## 3 Results and Discussion  
### Drying Kinetics  
Drying kinetic curves indicated a change in the water content in the samples depending on the drying time (Figure 2a). At first, the moisture was evaporated from the surface of the samples, so the drying rate was constant. Then, the water evaporated from deeper layers of the dried material, and the water vapor moved to the surface of the apple, which resulted in a decreasing rate of drying. The samples subjected to 10 min of US pre-treatment and US-assisted drying with 200 W of US power (T_10\(D\)200W) and 30 min of US pre-treatment and US-assisted drying with 120 W (T_30\(D\)120W) were characterized with the shortest drying time of 125 min. As a result of the ultrasound application, while processing the samples, the drying time was reduced by 11%. This effect was linked with cavitation and/or the sponge effect [2]. For the sample subjected to 10 min of US pre-treatment and US-assisted drying with 200 W of US power (T_10\(D\)200W), high cavitation occurred during the short pre-treatment time (10 min). The applied high ultrasound power (200 W) during drying intensified cavitation, where the rapid formation and collapse of microbubbles occurred and led to the disruption of the cell walls and enhanced water diffusion. Though the pre-treatment duration was short (10 min), the strong cavitation effect during drying was compensated, allowing for rapid moisture removal. However, in the case of apples treated with 30 min of US pre-treatment and US-assisted drying with 120 W (T\({}_{30}\)D\({}_{-}\)120W), a longer US pre-treatment time (30 min) promoted the sponge effect, where cyclic compression and expansion of the tissue structure form microscopic tunnels, through which water was removed from the tissue more easily. Even though the ultrasound power during drying was relatively low (120 W), the pre-formed microchannels significantly improved water transport and effectively reduced drying time.  
Several studies in the literature report the use of ultrasound pre-treatment and ultrasound-assisted convective drying as methods to shorten the drying time. [PERSON] et al. [40] observed a decrease in processing time and an enhancement in drying when samples of mulberry leaves were pre-treated with ultrasound. [PERSON] et al. [26] stated that the application of ultrasounds during convective drying significantly shortened the drying time of apples, depending on the power used. An increase in the drying rate may be influenced by an increase in the permeability of the cell membrane and damage to the structure of the cell walls of the material. In addition, using sonication caused a sponge effect and the formation of microscopic tunnels in the plant tissue, which facilitated water evaporation [41].  
Based on Figure 2b, it can be presumed that the highest and lowest tested ultrasonic power applied during drying provided the shortest drying time. This finding was further confirmed by a Pareto plot analysis (Figure S1), according to which a quadratic effect of the impact of the ultrasonic power used during on drying time was found. The shortening of drying time was a result of the presence of a greater or lesser sponge effect in individual samples according to the mechanism of the sonication [42; 43]. Based on the RSM graph, it can be stated that the shortest drying time was achieved for the highest and the lowest ultrasound power, regardless of the sonication time before drying. Therefore, the evidence from this study implies that the time of ultrasound treatment was not crucial for shortening the drying time when hybrid drying with a sonication effect (power of US 120, 160, and 200 W) was used as a drying technique for apples.  
Figure 2: (**a**) The kinetics of apple drying using ultrasonic treatment with a hybrid method of drying with drying time in min to obtain MR = 0.01; (**b**) the effect of US treatment time and the US power applied during drying on the RSM for apple drying time to obtain MR = 0.01. Blue dots on the figure shows research data.