If the above situation without reaction in a stable system Dc c a2 D AB 2 2 2 This is Fick's second Law 5.2 Importance of Study on Transport phenomena There are microbes, substrate and metabolism products effect on the viscosity of the bio-reaction systems, and then effect on the momentum transfer. heat transfer and mass transfer. Further the transport factors effect on the bio- reactions, design of reactors and general output of the whole bio-process
If the above situation without reaction in a stable system: This is Fick’s second Law. 5.2 Importance of Study on Transport phenomena There are microbes, substrate and metabolism products effect on the viscosity of the bio-reaction systems, and then effect on the momentum transfer, heat transfer, and mass transfer. Further the transport factors effect on the bioreactions, design of reactors and general output of the whole bio-process. ( ) 2 2 2 2 2 2 z c y c x c D Dt Dc A A A AB A + + =
Viscosity Fluid kinetics/power required Heat transfer Mss transfer Raw material feed Fermentation Purification and recovery of (Pumping (cells dispersion heating, cooling oxygen dissolved, proaucts and mixing temperature (Pumping, heating, cooling and separation) Cells growth products formed morphology Ⅴ 1scosit Design and 'economics
Viscosity Fluid kinetics/power required Heat transfer Mss transfer Raw material feed (Pumping, heating, cooling and mixing) Fermentation (cells dispersion, oxygen dissolved, temperature ) Purification and recovery of products (Pumping, heating, cooling and separation) Cells growth products formed morphology Viscosity Design and economics
5.3 Rheological Propertics of The Process Materials (1) Pure viscous fluids a)Newtonian fluids u(constant) [: shear stress, N/m2 b)non Newtonian fluids y shear rate. s +constant) A viscosity, kg/ms (2)viscoelastic fluids r=f(r, extent of deformation) Most non-Newtonian fluids follows the power-law model t=k(r n
5.3 Rheological Propertics of The Process Materials (1) Pure viscous fluids : a)Newtonian fluids = (=constant) :shear stress, N/m2 b)non-Newtonian fluids :shear rate, s-1 = ( constant) :viscosity, kg/ms (2) viscoelastic fluids = f ( ,extent of deformation) Most non-Newtonian fluids follows the power-law model = K( )n
Bingham plastics Fig 5.1 General shear behavior of pseudoplastic rheologically time-independent fluid Newtonian classes dilatant 5.4 Basic Dispersion Concepts The oxygen transfer rate from the gas bubble to the medium is largely determined by k, and the interfacial area a Main variables which influence a bubble size dB. the terminal velocity of the bubble U and the gas hold-up E
dilatant Newtonian pseudoplastic plastics Bingham Fig.5.1 General shear behavior of rheologically time-independent fluid classes 5.4 Basic Dispersion Concepts The oxygen transfer rate from the gas bubble to the medium is largely determined by kL and the interfacial area a. Main variables which influence a : bubble size dB, the terminal velocity of the bubble UB and the gas hold-up
Basic correlation For small, rigid interface bubbles follow Stokes equation 18 B which is valid for Re〈1 For mobile interface bubbles 16B 5-2 At higher bubble Reynolds numbers 20 B B (5-3A) .2 B When the gravity stresses are higher than the surface tension stresses B guB (5-3B) 2
Basic correlation : For small,rigid interface bubbles follow Stokes equation: UB= dB 2 (5-1) which is valid for Re 1. For mobile interface bubbles : UB= dB 2 (5-2) At higher bubble Reynolds numbers: UB= (5-3A) When the gravity stresses are higher than the surface tension stresses: UB= (5-3B) 18 g 16 g 2 2 B B gd d + 2 gdB