## Lesson 26. SOLVING NUMERICAL

Module 6. Sterilizing & packing equipment

Lesson 26
SOLVING NUMERICAL

26.1 Thermal Process Calculation

26.1.1 Commercial sterility

It is defined as a condition in which microorganisms which cause illness, and those capable of growing in food under normal non refrigerated storage and distribution, are eliminated.

26.1.2 Microbial inactivation rates at constant temperature

Rate of microbial inactivation: When a suspension of microorganisms is heated at constant temperature, the decrease in the number of viable organisms follow a first order reaction.
Let N = number of viable organisms.

Where ‘K’ is the first order rate constant for microbial inactivation. Integrating equation and using the initial condition, N = No, at t = 0 temperature.

Integrating the above

The above equation suggests a linear semi logarithmic plot of N against‘t’. The equation can also be expressed in common logarithms.

Where ‘D’ is the decimal reduction time, or the time required to reduce the viable population by a factor of 10.
Thus, the decimal reduction time and the first-order Kinetic rate constant can be easily converted for use in equations requiring the appropriate form of the kinetic parameter.

26.1.3 Shape of microbial inactivation curves

Fig. 26.1 Microbial inactivation curves

Microbial Inactivation process is a logarithmic function with time according to equation (3). However, although the most common inactivation curve is the linear semi logarithmic plot, several other shapes are encountered in practice.

Figure ‘B’ shows an initial rise in numbers followed by first order inactivation. This has been observed with very heat-resistant spores, and may be attributed to heat activation of some spores which otherwise would not germinate and form colonies before the heat treatment reached the severity needed to kill the organism.

Fig ‘C’ shows an inactivation curve which exhibits an initial log or induction period. Very little change in numbers occurs during the log phase. The curve represented can be expressed as.

Where,

t L= the log time, defined as the time required to inactivate the first 90% of the population.

In most cases, the curved sections of the inactivation curve do not extended beyond the first log cycle of inactivation. Therefore defining tL as in equations (4) above, eliminates the arbitrary selections of the log time from the point of tangency of the curved-line and the straight-line position of the inactivation curve. In general, tL approaches D as No becomes smaller and the temperature increases. When tL=D, the first-order inactivation rate starts from the initiation of heating and equation (4) reduce to equation (3) equation (4) is not often used in thermal powers calculations unless the dependence of tL on N0 and T are qualified. Microbial inactivation during thermal processing is after evaluated using equations (3).

Figure ‘D’ represents the inactivation of each species is assured to be independent of the inactivation of others.

From equations (3), the number of species A and B having decimal reductions times of DA and DB at any time is.

If DA< DB, the second term is relatively constant at small values of t and the first term dominates, as represented by the first line segment in fig ‘D’. At large value of t, the first term approaches zero and microbial numbers will be represented by the second line segment in fig (3).

The heating time required obtain a specified probability of spoilage from a mixed species with known ‘D’ values is the largest heating time calculated using equations (3) for any the species.

Figure ‘E’ shows an inactivation curve which exhibits tailing. Tailing is often associated with very high N0 values and with organism which have a tendency to chump. In the case of lag in the inactivation curve, the effect of tailing is not considered in the thermal process calculation unless the curve is reproducible and the effects of initial number and temperature can be quantified.

Last modified: Thursday, 4 October 2012, 5:19 AM