Diffusion of sucrose in xanthan gum solutions

Molecular diffusion of solutes, like sucrose in the xanthan gum fermentation, is important in order to understand the complex behavior of mass transfer mechanisms during the process. This work was focused to determine the diffusion coefficient of sucrose, a carbon source for xanthan production, using similar sucrose and xanthan concentrations to those occurring in a typical fermentation. The diaphragm cell method was used in experimental determinations. The data showed that diffusion coefficient of sucrose significantly decreases when xanthan gum concentration increases. Theoretical and semiempirical models were used to predict sucrose diffusivity in xanthan solutions. Molecular properties and rheological behavior of the system were considered in the modeling. The models tested fitted well the behavior of experimental data and that reported for oxygen in the same system.List of Symbols A constant in eq. (5) - C_pg cm^–3 polymer concentration - D cm² s^–1 diffusivity - D_ABcm² s^–1 diffusivity of A through liquid solvent - D_APcm² s^–1 diffusivity of A in polymer solution - D_AWcm² s^–1 diffusivity of A in water - D_Pcm² s^–1 diffusivity of polymer in liquid solvent - E_D gradient of the activation energy for diffusion - H_P hydratation factor of the polymer in water (g of bound water/g of polymer) - K dyn sⁿ cm^–2 consistency index - K₁ constant in eq. (5) - K_P overall binding coefficient [g of bound solute/cm³ of solution]/[g of free solute/cm³ of polymer free solution] - n flow behavior index - M_Bg g mol^–1 molucular weight of liquid solvent - M_Pg g mol^–1 molecular weight of the polymer - M_Sg g mol^–1 Molecular weight of polymer solution (= M_BX_B+M_PX_P) - R cm³ atm g mol^–1 K^–1 ideal gas law constant - T K absolute temperature - V_Bcm³ g mol^–1 molar volume of liquid solvent - V_Pcm³ g mol^–1 molar volume of polymer - V_Scm³ g mol^–1 molar volume of polymer solution - X_B solvent molar fraction - X_P polymer molar fraction - polymer blockage shape factor - _P volume fraction of polymer in polymer solution - g cm^–1 s^–1 viscosity - _ag cm^–1 s^–1 apparent viscosity of the polymer solution - _icm³ g^–1 intrinsic viscosity - ₀ g cm^–1 s^–1 solvent viscosity - _Pg cm^–1 s^–1 polymer solution viscosity - _R relative viscosity (= /₀) - ₌₀ g cm^–1 s^–1 viscosity of polymer solution obtained at zero shear rate - ₀ g cm^–3 water density