## 2 Materials and Methods
### Drying Procedure  
The apple cubes were dried using a hybrid drum dryer constructed by Promis-Tech (Wroclaw, Poland). A scheme of the dryer is presented in Figure 1.  
This apparatus enables convective (CV) and microwave drying (MW) separately as well as in different combinations (hybrid processes), with ultrasound (US) enhancement. The acoustic waves are generated by the Airborne Ultrasound System (AUS) developed and delivered by Pusonics (Madrid, Spain). The transducer (Figure 1(13)) is assembled at the door of the dryer, and emits a focalized acoustic field directly at the material placed in a rotatable drum (Figure 1(12)). It means that the waves' intensity converges with increasing distance from the transducer, and at about 420 mm from the radiator; it attains a maximum (160-170 dB). The distance between the emitter and samples was fixed at about 415 mm to ensure that samples stayed in the focusing area during the treatment. The intensity of the ultrasound may be adjusted continuously in the range of 1 W to 200 W. However, this value does not refer to the acoustic power delivered to the material but to the current consumed by the generator. The mass of the sample was measured automatically during the process with the use of a balance (Figure 1(11)). During measurement, the balance was raised with a pneumatic lift, and the stream of hot air was forwarded to the outlet (Figure 1(7)) with a pneumatic valve (Figure 1(6)) to avoid disturbances. The temperature of the material was measured with two methods. For convective processes (CV, CVUS), this parameter was recorded automatically during the process with the use of an HTDL-30 autonomic recorder, produced by Dwyer (Michigan, IN, USA), and placed inside the drum. In the case of microwave programs (CVMW, CVMWUS), the temperature of the material was measured with the use of a Flir ThermaCAM B2 IR camera (ATEC, San Diego, CA, USA). Because this measurement requires direct access to the material being dried, the drying operation was periodically interrupted (for about 30 s for each 10 min of the process) while the thermogram of the samples was captured. Such interruptions did not meaningfully influence the overall kinetics of the process, which was checked through comparison with continuous processes without temperature measurements (interruptions). Five different programs of drying were carried out in triplicate and the average values of measured parameters were calculated and utilized for further processing. Detailed descriptions of the particular schedules are provided in Table 1.  
Figure 1: Scheme of drying system: 1: Blower (Fan), 2: AUS controller, 3: AUS preamplifier, 4: Microwave feeders, 5: Heater, 6: Pneumatic valve, 7: Air outlet, 8: Pyrometer, 9: Drum drive, 10: Microwave generators, 11: Balance, 12: Rotatable drum, 13: AUS transducer, 14: Control unit. The kinetics of each process were assessed on the basis of the evolution of the relative moisture content (MR) and temperature (T) of the samples. Relative moisture content at a given time of process was calculated in accordance with Equation (1):  
\[\text{MR(t)}=(\text{MC(t)}-\text{MC}_{\text{eq}})/(\text{MC}_{0}-\text{MC}_{ \text{eq}}), \tag{1}\]  
where MC(t) is the moisture content at a given time of the process (kg/kgd); MCeq and MC0 are equilibrium and initial moisture content, respectively (kg/kgd). Equilibrium moisture content was constant for each variant of the process (MCeq = 0.05), while the moisture content at a given time in the process (MC(t)) and initial moisture content (MC0) were calculated with the use of Equations (2) and (3):  
\[\text{MC}_{0}=(\text{m}_{0}-\text{m}_{\text{s}})/\text{m}_{\text{s}}, \tag{2}\]  
\[\text{MC}(t)=(\text{m}(t)-\text{m}_{\text{s}})/\text{m}_{\text{s}}, \tag{3}\]  
where m0 and m\({}_{\text{s}}\) are the mass of the fresh samples and the mass of the dry matter, respectively (kg), and m(t) is the mass of the samples at a given time in the process (kg).