Highlights Flavonoids was extracted from peanut shells using an ultrasound-assisted process. Ultrasound used as intensification tool with highest flavonoids yield of 9.263 mg/g. UAE gave higher yield as compared with that of SE and HRE. Phenomenological model was fitted for kinetic modelling and it’s validation. Comparison of two models have been introduced to describe the extraction kinetic of flavonoids.

To obtain a better insight into comprehending the unusual role of ultrasound frequency and enhance the extraction yield of total anthocyanins (TA) from purple sweet potatoes (PSPs), an approach of wide frequency‐based ultrasound‐assisted extraction (WF‐UAE) was applied to evaluate the influence on the extraction of TA under process parameters at different levels, ultrasound frequency (20–84 kHz), ethanol concentration (20–65%), solvent to solid ratio (10–70 ml/g), ultrasound power (50–280 W), temperature (30–70°C), particle size (0.147–0.908 mm), and treatment time. The results showed that ultrasound frequency has more influence on the extraction yield, followed by temperature, treatment time, and other extraction parameters. The maximum yield of 0.567 ± 0.005 mg/g of TA was obtained at optimized parameters, which was significantly higher than Soxhlet extraction where only 0.324 ± 0.002 mg/g was achieved at 98°C for 720 min, as well as higher than ultrasound‐assisted extraction where only 0.465 ± 0.006 mg/g was obtained at 300 W and 20 kHz for 45 min. The extraction kinetics were performed at different levels of process parameters by Peleg's model. Model constants and equilibrium concentration for different process parameters were predicted. Model validation was done by depicting predicted and experimental values from extracted TA. The obtained values of regression coefficient (R2 > 0.972) and root mean square deviation (RMSD < 0.218) indicated that this model has a good agreement with the experimental results. Novelty impact statement This work is the first to evaluate the effects of ultrasound frequency span a wide range from 20 to 84 kHz and other process parameters on the extraction of TA from PSPs by using an approach of WF‐UAE that was based on a frequency search device with eight extraction tanks controlled by a computer. The application of WF‐UAE technology could not only efficiently extract TA from PSPs, but also be promising for extracting active components from different natural materials in the industry.