第4章生物膜动力学

1、Bruce E.Rittmann and Perry L. McCarty, Environmental Biotechnology:Principles and Applications. pp207-2302The Idealize biofilm 理想生物膜 Bulk liquidDiffusion layerBiofilmLXf, density（ MxL-3）Lf,thicknessFull penetratedshallowDeepssssSwssfzPhysical propertesCharacreristic concentration profilesThe biofolm

2、 has a uniform biomass density Xf(Mx/L)It has a locally uniform thickness of Lf Mass-transport resistance can be important inside the biofilm and to the biofilm3Substrate phenomenanAt any position inside the biofilm,Substrate utilization:nThe substrate is transported into the biofilm by molecular di

3、ffusion, give by Ficks second law: rdiff =rate of substrate accumulation due to diffusion(MsL-3T-1)fffutSKSXqr22dzSdDrffdiff4For a steady-state concentration profile in the biofilm. The substrate mass balance is: The equation requires two boundary conditions: no flux into the attachment surfaceAt th

4、e biofilm/water interface, the external mass transport is described according to Ficks first law:n D:molecular diffusion n coefficient in waterfffffSKSXqdzSdD0220fLzfdzdSDf:molecular diffusion coefficient of the substrate in the biofilm00)(zzffsdzdSDdzdsDSSLDJJ=substrate flux, M/J.T-1Parameters: K,D

5、f,D,L,q 5Illustration for First-order Kineticsn fffffSKSXqdzSdD022ffffSXkdzSdD1220SfKk1=rate coefficient (L3Mx-1T-1)=q/KIntegration of the equation yield closed-form analytical solutions for flux and Sf:111)/tanh(fsfLSDJ )/cosh()/ )cosh(11ffsfLzLSSJ1=substrate flux into a first-order biofilm (MxL-2T

6、-1)1=Df/k1Xf standard biofilm depth dimensiontanh(x)=(ex-e-x)/(ex+e-x)cosh(x)=(0.5(ex+e-x)标准深度是扩散速率于生物降解速率之比。Lf/1是无量纲生物膜厚度，它表示生物膜的深度。厚生物膜Lf/11完全穿透生物膜Lf/1 0 底层：底层： d(Xfdz)/dt0 For any position in the biofilm, the biomass is not at steady state, since Sf changes with position in the film.9The steady-s

7、tate biofilmn虽然生物膜内部生物增长随所处位置不同有净增长和减少，但对生物膜整体来虽然生物膜内部生物增长随所处位置不同有净增长和减少，但对生物膜整体来讲，仍然可以应用稳态的概念，即单位面积上的生物膜量是常数（讲，仍然可以应用稳态的概念，即单位面积上的生物膜量是常数（XfLf不随时不随时间变化间变化)。即表示生物量的方程延生物膜总厚度积分等于零：。即表示生物量的方程延生物膜总厚度积分等于零：dzXbdzXSKSqYdtdzXdfLfffLfLfff000)()(0dzXbdzXSKSqYdtdzXdfffff)()(fffutSKSXqr稳态生物膜的基本条件：单位面积上生物膜的生长量

8、与损失量平衡ffLXbYJ0 bJYLXff单位面积上生物膜量 bXJYLff生物膜厚度10The steady-state biofilm solutionnSubstrate mass balance equation:fffffSKSXqdzSdD022Substrate tranport to the biofilm:)(sSSLDJActive biomass in the biofilm:ffLXbYJ0 boundary conditions00zzffdzdSDdzdsD0fLzfdzdS求出：求出：J, XfLf（生物（生物膜积累量），膜积累量），Lf 在参数在参数q,K,D

9、f,D,L,Y,b,Xf 和和 S 已知已知时时。同时求解同时求解Rittmann and McCarty(1980)Pseudo-analytical solution see references11How steady-state biofilm respond to changes in substrate concentration S: The vertical axis also is proportional to the biomass accumulation per unit surface area, as XfLf=YJ/b1.for SSmin, J=0, XfLf

10、=0 S=0.07mg/cm3S=0.113. J 的斜率从无穷变化到的斜率从无穷变化到1，s0.074.对对deep biofilm， J与5. 对于非常大的对于非常大的S，J=k1/2S1/212需要估计的参数需要估计的参数：nBiomass density Xf: 5-200 mgVS/cm3, typical=40 mgVS/cm3nDiffusion coefficient in water, D (handbooks);nDiffusion coefficient in the biofilm, Df=0.8D;nThickness of the effective diffusi

11、on layer:n L=D/km km质量传递系数质量传递系数nOr:nThe overall biofilm-loss coefficient b=b+bdet bdet=specific biofilm-detachment loss coefficient(T-1) (It is related to the shear stress .)uScDLm7 . 5)(Re67. 075. 013Average biofilm SRTn biomassactiveofrateproductionbiofilmtheinbiomassactivecdetdet1bALXbALXcbffbfAb=biofilm surface areaThe key conclusion is that the average SRT for a steady-state biofilm is equal to the reciprocal of the specific detachment rate.14Completely mixed biofilm reactor V, hV: 液体体积液体体积a