Mathematical modeling of the impact of encapsulating agents and drying techniques on the moisture adsorption and thermodynamic properties of mulberry leaf extract powder

Abstract

The impact of encapsulation techniques on the stability of mulberry leaf extract powder ( M L E P ) was assessed based on the concepts of water activity ( a w ) and glass transition temperature ( T g ). The moisture adsorption isotherms obtained at 25, 35, and 45 °C revealed that encapsulated M L E P s exhibited significantly ( p < 0.05) lower equilibrium moisture content ( X e ) compared to unencapsulated powder, having the highest moisture uptake ( X e = 0.48 g H 2 O . g − 1 d s at a w = 0.85 , 25 ∘ C ) . Mathematical modeling has identified the P e l e g model as the most accurate fit for adsorption behavior ( R 2 > 0.997 ) , while the C a u r i e model demonstrated that encapsulation reduced monolayer moisture content ( X m ) from 0.66 g/g (unencapsulated, a w = 0.85 , at 25 ∘ C ) to range of 0.44–0.56 g/g for encapsulated powders. The G o r d o n − T a y l o r model, which best predicts the T g ( R 2 > 0.991 ) , highlighted higher plasticization effect in freeze-dried carboxymethylcellulose powder ( K g t = 3.40 at 25 ∘ C ). Thermodynamic analysis showed that encapsulation significantly decreased ( p < 0.05) both differential enthalpy ( Δ H d i f ​) and entropy ( Δ S d i f ), with carboxymethylcellulose and spray dry powders having lower values ​​than those encapsulated with maltodextrin and freeze dry, respectively. Freeze-dried carboxymethylcellulose powder exhibited the lowest Gibbs free energy at the isokinetic temperature ( Δ G β = 0.209 j . m o l − 1 ). The pore size analysis indicated that freeze dried carboxymethylcellulose powder had the largest effective pore radius ( r p = 6.34 nm at X e = 0.16 g H 2 O . g − 1 d s ). State diagrams identified critical storage thresholds ( C X e = 0.066 – 0.183 g H 2 O . g − 1 d s ; C a w = 0.231 – 0.789). The synergetic combination of spray dry and carboxymethylcellulose emerged as the most effective encapsulation system, maintaining the M L E P in a stable glassy stated and reducing porosity, thus improving the shelf-life.