*2.1. Continuous Flow Testing*

Our experimental setup consisted of one 10 kDa Hydrosart® regenerated cellulose membrane of 25 mm diameter (Sartorius Stedim Biotech GmbH, Goettingen, Germany) enclosed into a metal-free polyether ether ketone (PEEK) filter holder (Wyatt Technology Europe GmbH, Dernbach, Germany). After deposition of the NPs onto the membrane, a high-performance liquid chromatography (HPLC)-type piston pump (Postnova Analytics

GmbH, Landsberg am Lech, Germany) delivered the continuous flow of medium into the ultrafiltration cell at rates between 0.2 to a few mL.min−<sup>1</sup> (Figure 1). The exposed solution was then collected at the outlet using an auto-sampler and analyzed for dissolved elemental concentrations. This setup allows the direct separation between the nanoparticulate and dissolved fractions, which are defined by the nominal cut-off of the ultrafiltration membrane, here equal to 10 kDa (10.000 g.mol−1), which corresponds to a spherical particle of ~3 nm diameter. Nanoparticles are deposited onto the membrane filter through the injection of a NPs dispersion. The number of nanoparticles deposited at the surface of the membrane is controlled by the concentration of the NPs suspension and the volume injected. In contrast to previous continuous flow dissolution testing, where milligrams of NPs powder are loaded between two membranes, such a method allows to inject smaller amount of ENMs and to have a visible homogeneous coverage of ENMs at the surface of the membrane [10,40]. In particular, a PTFE tube was used as an injection loop for all experiments, in order to inject a volume of 500 μL of the NPs dispersion. This injection loop was connected to the flow-through setup with an injection valve (Figure 1). At the beginning of the experiment, the flow-through system was started in order to let the eluent solution flush the whole system. After a few minutes, the injection loop was connected to the system in order to inject the Ag NP dispersion.

**Figure 1.** Representation of the setup used for the flow-through dissolution experiments.

### *2.2. Survey of Surface Water Hydrochemistry*

In order to define a media composition more representative of surface aquatic environments, a survey on selected parameters known to influence the dissolution of ENMs was performed for several river systems. Specifically, pH, Ca2+, Mg2+, dissolved organic carbon (DOC), orthophosphates, and conductivity were chosen as key factors [21–23,42–44]. Data for the Danube River were extracted from the TransNational Monitoring Network (TNMN) dataset of the International Commission for the Protection of the Danube River (ICPDR) database [45]. For the Rhine river, data were extracted from the FGG Rhein database for two measuring stations, Karlsruhe and Bad Honnef, located along the Rhine main tributary [46]. Data for the Elbe River were obtained from the specialized information system (FIS) of the FGG Elbe database which have been collected at important measuring stations in the area of the Elbe catchment within the national measuring programs [47]. For these databases, values from 2015 to 2017 were extracted, corresponding to specific sampling locations and times [45–47]. In addition, data of the same parameters were extracted from the Forum of European Geological Surveys (FOREGS) [48] and the European Environment Agency (EEA) [49] databases in order to represent a large and global pool of European surface waters. From these data sets, minimum and maximum values, and median, first (Q1), and third (Q3) quartiles were calculated and plotted.
