# Thermal treatments

## First Bigelow's Law

A thermal process of pasteurization is an operation that aims to reduce the initial number $N_0$ of microbial pathogens that are in a state of vegetative cells. The reduction of the number of microorganisms can be represented by the following equation:

$$N_0 \to N$$

Where $N_0$ is the initial number of microorganisms and N is the number of mircoorganisms at time t. From this general expression it is possible to derive a rate law of the form:

$$\frac{dN}{dt} = - k \cdot N^{\alpha}$$

Where $\alpha$ is the reaction order and $k$ is the rate constant. This is a differential rate law, which it describes that the variation of $N$ as a function of time is equal to the product of the rate constant $k$ and the concentration of $N$.

The thermal inactivation of microorganisms, generally, follows a first order reaction. Thus, for $\alpha$ = 1, the integration of such rate law gives the expression of $N$ as a function of time:

$$ln(N) - ln(N_0) = - k \cdot t$$

It should be noted that the unità of measurement of the rate constant are $s^{-1}$.

In addition, the symbol $ln$ is the natural logarithm. The logarithm of a number "x" is the exponent to which the base (the Neper number, 2.71828...) must be raised, to produce that number "x".

The representation of the above rate law with the Bigelow's law requires the following modifications:

• Natural logarithms should be replaced with decimal logarithms
• The rate constant should be replaced with its reciprocal, in order to express the rate in terms of a time and not in terms of a frequency.

Since $e = 2.72$ and $log_{10}(10) = 1$, thus:

$$ln(10) \cdot log(e) = log(10) = 2.301 \cdot 0.4343 = 1$$

By substituting $ln$ with $log$:

$$log(N) - log(N_0) = - \frac{k}{2.3} \cdot t$$

Now, it is possible to substitute $k/2.3$ with $1/D$, where D is the decimal reduction time:

$$log(N) - log(N_0) = - \frac{t}{D}$$

The D-value means the time required to reduce the initial content of N of 1 log-cycle (or 90%).

This expression can be referred as first Bigelow's law. It can be found in logarithmic form:

$$log\frac{N_0}{N} = \frac{t}{D}$$

or in its exponential form:

$$N = N_0 \cdot 10^{-\frac{t}{D}}$$

It follows the decimal reduction time of some relevant pathogens:

Microorganism Temperature (℃) D (min)

A graphical representation of the meaning of the D-value is depicted below:

## Second Bigelow's Law

The decimal reduction time (D-value) varies as a function of several parameters, like pH, presence of sugards, water activity, etc. However, the most important parameter that affects the value of D is certainly the temperature.

The rate constant of a reaction varies as a function of temperature following a so-called Arrhenius relationship:

$$k = A \cdot exp(- E_a \cdot T)$$

The same relationship can be assumed valid also for the D-value:

$$D = a \cdot exp(- b \cdot T)$$

This expression can be turned into a logarithmic form:

$$ln(D) = ln(a) - b \cdot T$$

Without any attempt to provide a physical meaning to the parameters, from the mathematical point of view we can express the equation above at two distinct temperatures:

$$ln(D_1) = ln(a) - b \cdot T_1$$ $$ln(D_2) = ln(a) - b \cdot T_2$$

Since the parameters $a$ and $b$ are constants, we can derive $a$ with the following general form:

$$ln(a) = ln(D) + b \cdot T$$

By substituting the expression of ln(a) into the expression of $D_1$:

$$ln(D_1) - ln(D_2) = - b \cdot T_1 + b \cdot T_2 = b \cdot (T_2 - T_1)$$

As for the first Bigelow's law, it is more convenient to transform the natural logarithms into decimal logarithms. Since ln(x) = 2.3 \cdot log(x), thus:

$$log\frac{D_1}{D_2} = \frac{b}{2.3} \cdot (T_2 - T_1)$$

If we define now a new variable $z$ that is equal to:

$$z = \frac{b}{2.3}$$

Then, we can derive the second Bigelow's Law, in its logarthmic form:

$$log\frac{D_1}{D_2} = \frac{(T_2 - T_1)}{z}$$

The same law can be expressed in its exponential form:

$$D_1 = D_2 \cdot 10^{\frac{(T_2 - T_1)}{z}}$$

In this expression, $z$ is the temperature difference that changes the values of D of 90%. Thus, $z$ is a temperature (and its unit of measurent are Celsius degree or Kelvin). If we increase the temperature of a process of exactly "$z$" degree Celsius, then, the D-value of that process would become ten times lower.

Often, the value of $D_2$ refers to a reference value of D, at a specific temperature. For instance, the D value of the spores of Clostridium botulinum is often reported at 121℃ and equals to 0.2 min. In this case, assuming a z-value = 10℃, it is straightforward to know that a process performed at 131℃ needs only 0.02 min to assure the same effect on the reduction of the spores.

As a rule-of-thumb, the z-value of the following reactions should be always kept in mind:

• Thermal death of vegetative cells: $z$ = 5℃.
• Thermal death of spore forming bacteria: $z$ = 10℃.
• Nutritional loss of vitamins: $z$ = 30℃.

These values of $z$ mean that the higher the z-value, the lower is the effect of temperature differences on the changes of D-value. Thus, the thermal distruction of vegetative cells of microorganisms is very sensitive to temperature changes. Just an increase of 5℃ would reduce ten times the D-value of the process. Instead, spore forming bacteria are more thermal resistant. In order to have a 90% reduction of the D-value, it is required an increase of temperature of 10℃. Even more stable process are the chemical degradation of vitamins, which have z-values of about 30℃.

A graphical representation of the meaning of the z-value is depicted below:

## Thermal treatments

During the transformation of fruits into products, several heat treatments are often necessary. Some of the most common thermal operations are the following:

• Blanching
• Hot-break
• Pasteurization
• Sterilization
• Evaporation

### Blanching

Blanching aims to heat the product (sometimes only the surface) to high temperatures for a short period of time. This is often accomplished by using steam, either indirectly as for fruit juices, or directly for vegetables. The effect of this operation is to inactivate enzyme activity, which could otherwise cause rapid degeneration of quality. In addition, blanching may also remove air from the product, reduce the product volume and soften the tissue.

In practice, blanching can be performed by immersion in hot water (80 to 100℃) or by exposing the product to steam (as depicted below). The operation lasts typically in about 1 minute.

Blanching units installed in fruit processing industry have a working capacity of 5.000 up to 30.000 kg/h. The length of these units goes from 10 to 30 m. The width of the conveyor belt is approximately 2 m. Steam consumption can go from 500 to 2.000 kg/h. Water consumption goes from 10 to 40 m$^3$/h

### Hot-break

The hot break process is a thermal treatment that completely inactivates pectin enzyme activity and impede syneresis on the fruit juice or puree. Synerisis causes the separation of liquids from the product.

The hot break process heated the product up to 85-95℃. The fresh fruits are generally chopped during heating. Alternatively to hot-break, cold break is also a thermal treatment where the fruit is chopped at lower temperatures, ranging from 65 to 75℃.

The difference between the two processes lies in the apparent viscosity, measured in Bostwick centimeters. The Hot Break product is more viscous and therefore denser. An average Bostwick viscosity for tomato sauces treated with the hot break process results in values ranging between 3.5 and 6 centimeters. Cenversily, the cold-break product is less viscous, therefore less dense. Normally, the tomato sauce treated with a cold break process measures from 9 to 16 Bostwick centimeters.

The hot break product is usually desired for fruit sauces concentrated at a level of 30°Bx. The cold break process is more useful when higher brix values (i.e. 40°Brix) and higher fluidity of the product is desired.

It has been demonstrated that if pectolytic enzymes, naturally present in tomatoes and fruit, are exposed to oxygen during the chopping process, they are revitalized and begin to destroy pectin. Pectin is the substance which gives consistency to the tomato paste. It has also been observed that the pectolytic enzymes can be deactivated at temperatures exceeding 85℃. Therefore, all enzyme deactivation systems, known as Hot Break Units, raise the product’s temperature up to 85° C and over so as to deactivate the enzymes as quickly as possible and therefore preserve the product’s natural viscosity.

This operation can be done, as a first step, in the evaporator.

### Pasteurization

Pasteurization is a thermal process performed at temperature typically below 100℃. The goal of pasteurization is to kill microbial pathogens in a state of vegetative cells. Examples of pathogens in such state are the following:

• Eschelichia coli
• Salmonella enterica
• Shigella
• Listeria monocytogenes
• Campylobacter jenunii
• Staphylococcus aureus
• Yersinia enterocolotica

All the above microorganisms are non-sporulent. Thus, their thermal stability is weak and a simple treatment for a few seconds at temperatures above 60℃, generally, will suffice to reduce the level of contamination.

It follows the D-values of some relevant pathogens at specific reference temperatures. You might notice that spore forming bacteria (i.e. Cl. botulinum) use as reference temperature values above 100℃, whereas vegetative cells use always reference temperatures below 100℃.

Microorganism Temperature (℃) D (min.)

### Alteration of juices by Alicyclobacillus acidoterrestris

Pasteurization has also the goal to inactivate microrganisms and enzymes that can alter the product quality. Unfortunately, many fruits and vegetables are contaminated by Alicyclobacillus acidoterrestris spores. Alicyclobacillus acidoterrestris is a thermoacidophilic, nonpathogenic, sporeforming and aerobic microorganism, which has been isolated and identified in several spoiled commercial pasteurized fruit juices, such as orange and apple juices.

It follows a table with the main parameters of growth for Alicyclobacillus acidoterrestris:

Parameter Value

During growth, the metabolism of Alicyclobacillus acidoterrestris produces an unpleasant smell evocative of disinfectants (2.6-dibromofenol and 2-methoxyphenol that is guaiacol). Also, changes in pH, color and texture can contribute to the emergence of a white precipitate.

It has been reported that degassing and/or reduction of the oxygen content to 0.1% (apple and white grape juice) or create anaerobic conditions (orange juice) to inhibit the growth of A. acidoterrestris.

The most effective way to eliminate bacteria Alicyclobacillus spp. is ultrafiltration. However, due to the high cost of this operation, thermal pasteurization remains the most widespread operation used to control such microorganisms.

### Alteration of juices by Enzymes

Biochemical processes are the one of principal causes of fruit and vegetable deteriorations. The alteration of fruit products driven by enzyme activity is generally controlled by using severe thermal treatments, that are typically applied during the so-called hot-break process. During such operation, the operative conditions can achieve 90-95℃ for 1-3 minutes. other processes such as high pressure or pulsed electric fields have also been proposed, although, their effectiveness on enzyme inactivation is controversial.

Unfortunately, it is rarely possible to generalize D and z value of enzyme activity. The type of vegetable used, the initial content of enzymes, the presence of natuaral inhibitory substances (i.e. polyphenols), the pH of the medium give some uncertainty. Furthermore, the same enzyme might be present in the product in the so-called iso-forms. An enzyme isoform is a protein that is highly similar to the original one. It has been expressed from the same gene family. By the way, during its expression results with some genetic differences. Such differences are in fruits typically observed whith enzymes like POD, PME or PPO with very high thermal resistence.

To design the right thermal treatment, and account also for isoforms, fruit industry relies on the peroxidase (POD) activity. This enzyme is a good indicator of the suitability of a thermal process. This is because this enzyme is present in fruit, generally, in high concentrations. In addition, POD shows a very high thermal stability. Finally, POD assays are generally simple and quick to perform. The fact that POD has a very high thermal stability is good as it provides a safety margin. If peroxidase is inactivated, it is a reasonable assumption that other quality-related enzymes have also been inactivated. On the other hand, a thermal process designed in such way may result in overestimated heat treatments. This may cause other quality problems.

Medium Enzyme D-value z-value

Where, PME is pectin methyl estherase; POD is peroxydase; PPO is polyphenoloxidase; PG is pectin galacturonase.

### Sterilization

Sterilization is a severe thermal process, typically performed at temperature above 100℃. The aim of sterilization is to kill all microorganisms, either vegetative cells or spore forming bacteria. When applied to fruits, we refer implicitly to commercial sterilization. This means that the concentration of spore forming pathogen, like Cl. botulinum is reduced by at least 12D (i.e. D is the decimal reduction time). Sterilized products generally have a shelf-life of two years or more.

Sterilization aims to the complete destruction of microorganisms. Because of the resistance of certain bacterial spores to heat, this frequently means a treatment of at least 121℃ of indirect steam spray for 15 min. or equivalent. It also means that every particle of the food must receive this heat treatment. If a can of food is to be sterilized, then immersing it into a 121℃ pressure cooker or retort for the 15 minutes will not be sufficient because of relatively slow rate of heat transfer through the food in the can to the most distant point.

When to apply sterilization? Sterilization is expensive. In addition, high temperatures may generate off-odors or off-flavors, which are not desired by the consumers. Nowadays, there are direct heat exchangers that allow thermal treatments of 140℃ for a few seconds, obtaining a final product of excellent quality, very stable and safe. However, when the product has a pH below 4.5, its shelf-life can be shorten of a few months, then the investment on sterilization process is economically unsustainable. Most of the acidic fruit juices or puree can be processed by a simple pasteurization process, that is following to a hot-break process. Instead, sterilization becomes important when the product has a pH of 4.5 or higher and when its shelf life must be assured for 2 or more years. Tomato sauces in cans are a typical example. The pH of tomato is around 5.0. Thus, a simple pasteurization process does not allow its storage at room temperature for prolonged times, since spores of pathogen bacteria can germinate (even in absence of oxygen) and produce toxins.

As a general rule-of-thumb, consider the following decision tree to decide which thermal treatment should be applied to your product:

According to the above decision tree, it is possible to define the following products:

(I) Acidic fruit juices.
This is a relatively safe product. As soon as the pH is so low, no growth of pathogens is expected. Shelf life can be long. The manufacturing comprises a first hot-break process at 95-98℃ for 10-30 seconds, followed by a second pasteurization step at 95℃ for 15 seconds. Store at room temperature. Example: apple or grape juice.
(II) Pasteurized medium acidic juices.
This product requires refrigeration, otherwise spore forming bacteria can germinate and produce toxins. The manufacturing requires longer times, typically some minutes at 95-98℃, since PME is very stable at the high pH of these fruits (i.e. figs, cantaloupe, tomatoes). Shelf life is short. If possible, add acids to lower the pH.
(III) Sterilized medium acidic juices.
This is a safe product. Sterilization assure the killing of spore forming bacteria. Store at room temperature. Shelf-life can be long.
(IV) Pasteurized smoothies (limited conservation)
This product requires storage at refrigeration temperatures, otherwise spore forming bacteria can germinate and produce toxins. Shelf-life is very short. Examples include fresh juices of carrots (pH ≈ 6.0), watermelon (pH ≈ 5.5) or papaya (pH ≈ 5.5). If possible, add acid and lower the pH. Consume fresh, preservation is difficult.
(V) Sterilized cans of low acidic juices or sauces.
This is a safe product. Sterilization assure the killing of spore forming bacteria. Shelf-life can be long. Store at room temperature. As an example, canned tomato sauces fall in this category.

It follows a simple classification of thermal treatments:

Methods Temperature (°C) Hold time