## 1 Introduction
An interesting review [18] described the parameters affecting the mobility and bioavailability of the TiO\({}_{2}\) nanoparticle in soil as being the soil pH, the organic matter content, the soil texture and ionic strength that may affect the nanoparticle's zeta potential, surface charge/affinity and aggregation. Furthermore, studying the transport of polyvinylpyrrolidone-coated Ag-NP in a spiked solution applied to 11 soils in saturated columns, some authors [19] observed that the nanoparticle would rapidly interact with the soil colloids such as maghemite or montmorillonite, which would rapidly limit their mobility. The authors concluded that the interactions of the nanoparticles that led to the aggregation with soil colloids (heteroaggregation) played a key role in the transport of the nanoparticles, which ultimately depended on the size of the aggregate. From this perspective, biochar, being a porous and negatively charged material thanks to the functional groups on its surface, is very likely capable of interfering with the mobility of nanoparticles in soils. Hence, it can be an important tool for soil remediation when it is about nanoparticle contamination. Porous media interfere with the mobility of contaminants in soil, the reason being that they impede their movements by straining or physically filtering the particles: the ones that are larger than the pores are trapped, while the others are removed by interception, diffusion and sedimentation [20]. The surface charges of the nanoparticles--hence, their interaction with the soil aggregates and the biochar particles--depend on the pH. A study of the nanoceria uptake by cells as a function of the amount of surface charge on the nanoparticles indicated that factors such as the pH have a considerable impact on the surface charges of nanoceria particles [21]. Not only the nanoparticles but also the biochar and, in general, pyrogenic carbonaceous material contain C-rich nanoparticles that can interact with engineered metal nanoparticles and have a significant influence on both heteroaggregation and homoaggregation phenomena that influences the metal nanoparticles' mobility in soil [22]. In facts, porous materialshave been applied to reduce the aggregations of metal nanoparticles; among these porous materials with higher surface areas and ion exchange capacities, biochar has become one of the most widely used supporting materials for metal nanoparticles [23]. Last, but not least, biochars have a great impact on the soil pH. In fact, it changes the soil properties, and the variations in terms of mobility may be due to variations in the CEC; porosity and other factors, such as pH, Ca ion concentration and the presence of other types of natural colloids that are the likely final sink of the nanoparticles [24]. Citrate-capped Au nanoparticles, for instance, have been observed to be retained by biochar-amended soils that were significantly more effective from this point of view than sandy soils [25]. In this interesting study, the authors evaluated several aspects, such as the charge neutralization, the pore penetration, the hydrogen bonding and the charge transfer between the biochar and the nanoparticles. The role of the functional groups is clearly very important, which emphasizes the interaction of the biochar with the new contaminants that is not limited to the physical level. Given the assumption that the transport of nanoparticles in soil is affected by the soil's physical and chemical properties, we hypothesize that biochar may have different effects on the nanoparticle's mobility and be useful for the remediation of CeO\({}_{2}\)NP-contaminated soils. Such an effect may be influenced by the quenching process at the end of pyrolysis. The quenching process can be dry or water quenching. The first one consists in letting the biochar cool down for the time necessary to reach room temperature; the second is performed by adding water directly onto the hot biochar at the end of pyrolysis.