8.2.Kinetics of heat sterilisation dN =-kN dt =知 k(min)is the death rate constant In(N)In(No)-kt N=Noe k
kN dt dN = − kt No N ln( ) = − ln( N) = ln( No) − k t kt N Noe− = k (min-1 ) is the death rate constant 8.2. Kinetics of heat sterilisation
1n(N) 1n(N) In(No) In(No) Increased k 0 t 0 Heat inactivation curves.The left hand figure shows two inactivation curves with different death rate constants.The right hand figure shows some deviations from the model: 1.This form may be caused by super-dormant spores,which are activated by the first heat treatment and do not germinate unless they get this treatment; 2.This may be caused by delayed heat transfer in the experiment or it may be observed in samples that contain aggregates of cells,since analysis is made by viable count that gives number of colony forming units rather than number of cells. The viable count does then not decline until the last cell in an aggregate is killed; 3.Non-uniform heat resistance in the population,e.g.when the sample contains species with different thermal sensitivity
k=Ae-ABIRT 风)=n0-☑习 1.28 ( 0.32 Spores ￥0.08 Thiamine 0.02 2.2 2.4 2.6 2.8x103 1T(K) Arrhenius plots of inactivation of B.stearothermophilus spores and thiamine.Note that a temperature increase has a larger effect on the spore inactivation rate than on the vitamin inactivation rate
E RT k Ae− / = R T E k A 1 ln( ) ln( ) = − t c k Co C ln( ) = −
8.3.Calculation of sterilisation time F= 又=Fk,=Frgkrd,F=Re 8.3.1.Batch sterilisation V=th=tAe ABIRT VI=AP (eIRT yit (e-AE/RT)d V=FAe -AE/RTrer Fref(e-EIRT)di
ln( ) f o N N = k F = T ref ref F k F k T = = ( ) 1 1 R Tref T E F F e T ref − − = 8.3.1. Batch sterilisation E RT t t k tAe− / = = t A e dt t E RT − = 0 / ( ) E RTref FAe− / = dt E RT e ref F t dt E RT e t ) / ( 0 ) / ( − − = 8.3. Calculation of sterilisation time
130 100 9 50 0 0 20 40 60 Time (min) Simulation of the progress of sterility (V/V)and inactivation of a temperature sensible compound (C/Co)during a batch sterilisation.The sterility was calculated according to eq.11 and the concentration of compound according to eq.6 and eq.4. Parameters:V=20,A=1035.8 sec-1 and 109 sec-1 for sterilisation and chemical reaction, respectively.AE=282 kJ mole-1 and 92 kJ mole-1,respectively.R=8.31 J mol--1K-1