Chapter 6 Transport Phenomena In Biochemical reactors Mass Transfer Criteria for simple and Complex Systems (1)
Chapter 6 Transport Phenomena In Biochemical Reactors Mass Transfer Criteria for Simple and Complex Systems (1)
参考阅读: 《生化反应动力学与反应器》 戚以政汪淑雄编著 第6章生化反应器的传递过程 第5章生化反应器的设计与分析 第7章生化反应器的流动模型与放大
参考阅读： 《生化反应动力学与反应器 》 戚以政 汪淑雄 编著 • 第6章 生化反应器的传递过程 • 第5章 生化反应器的设计与分析 •第7章 生化反应器的流动模型与放大
Chapter 5 Basic Concepts of Transport Phenomena In Bio-engineering and chemical Engineering 25 1 Transport phenomena and reaction are the basic phenomena in the nature, Chemical Engin. and Bio engin. concentration gradient, there must be momento If there is velocity gradient, temperature gradient, transfer, heat transfer and mass transfer For momentum transfer there is newton 's law of viscosity as follows xx==1
dy dvx yx = − Chapter 5 Basic Concepts of Transport Phenomena In Bio-engineering and Chemical Engineering 5.1 Transport phenomena and reaction are the basic phenomena in the nature, Chemical Engin. and Bioengin. If there is velocity gradient, temperature gradient, or concentration gradient, there must be momentum transfer, heat transfer, and mass transfer. For momentum transfer, there is Newton’s Law of Viscosity as follows:
-shear stress, u -----viscosity of the fluid. Momentum flux=-viscosity velocity gradient Fluids tha at behave in this fashion are termed newtonian fluids, Fluids that do not obey this law are referred to as non Newtonian fluids. The subject of non-Newtonian flow is a subdivision of rheology For the heat transfer. there is fourier 's law of heat Conduction as follows q q/a-The local heat flow per unit area; heat flux k-m- thermal conductivity Heat flux= thermal conductivity temperature gradient
-----shear stress, -------viscosity of the fluid. Momentum flux = - viscosity velocity gradient Fluids that behave in this fashion are termed Newtonian fluids, Fluids that do not obey this law are referred to as nonNewtonian fluids. The subject of non-Newtonian flow is a subdivision of Rheology. For the heat transfer, there is Fourier’s Law of Heat Conduction as follows: q/A -----The local heat flow per unit area; heat flux k ----- thermal conductivity. Heat flux = thermal conductivity temperature gradient dy dT k A q = −
For the mass transfer there is Fick's first law D 4 AB A the molar diffusion flux of a in a binary system D AB mass diffusivity; p mass density Molar diffusion flux=mass diffusivity* density gradient Assumption of Constant C and dab in a binary system with chemical reaction, the molar diffusion differential equation DARO 2 )+R ay az RA- the molar rate of production A
jA- -----the molar diffusion flux of A in a binary system; DAB ----- mass diffusivity; ------- mass density; Molar diffusion flux = mass diffusivity density gradient Assumption of Constant C and DAB in a binary system with chemical reaction, the molar diffusion differential equation: RA ------ the molar rate of production A dy d j D A A AB = − For the mass transfer, there is Fick’s First Law: A A A A AB A R z c y c x c D Dt Dc + + + = ( ) 2 2 2 2 2 2
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