Microwave hydrodiffusion and gravity model with a unique hydration strategy for exhaustive extraction of anthocyanins from strawberries and raspberries

•MHG was efficient in the fractional extraction of anthocyanins from berries.•90% of anthocyanins were extracted from both fruits up to the 3rd fraction.•MHG is economically viable and distilled water is the best extraction solvent.•MHG can be a sustainable exhaustive extraction alternative for strawberries and raspberries.•The extract and co-product obtained can be consumed directly or applied to food.