Addendum

Thermal treatment for products

Thermal treatment is normally applied to the product to reduce its microbial load and guarantee the required shelf life. Heat acts on the proteic structures inside the microorganism cells and can kill the microorganism or deactivate its reproduction capability. Effectiveness of a heat treatment is normally expressed in pasteurizing unit:

K = constant,
t_s = sterilization time in minutes
T_s = sterilization temperature in °C. 

Heating and cooling time are not considered in the determination of the heat treatment time, although they contribute to the sterilization performance. Thus, holding time and not heating time is used as a treatment parameter. Temperature is the most effective microorganism killing agent and the most relevant treatment parameter. Its sterilizing effect is growing exponentially when temperature is raised. High efficiency can be reached from 80°C upwards. For example, 100 P.U. can be applied to orange juice by treating it at 130°C for 1 second holding time or by treating it at 90°C for 50 seconds holding time. It is normally necessary to make compromises between treatment parameters and product decay after treatment to determine a treatment that allows the product to reach the required shelf life at the lowest possible decay of organoleptic properties. P.U. are useful to compare different treatment and determine their overall efficiency, but analysis of the actual product according to reference microorganisms is necessary to determine the actual killing action of a given treatment.

When a microbic colony is heated for a given time at a given temperature, the speed of the reduction in the number of microorganisms is directly proportional to their concentration

according to the relation:

Where K is the reaction speed constant, depending from reference microorganism, temperature and environment conditions.

By integrating between t₁ = 0 and t₂ = t we obtain:

or, in general terms:

Switching from natural logarithms to base 10 logarithms and highlighting N = N₀ / 10 we obtain:

where D (decimal reduction time) represents the timeframe where the number of microorganisms is reduced by a factor of 10.

By substituting the found value we obtain the first Law of Bigelow:

Values for D change according to the different reference microorganism. The higher the value of D, the more resistant is the microorganism.

We can infer from the First Law of Bigelow that a longer time is required if N₀ is a big number.

Moreover, it is not possible to completely kill all microorganisms, as this would imply an infinite treatment time. Killing time becomes shorter as the treatment temperature becomes higher (see "Graphic representation of Second Law of Bigelow").

The inclination of TDT is represented as z, equal to the number of degrees needed to reduce D by a factor of 10. The relation between D(t) and z can be expressed as:

If we assume the value D_121°C we obtain the canonical form of the Second Law of Bigelow:

This second law enables us to know the value of D at the required temperature if we know D_121°C and z.

For example, we know that for Clostridium botulinum z is equal to 10°C and D_121°C value is 0.2'; we can then calculate the value for D at the temperature of 100°C:

D and z express the resistance of a reference microorganism; you have to take into account also the composition of the product, as the ingredients of a certain product feature a different resistance to heat. The time required (expressed in minutes) to reach a certain sterilization degree is called sterilizing effect F_T^z and can be calculated using the following formula:

n is defined as the number of log reductions.

For a temperature of 121°C we obtain

From a technical point of view F_T^z is the sum of the killing contribution of each temperature for the microorganisms hosted inside the foodstuff; in other words it is the integral of the heat penetration curve.

The killing action is defined as the relationship between F₀ and F_T^z.

It is then necessary to know the thermal history T(t), that is the heat penetration curve into the product. The sterilization effect can be expressed as:

where t_P is the sum of times due to heating time, contact time and cooling time.

Graphic representation of Second Law of Bigelow