used for the rectangular geometry, while the volume surrounding the mixers was discretized with unstructured meshes. Numbers of elements in the order of 200,000 provided acceptable resolution. Governing equations were applied based on the approach developed by [PERSON] et al. [9] and [PERSON] et al. [12]. Ion flux is described by the Nernst-Planck equations and the Butler-Volmer law is used to define electrode reaction kinetics, while [PERSON]'s law was applied to give the velocity in the porous electrode. Some elements of the model were taken from [PERSON] et al. in relation to fluid parameters [14] and the treatment of the boundaries between the membrane and electrodes [29]. Selected SOC values were simulated for model validation as described by [PERSON] et al. and [PERSON] et al. [30]. The coupled electrochemical and fluid equations were solved using the finite element method with software package COMSOL Multiphysics using the UNSW Sydney computational cluster, Katana. The general parameters shown in Table 1 were applied to each case. Figure 2: CAD renders of (**a**) 2-element blade-type mixer and (**b**) a section of a unit-width full-cell with mixers in both half-cells. The mixer is 8 mm long and the cell domain is 200 mm long and 4 mm wide. The inlet velocity was set to deliver a flowrate of 7.5 stoich. This was chosen as it is the average of the common five and 10 stoich flowrates used in previous studies of mixers and wedge geometries [17; 26]. The electrolyte is assumed to have constant physical properties.