E
Q U A T I O N S
of
Heat-Pasteurization/Sterilization Technologies
°C
= [°F - 32] * 5/9
°F = [°C *9/5]+32
z (°C) = z (°F) * 5/9
z (°F) = z (°C) * 9/5
From the exponential inactivation theory:
Nt/No
= e-k
* t
Nt = No * e-k * t
Ln Nt = Ln No - k * t
k= inactivation
Rate Constant
Nt = No * 10-k' * t
k' = 1/D
Decimal Reduction Time, D:
D = 2.303 / k
Nt/No = 10-t/D
Nt = No * 10-t/D
Log Nt = Log No - t /D
D = t / [Log No - Log Nt]
Tr = Reference Temperature
DTr = Decimal Reduction Time at Reference Temperature
DT
= a * 10 [ - b * T ]
DTr = a
* 10 [ - b * Tr ]
b = 1 / z
z
= [Tr - T] / [Log DT
- Log DTr]
DT
= DTr * 10 [Tr - T]/z
DTr = DT
/ 10 [Tr - T]/z
tT
=
Treatment
time at temperature T
tTr=
Treatment
time at temperature Tr
tT
= tTr*
10[Tr-T]
tTr
= tT / 10[Tr-T]
T
= Tr - z * [Log DT - Log DTr
]
T
= Tr - z * [Log tT
- Log tTr
]
z = 10/Log Q10
Q10 = 1010/z
Fo = Equivalent Treatment at 121.1°C
= 250°F
FT
= Fo/ 10 [121.1°C - T] / z
FT = Fo * 10
[121.1°C
- T] / z
Fo
= FT / 10 [250°F
- T] / z
FT = Fo * 10
[250°F
- T] / z
Te= Expected Temperature at which the Treatment time FT = Fo
Te
=121.1°C - z * [Log FT - Log
Fo]
Ns = Expected average Number of survivors / unit [see Halvorson
& Ziegler ]
Ns
= - Ln [sterile units / total units]
ts=
time
for S% survival = D*Log [100/S]
From the Tailing Inactivation Model:
[Casolari, A. 'Microbial Death' in "Physiological
Models in Microbiology",
vol.II, pp. 1-44, 1988, CRC Press Inc., Boca
Raton, FL.]
Heat:
|
Co
= Ct (1 + M*t)
|
|
M
= exp[94.519 +2 * Log W - 2 * Ed /R*T
|
|
Ct
= Co1/{ 1 + t * exp [94,52 + 2 * Log W - 2 * (Ed/R
* T)] }
|
W = g water/g medium
R = 1.987 cal/mole
T=°K
Ed = lethal energy = 0.5*R*T*[103.7293 - Log M]
M
= [(Log Co/Log Ct)-1] / t
Log
Ct = Log Co /[1 + M*t]
P10,T
= 1 / [M*Log Ct]
Radiation:
Cd
= Co1/[1 + S*d²]
Ionizing
radiation: S = 105 / [surface -SH/cell
d = Mrad
Ultraviolet
radiation: S = [Thymine / cell]/108
d
= watt / cm2