## 2 Description of the LBM Model and Simulation Parameters  
All numerical models of RFB systems available in the literature use solvers of the control volume method to solve boundary value problems. The boundary value problems are formulated as a system of partial differential equations (PDE) of the conservation of macroscopic properties (mass, momentum, and energy) complemented with the initial and boundary conditions. These models belong to the so-called category of macroscopic models of fluid. In our study, we will formulate the model of microflows in the framework of the lattice-Boltzmann method (LBM), which, instead of solving conservation equations of macroscopic properties, uses the Boltzmann Transport Equation (BTE) to describe the statistical behavior of a thermodynamic system in the nonequilibrium state. The BTE equation arises from [PERSON]'s kinetic theory of gases, which belongs to the category of mesoscopic models of fluid systems. Contrary to molecular dynamics (microscopic fluid model), where molecular movement is governed by [PERSON]'s dynamics, LBM does not track individual molecules. Rather, it tracks distributions or representative collections of molecules [35]. The LBM is not just another numeric algorithm of solving the PDE's system but rather a new way of describing the physical state of matter and dynamic systems. Although LBM was devised with the specific intent of providing an alternative to the discretization of the NSE, with his strong physical background, it is now a full-featured method whose applicability goes beyond the macroscopic physics of fluids described by NSE [36; 37]. For computational microfluidics, LBM presents several advantages that go directly out from its mesoscopic nature, including the physical representation of microscopic interactions and the easiness of dealing with complex boundaries. In addition, LBM-like algorithms have been developed to solve microfluidics-related processes and phenomena such as heat transfer, electric/magnetic field, and diffusion [38]. However, in most publications, the resolved microflow cases relate to simplified geometries selected for the code validation or algorithm performance analysis, with no practical reference to the real processes and devices. In the study, we exploit the LBM to perform an in-depth analysis of microflows in micro photovoltaic DSSC cells to explain the underlying phenomena and their influence on cell performance and scalability. For a description of the fluid flow phenomena in microchannels, we use the discretized in momentum \(\mathbb{R}^{3}\) space on the \(\mathrm{D}_{3}\mathrm{Q}_{19}\) lattice form of BTE [39] with an external body force term. The collision operator was approximated with the most popular Bhatnagar-Gross-Krook model [40], while the external body force term was approximated with the He-Shan-Doolen scheme [41]. A detailed description of the model and an analysis of its accuracy, as well as the results of the validation of the algorithm, were discussed in detail in our previous publication [42]. We used our open-source Microflow 3D (MF3D) solver of the CFD/LBM method to solve boundary value problems [43]. The model solution was obtained for three full-3D periodic channel geometries; periodic segments of numerical  
In MF3D, all of the solution parameters are collected in two text files: case_params.cfg and thread_params.cfg. The thread_params.cfg file links boundary surfaces and selected grid volumes (called threads) that are defined in separate text files with boundary or initial conditions. All of the configuration and geometry files necessary to run the simulations are available in the additional resources of the article (Supplementary Files: S1--the MF3D serpentine channel case, S2--the MF3D hexagonal channel case, and S3--the MF3D circular channel case). The detailed description of the MF3D case preparation protocol was provided in our previous article [42]. The flow simulations were performed for the force-induced fluid flow.