## 2 Materials and Methods
### Nanobubble Generation and Nanobubble and EB Process  
The experimental equipment including a nanobubble treatment unit and electron-beam irradiation unit was built in the laboratory (Figure 1). The installation comprised two stages. The first stage is responsible for nanobubble generation. A CASHIDO pump (CAHIDO, Type MIB 25X UP, Taiwan, China) was used to generate bulk microbubbles. A nozzle was installed inside the stainless-steel container where 2000 mL of the liquid solution with DCF was kept. No additional air was added during the generation of bulk microbubbles. Microbubbles was produced by hydrodynamic cavitation. \"White water\" was seen inside the container after the pump was started. Dynamic Light Scattering was used to measure the nanobubble size; however, no nanobubbles were observed in this work. The examined solution was circulated between the nanobubble generator (Cashido, Taiwan, China) and the container. As nanobubble generator operation causes solution heating, which may affect the concentration of diclofenac, a cooling system was implemented. It contained a cooling unit equipped with a pump ([PERSON], Seelbach, Germany) and cooler in the form of a stainless-steel tube coil immersed in the container with the diclofenac solution. Distilled water, used as a cooling liquid, was circulated between the cooler and cooling unit. The second stage was structured to allow for the irradiation of liquids in flow mode. The main element was the irradiation chamber, which was made of silicone tubes: one tube with inner diameter of 3.5 mm connected with a tee to two tubes with an inner diameter of 1.5 mm and wall thickness of 0.75 mm. It divided the liquid stream into two separate streams to increase the radiation efficiency with a lower overall flow rate. The exits of the smaller tubes were connected again with another tee to merge both streams back to one, so that the irradiated solution could be collected in the container. The tubes forming the irradiation chamber were attached to a wooden base to keep them straight and placed under an electron accelerator exit window for irradiation. To directly examine the solution through this chamber, a peristaltic pump (Aqua-trend, Poland) with adjustable and remotely controlled rotation speed was employed. The dose rate was adjusted by changing the peristaltic pump rotation speed and thus the flow rate or electron accelerator parameters (beam current and frequency).  
The dosimetry of the experimental system was estimated with a 0.2 M L-alanine solution according to the method of [PERSON] et al. [32] using conductivity measurements. The prepared 0.2 M L-alanine solution was calibrated against alanine pellets (Aerial, Illkirc, France). Solution samples (50 mL) were placed under a 10 MeV Elektronika 10/10 electron accelerator (Siberia, Russia) and irradiated with alanine pellet dosimeters. The conductivity of the irradiated alanine solution samples was measured at 20 \({}^{\circ}\)C using a conductivity meter (Elmetron CX 461, Warsaw, Poland) and the alanine pellet absorbed dose was measured using an EPR spectrometer MagnetTech MS 5000 (Freiberg/Bruker, Berlin, Germany). Conductivity values were correlated with absorbed dose values, which allowed for the creation of a calibration curve and equation. Later, the same solution was entered into the experimental setup, nanobubbled, and then irradiated. The nanobubbling of alanine solution before irradiation was conducted to keep the same irradiation conditions for both the dosimetric solution and diclofenac solution. The absorbed dose was estimated by conductivity measurements performed under the same conditions as those given above and the results were correlated to electron accelerator work parameters and peristaltic pump adjustment. This allowed us to determine the calibration curve and equation correlating the absorbed dose and peristaltic pump adjustment fitted to the specified electron accelerator parameters.