## 1 Introduction  
Anaerobic digestion (AD) is a process that utilizes microbial metabolic activity to decompose organic matter in the absence of oxygen, producing biogas and digestate as by-products. Biogas, consisting mainly of methane (CH\({}_{4}\)) and carbon dioxide (CO\({}_{2}\)), is used as a renewable source of energy, while digestate can be used as an organic fertilizer [1, 2, 3]. Despite its benefits, the efficiency of anaerobic digestion can be limited by various factors; key aspects include the organic load of the digester, both in terms of retention time and the concentration of solids, as well as the influence of process design and the type of substrate to be treated, which may contain contaminants [4, 5, 6, 7, 8, 9]. Recent advances in anaerobic digestion have focused on improving process efficiency and operational stability by optimising process conditions and substrate pre-treatment/mixing [10, 11]. These efforts seek to overcome limitations such as the low degradation rate of solids and low methane yields, while improving versatility in operating conditions [12; 13]. Nevertheless, new developments and technologies are still required to harness the full potential of AD. In this context, incorporating various types of fillers into the reactor, which serve as support structures for microorganisms and facilitate electron transfer, opens up new opportunities. Among these, conductive carbon-based materials such as biochar and nanotubes are particularly noteworthy due to their excellent biocompatibility and relatively high conductivity, making them highly promising for such applications [14; 15; 16]. The benefits of these materials are closely tied to their ability to enhance electron transfer, which plays a crucial role in the metabolic pathways of methanogenic microorganisms. In this sense, magnetite nanoparticles with high conductivity have also been used, demonstrating an improvement in electron transfer mechanisms; however, additional research is necessary to fully comprehend this concept [17]. It should be noted that these works are based on biochar, graphite or magnetite, and to our knowledge, no 3D-printed conductive materials have been studied as fillers in AD in such a way that they can improve electron transfer due to the larger surface area available due to their design. On the other hand, biochar or magnetite nanoparticles that are not easily recoverable increase the solids content of the digestate, which may impact its further use, while 3D-printed materials can be designed to be of a size that allows them to be separated by simple physical processes and/or kept in the digester. These pathways can be further stimulated by integrating bioelectrochemical systems (BES)--an emerging technology that combines electrochemical principles with microbiology--within the digester, an approach that not only improves the quantity and quality of the biogas produced but also optimizes solid degradation and mitigates the adverse effects of compounds that could hinder the process [6; 18; 19; 20; 21]. This positions BES as a groundbreaking solution for advancing sustainable and efficient wastewater management practices [22; 23; 24; 25]. Thus, the introduction of electrodes into anaerobic digesters has been shown to be an effective technique to improve the efficiency of anaerobic digestion by facilitating electron transfer, which can accelerate the decomposition of organic matter and reduce the accumulation of toxic intermediates. The presence of polarised electrodes inside the bulk on which biofilm formation can occur, thus allowing direct contact between the electroactive micro-organisms and the electron circuit, favours the reactions necessary for methanogenesis, as well as a great diversification of populations, which makes the system more robust [26]. [PERSON] et al. [27] found that side stream voltage applied in separated vessels in the sludge recirculation has a similar effect to direct voltage supply in an AD reactor.