WO1995030118A1

WO1995030118A1 - Method and device for controlling vacuum lyophilization

Info

Publication number: WO1995030118A1
Application number: PCT/FR1995/000563
Authority: WO
Inventors: Frédéric Rene; Noël GENIN; Georges Corrieu
Original assignee: Institut National De La Recherche Agronomique
Priority date: 1994-05-03
Filing date: 1995-04-28
Publication date: 1995-11-09
Also published as: DK0756692T3; FR2719656A1; EP0756692A1; DE69505245D1; AU2449895A; FR2719656B1; ES2122603T3; ATE172022T1; EP0756692B1; DE69505245T2

Abstract

Method for controlling the water content of a product being dehydrated and corresponding device. The invention also concerns a method for detecting that the dehydration phase has been completed and a corresponding device.

Description

METHOD AND DEVICE FOR CHECKING THE VACUUM FREEZE SOU _S

The present invention relates to a method for controlling the dehydration of products and in particular to a method for controlling the dehydration by freeze-drying under vacuum of initially frozen products. It also relates to a method for detecting the end of dehydration and in particular a method for detecting the end of sublimation of a product during lyophilization. The methods according to the invention can also be applied to other methods for drying products, not necessarily frozen beforehand, in which heat can be supplied to the products by a hot gas, by direct contact or by thermal radiation or infrared. The invention also relates to devices for implementing these methods. By "products" is meant any liquid, pasty, solid or divided solid material of animal, vegetable or mineral origin, capable of undergoing dehydration. These materials can be processed in bulk or packaged in containers.

The present invention applies more particularly to materials for which the final water content of the product is a determining criterion or which can suffer significant damage when they continue to be strongly heated after disappearance of the water which they contained. This is particularly the case for all food products and pharmaceutical products which may undergo an alteration in their characteristic properties (texture, color, aromas, biological activity, therapeutic activity, etc.).

The drying methods to which the invention applies are all those for which the water content of the product can be measured. The invention applies very particularly to lyophilization processes.

We know that freeze-drying is a low temperature process during which most of the water contained in a product is removed by sublimation. As with other dehydration processes, the goal of freeze-drying is to reduce the water activity of the products in order to ensure their conservation. It is a technique particularly well suited to temperature-sensitive products and which allows most of the original characteristics of the products to be preserved. Dehydrated products also have a high porosity which promotes rehydration or allows rapid dissolution. The quality constraints of freeze-dried products and the high costs of the operation require a good understanding of the kinetics of dehydration (speed of elimination of water) in order to be able to determine the instant corresponding to the end of sublimation and therefore the 'when to stop the process.

Until now, in the absence of a satisfactory method, the online measurement of the residual water content of the products has never been carried out and users have most often limited themselves to monitoring of different sizes making it possible to more or less finely assess the end of freeze-drying. The decision to stop freeze-drying is made according to pre-established empirical rules, generally on the basis of a time after the appearance of a phenomenon such as the rise in temperature of a product or the stability of total pressure. after isolation of the lyophilization enclosure. To continuously estimate the kinetics of dehydration, it is possible to measure the weight of the products being dehydrated. During freeze-drying, it is also possible to use the measurement of the weight of the ice trapped on the condenser. This requires designing the installation so that weighing can be carried out continuously and is difficult to adapt to an existing installation. It is also possible to carry out the heat balance at the condenser level. Finally, simulation by calculation using a mechanistic model can allow this kinetics to be assessed. This requires a priori knowledge of the quantities relating to the product, namely: value of the porosity of the material, the thermal conductivity of the frozen material and the dry material, the water content, the geometry of the sample as well as the heat transfer coefficients (conduction, convection, radiation) and internal material transfer (value of the diffusivity of water in the dry product) and external (diffusivity of water vapor in the enclosure to the cold room). Such a simulation is therefore relatively complex. In order to detect the end of dehydration and in particular, the end of lyophilization, different principles can be used. A first set of methods consists in using indirect measurements such as the measurement of the temperature of the product or of its electrical properties, measurements of partial pressure of water vapor or other volatile compounds, or else the composition of the gas present. inside the enclosure. In the case where the lyophilization enclosure can be isolated from the rest of the installation, in particular from the condenser, the total pressure rise in the enclosure characterizes a water departure from the product. The absence of pressure build-up after isolation of the enclosure can be a criterion for the end of freeze-drying. Finally, the technique of simple nuclear magnetic resonance or by imaging can also be used. Another approach consists in regularly taking samples in the lyophilization enclosure and in measuring the water content, but it is not practicable on an industrial scale and is therefore limited to exploratory studies on the scale of small freeze-dryers. .

These methods for assessing the end of dehydration and in particular lyophilization, are not very capable of assessing both the final water content of the product and the dehydration kinetics characteristic of the process. To remedy these drawbacks, the invention proposes to evaluate in real time the residual water content of the product being dehydrated in order to cause, possibly automatically, the stopping of dehydration and / or the change in operating conditions. In addition to determining the kinetics, an end of dehydration estimator makes it possible to trigger, possibly automatically, the stopping of dehydration or a reduction in the heating temperature in order to preserve the quality of the already dry products.

Thus, the invention relates to a method for controlling the water content of a product being dehydrated in a lyophilization apparatus comprising means for condensing the water vapors, these escaping from the product towards said means to condense.

According to the invention, the method consists in continuously determining the water content from the value of the mass flow rate of water vapor escaping from the product, which is placed in a lyophilization enclosure, this value being determined from the measurement of the total pressure values of the freeze-drying enclosure and of the partial pressures of water vapor in the vapor flow between said product and said means for condensing water vapors and on the surface of said means , an adjustment procedure carried out initially having established, for the product in question, the relationship between these different values.

Throughout the description, the term "mass flow rate of water escaping from the product" means the quantity of water escaping from the product, per unit of time.

The invention also relates to a method for detecting the end of the dehydration of a product, which is characterized in that it consists in establishing the values of the quantity of water vapor escaping from the product on the one hand , according to a mixed convection-diffusion mode valid at during dehydration and on the other hand, in a purely diffusive mode valid at the end of dehydration and to determine the difference between these two values, the end of dehydration being reached when this difference is close to the value 0.

Preferably, the product being lyophilization in a lyophilization apparatus comprising a chamber in which said product is placed and means for condensing the water vapors, the two values of the quantity of water vapor escaping from the product are determined from the measurement of the values of total pressure of the lyophilization enclosure and of the partial pressures of water vapor in the flow of vapor between said product and said means for condensing the vapors and at the surface of said means, the end of the sublimation being reached when the difference between the two values is close to the value O.

The invention also relates to a device suitable for implementing the process for controlling the water content of a product being dehydrated in a lyophilization apparatus.

The device comprises three sensors, the first detecting the total pressure in the lyophilization enclosure, the second, the partial pressure of water vapor between the product being lyophilized and the means for condensing the water vapors and the third , the partial pressure of water vapor on the surface of said means, as well as an interpretative device connected to these three sensors and determining the instantaneous mass flow rate of water vapor escaping from the product from the values measured by said sensors, said member thus being able to determine, continuously, the water content from the value of the mass flow rate of water escaping from the product. Preferably, the device is connected to a control member of the lyophilization apparatus. The invention finally relates to a device for implementing the method for detecting the end of dehydration of a product.

Such a device comprises means determining the values of the quantity of water vapor escaping from the product on the one hand, according to a mixed convection-diffusion mode valid during dehydration and on the other hand, according to a purely mode diffusive valid at the end of the dehydration, as well as an interpretative organ determining, continuously, the difference between these two values, the moment when this difference reaches appreciably the value O corresponding to the end of the dehydration.

In particular, the invention relates to a device for implementing the method for detecting the end of sublimation of a product during lyophilization in a lyophilization apparatus. This device comprises three sensors, the first detecting the total pressure in the lyophilization enclosure, the second, the partial pressure of water vapor between the product being lyophilized and said means for condensing the water vapors and the third , the partial pressure of water vapor on the surface of said means, as well as an interpretative member connected to these three sensors and determining the difference between the values of the quantity of water vapor escaping from the product towards said means according on the one hand, a mixed convection-diffusion mode, valid during sublimation and on the other hand, a purely diffusive mode, valid at the end of sublimation, the moment when this difference reaches appreciably the value 0 at the end of the sublimation.

Preferably, the device is connected to a control member of the dehydration device which, when the water content has reached a predetermined value, automatically proceeds to a new phase of operation, in particular the procedure for stopping the installation. , a modification of operating conditions or other treatment, of a physical, chemical or mechanical nature.

The invention will be better understood and other objects, advantages and characteristics thereof will appear more clearly on reading the description which follows, made with reference to the appended drawings in which:

- Figure 1 schematically illustrates an installation for an example of implementation of the method according to the invention, - Figure 2 illustrates a first variant of device for an example of implementation of the method, adapted to a first configuration of apparatus of freeze-drying (with internal condenser), FIG. 3 illustrates a second variant of device for an example of implementation of the method, adapted to a second configuration of freeze-drying device (with external condenser),

FIG. 4 is a curve illustrating the results of tests provided by the method and the device according to the invention for the lyophilization of semi-skimmed milk and,

- Figure 5 is a curve illustrating the test results provided by the method and the device according to the invention for the lyophilization of banana rings.

The elements common to the different figures will be designated by the same references.

With reference to FIG. 1, 1 denotes a dehydration apparatus. Such an apparatus comprises, conventionally, an enclosure in which the products to be treated are placed.

Reference 2 designates sensors placed in suitable places in order to continuously record determined values which will be defined more precisely. The method according to the invention is based on the study of the quantities of material escaping from the product during dehydration.

The quantity of material escaping from the product during dehydration can be determined directly, in particular by using infrared adsorption or nuclear magnetic resonance techniques.

It can also be determined using models, representative of material transfers. In known manner, during dehydration, the material escapes from the product in a mixed mode, of the convection-diffusion type. The model corresponding to this transfer mode is the Stephan-Nusselt model. In this regard, we can refer to the following work: BIRD R.B., STEWART W.E. and LIGHTFOOT E.N., 1960. Transport phenomena. John Wiley & Sons, New York, USA.

This model is based on the following assumption: in steady state established, the transfer of matter is carried out under the effect of a potential gradient within an inert fluid.

It takes the following form:

in which :

C _n : represents the molar concentration (mole. L " ³ )

D: represents the diffusivity (L ² .t ^-1 ) ξ: represents the molar fraction and

- * î: represents the direction of the transfer. The study of material transfers shows that at the end of dehydration the mixed convection-diffusion model tends towards a simpler expression. Physically, the transfer of matter becomes purely diffusive.

It is assumed that in steady state established, the transfer of material takes place only under the sole effect of a potential gradient. The Stephan-Nusselt model (1) can then be simplified and take the form:

where Jl * represents the molar flux density (moles.t ^_1 . " ² ).

This model (2) is commonly known as the Fick model.

The methods according to the invention are notably based on the use of these models when there are no means allowing direct determination of the quantity of water vapor escaping from the product during dehydration.

These models can be used for any type of dehydration process for which it is possible to determine the water content of the product.

They can, in general, be expressed in a simplified form. The sensors 2 make it possible to determine the values of the quantities involved in these models. The methods according to the invention are particularly applicable to lyophilization methods. In this case, the product is placed in a lyophilization apparatus comprising, in a conventional manner, an enclosure for the products and means serving to condense the water vapors, such as a condenser. For this type of process, the Stephan-Nusselt model (1) can be expressed in a simplified form.

In fact, in the case of such a transfer mode in a gas considered to be stationary, the instantaneous mass flow of water is proportional to the logarithm of the ratio of the partial pressure values of the stationary gas at the level of the condenser and in the enclosure of lyophilization.

Thus, from the measurement of the values of total pressure of the lyophilization chamber and of the partial pressures of water vapor in the vapor flow and at the surface of the condenser, it is possible to determine the desired kinetic information. The combination of these three measures is essential to assess the kinetics of dehydration. When the method used is a lyophilization method, the sensors 2 are provided for determining the pressure values. It can be noted that for a condenser operating in thermodynamic equilibrium, the value of partial pressure of water vapor of the condenser can be deduced from the operating temperature of the condenser. Designate by 3 an interpretation unit for the measurements made at each instant by the sensors 2. This interpretation unit which receives the data recorded by the sensors translates, as a function of the type of lyophilized product, of the geometry of the device. used and operating conditions, the average residual water content of the product being dehydrated, from the Stephan-Nusselt model (1).

At the end of dehydration, as indicated above, the transfer mode becomes purely diffusive. However, in the case of such a transfer mode, the Fick model (2) can be expressed in a simplified form. The instantaneous mass flow of water leaving the product is proportional to the partial pressure gradient of water vapor between the lyophilization enclosure and that of the condenser.

Thus, the interpretation unit 3 performs the calculation of the instantaneous mass flow of water leaving the product in the case of a mixed convection-diffusion transfer mode, and in the case of a purely diffusive transfer mode, in using the measurement results from the sensors 2.

The member 3 thus makes it possible to describe in real time the end of the dehydration by means of an encrypted indicator whose deviation from the zero value reflects the fact that the sublimation phase is completed or not. This indicator does not require any knowledge of the product during dehydration or any other parameter than the three quantities measured by the sensors 2.

The water content and the sublimation end estimator thus established can be directly transmitted to the operator who can then stop the lyophilization if the water content has reached a predetermined value. It can also modify the operating conditions, in particular the temperature and / or pressure, making it possible to continue the operation, in particular by means of a control member 5 controlling the operating conditions of the device 1.

The operator can also carry out another processing:

- physical in nature: such as grinding or desorption to allow the extraction of strongly bound water,

- mechanical: such as closing and crimping the bottles containing the products being dehydrated, - chemical: such as the spraying of flavors, colors, preservatives (antioxidant for example) or sugar 'coating; sterilization treatment.

The water content and the sublimation end estimator can also be directly transmitted to the control member 5 which automatically proceeds to the start of a new operating phase, when the water content has reached a predetermined value. This new phase can be, for example, the installation shutdown procedure, the modification of operating conditions or another treatment, of a physical, chemical or mechanical nature.

The quantities can in particular be transmitted to a display device 4.

It is also possible to provide that the interpretation member 3 performs the desired comparisons and acts directly on the control member 5. The processes according to the invention have more particularly been described for a product in the course of lyophilization but they are applicable to any other dehydration process. FIG. 2 represents a so-called lyophilization apparatus with internal condenser.

The reference 9 designates the hermetic enclosure in which the lyophilization takes place and the reference 10, the means making it possible to create and maintain the desired vacuum in the enclosure 9.

In the enclosure 9, a cold trap or condenser 6 is provided which is used to condense the water vapors and a system 8 for supporting and supplying the thermal energy necessary for lyophilization. The product 7 to be lyophilized is placed inside the system 8.

The device according to the invention essentially comprises three sensors 2a, 2b, and 2c and an interpretation member 3 connected to said sensors. These are placed inside the enclosure 9, the sensor 2c being placed near the condenser 6.

At each instant, the sensors 2a, 2b, 2c respectively establish the value of the total pressure in the lyophilization enclosure 9, the value of the partial pressure of water vapor in the enclosure 9 in the vapor flow between the produces 7 and the condenser 6 and the partial pressure value of water vapor at the surface of the condenser 6 and they transmit these values to the interpretative member. This member has in memory the coefficients making it possible to link the instantaneous mass flow rate of water vapor escaping from the product to the logarithm of the ratio of the partial pressures of the stationary gas to the condenser 6 and in the lyophilization enclosure 9. These coefficients have determined during an initial adjustment procedure which will be described later. The interpretive organ thus continuously calculates the instantaneous mass flow of water leaving the product 7 and therefore the residual water content of this product.

At the same time, the interpretation unit 3 calculates, from the values supplied by the same sensors 2a, 2b, and 2c, the difference between the real expression of the logarithm of the ratios of the partial pressures of the stationary gas to the surface of the condenser 6 and in the freeze-drying enclosure 9, expression corresponding to a mixed diffusion-convection transfer mode and the simplified expression corresponding to a purely diffusive transfer mode. This simplified expression is valid when the end of sublimation is reached. The rapid convergence of this value towards zero is characteristic of the end of sublimation.

FIG. 3 illustrates a device according to the invention for a lyophilization device called an external condenser. This device differs from the previous one in that the condenser 6 is placed in an enclosure 11 connected by a conduit 12 to the enclosure 9 containing the system 8 for supporting the product to be lyophilized and for supplying the thermal energy necessary for lyophilization.

The device according to the invention always comprises three sensors 2a, 2b, and 2c and a verification member 3. The sensor 2a is placed in the enclosure 9, the sensor 2b in the conduit 12 and the sensor 2c in the enclosure 11 .

The operation is identical to that described with regard to FIG. 2.

The process for controlling the end of dehydration has been described for a lyophilization process. However, this process is applicable to any dehydration process. It is based on the use of the Stephan-Nusselt and Fick models, the difference between the values of mass flow rate of water given by each of these models, converging towards the value O at the end of the dehydration. As far as the position of the sensors is concerned, the most satisfactory results are obtained as follows: the total pressure sensor is placed in the enclosure, the partial pressure sensor in the enclosure is placed in the vapor flow. more homogeneous (not near the condenser or the product) and the sensor determining the partial pressure on the surface of the condenser is preferably a condenser temperature sensor which is placed directly on the condenser, the partial pressure value being easily deduced the value of the condenser temperature.

For the implementation of the method according to the invention, an initial procedure for adjusting the device should be carried out, in relation to the dehydration apparatus 1, the operating conditions and the product 7 considered. This procedure is more particularly described for a lyophilization apparatus.

This procedure consists of tests which can be carried out as follows: product 7, the initial water content of which is known, is lyophilized for variable durations, previously chosen by a person skilled in the art according to the nature of the product and the operating conditions used. The sensors 2a, 2b and 2c continuously measure the values of the total pressure of the enclosure, of the partial pressure of water vapor in the enclosure between the product and the condenser and of. the partial pressure of water vapor on the surface of the condenser. After the freeze-drying has stopped, the final water contents of the product obtained for the different durations tested are determined. The values of the lyophilization durations and of the final water contents obtained are used for the determination of the coefficients necessary for the calculation of the kinetics of dehydration and which are stored in the interpretation unit 3. According to the degree of precision desired by the skilled in the art, the number of tests necessary for identification is between 1 and 3 per nature of product and by lyophilization operating condition.

Thus, the adjustment is made for a given device, depending on the product to be treated and the operating conditions used.

It should be emphasized that the method according to the invention can easily be implemented in existing installations. In fact, for example in lyophilization installations, two types of sensor are generally provided: a sensor measuring the total pressure of the enclosure and a sensor measuring the temperature of the condenser (from which the partial pressure of water vapor can be deduced on the surface of the condenser). It is therefore sufficient to provide a sensor for measuring the partial pressure of water vapor between the product and the condenser.

Figures 4 and 5 illustrate, for two types of tests, the results provided by the method and the device according to the invention.

FIG. 4 relates to the lyophilization under a pressure of 100 Pa of 25 glass vials containing 5 ml of semi-skimmed milk previously frozen at -20 ° C and placed on a plate heated to 50 ° C.

The crosses represent the kinetics of dehydration observed experimentally by regularly collecting the samples under vacuum and weighing them.

The curve in solid line represents the kinetic model of dehydration worked out by the interpretative organ after the preliminary procedure of adjustment and the curve in dotted line, the variation of the estimator of end of lyophilization.

FIG. 5 relates to the lyophilization under a pressure of 50 Pa of 52.9 g of banana rings previously frozen at -80 ° C. and placed in bulk on a plate heated to 60 ° C. in separate trays each containing about 26, 5 g of product. The crosses represent the kinetics of dehydration observed experimentally by collecting samples under vacuum and weighing them.

The solid line curve represents the kinetic dehydration model developed by the interpretative body after the prior adjustment procedure, and the dotted line curve, the variation of the end of lyophilization estimator.

These figures show that the method according to the invention makes it possible to precisely control the water content of a product during lyophilization and to determine, automatically, the end of lyophilization.

In addition, Table 1 shows how the present invention can be used to improve freeze drying. The example relates to the lyophilization of the button mushroom (Agaricus Bisporus) for which the residual octene-l-ol-3 level can be considered as representative of the loss of aromas suffered by the button mushroom during treatment . Thus, the higher the residual octene level, the better the quality in aromas of the lyophilized fungus.

Table 1 combines the results of six tests carried out under different operating conditions. However, in all the tests, the residual water content is identical.

TABLE 1

No. Test Conditions Residual rate Duration of operations in octene-l-ol-3 lyophilization (frozen product = (h) 100%)

El 60 ^β C / 5 Pa 28.4 16

E2 60 ° C / 50 Pa 16.9 14

E3 60 ° C / 100 Pa 8.7 12

E4 25 ° C / 100 Pa 10.9 20

E5 90 ^D C / 100 Pa 9.5 10

E6 90 ° C / 5 Pa up to 50% 30.1 10 of water then

60 ^β C / 50 Pa

The results show that different residual levels of octene-1-ol-3 are obtained depending on the operating conditions and also total variable lyophilization times, for the same final water content. Under fixed operating conditions, the maximum residual rate observed corresponds to 28.4% in the El test for a duration of 16 h of lyophilization. By using a change in the lyophilization operating conditions at an average water content of the product close to 50%, it is shown in test E6 that it is possible to obtain a residual rate of 30.1%, for a duration of 10 h freeze-drying.

Thus, the operating conditions of test E6 makes it possible to obtain both a gain in aromas and an energy gain.

The method according to the invention, by monitoring the kinetics of dehydration, therefore makes it possible to modify the operating conditions to minimize the loss of aromas. The only method known today that could to be used in this sense is the weighing method. However, as has been pointed out previously, this method can practically only be implemented in an installation designed for this purpose. It is very difficult to modify existing installations for this purpose.

The reference signs inserted after the technical characteristics mentioned in the claims, have the sole purpose of facilitating the understanding of the latter, and in no way limit their scope.

Claims

1. A method of controlling the water content of a product being dehydrated in a lyophilization apparatus comprising means for condensing the water vapors, the latter escaping from said product towards said means for condensing, characterized in what it consists in determining, continuously, the water content from the value of the mass flow rate of water vapor escaping from the product, which is placed in a freeze-drying enclosure (9), this value being determined from the measurement of the values of total pressure of the freeze-drying enclosure (9) and of the partial pressures of water vapor in the vapor flow between said product (7) and said means (6) for condensing the vapors of water and on the surface of said means (6), an initial adjustment procedure having established, for the product in question, the relationship between these different values.

2. Method for detecting the end of the dehydration of a product, characterized in that it consists in establishing the values of the quantity of water vapor escaping from the product on the one hand, according to a mixed convection mode -dif usion valid during dehydration and on the other hand, according to a purely diffusive mode valid at the end of dehydration and to determine the difference between these two values, the end of dehydration being reached when this difference is close of the value O.

3. Detection method according to claim 2 characterized in that said product (7) being lyophilized in a lyophilization apparatus (1) comprising an enclosure (9) in which the product and means (.6) are placed to condense the water vapors, the two values of the quantity of water vapor escaping from the product are determined from the measurement of the pressure values total of the lyophilization enclosure (9) and partial pressures of water vapor in the vapor flow between said product (7) and said means (6) for condensing the vapors and on the surface of said means (6), the end of the sublimation being reached when the difference between the two values is close to the value O.

4. Device suitable for implementing the control method according to claim 1, characterized in that it comprises three sensors (2a, 2b, 2c), the first (2a) detecting the total pressure in the lyophilization enclosure (9), the second (2b), the partial pressure of water vapor between the product (7) during lyophilization and the means (6) for condensing the water vapors and the third (2c), the pressure partial water vapor on the surface of said means (6), as well as an interpretative member (3) connected to these three sensors (2a, 2b, 2c) and determining the instantaneous mass flow rate of water vapor s escaping from the product from the values measured by said sensors, said member thus being able to determine, continuously, the water content from the value of the mass flow rate of water escaping from the product.

5. Device according to claim 4, characterized in that it is connected to a control member (5) of the lyophilization device (1).

6. Device suitable for implementing the detection method according to claim 2, characterized in that it comprises means determining the values of the quantity of water vapor escaping from the product on the one hand, according to a mixed convection-diffusion mode valid during dehydration and on the other hand, according to a purely diffusive mode valid at the end of dehydration, as well as an interpretative organ (3) determining, continuously, the difference between these two values, the moment when this difference reaches appreciably the value 0 corresponding to the end of the dehydration.

7. Device suitable for setting the method according to claim 3, characterized in that it comprises three sensors (2a, 2b, 2c), the first (2a) detecting the total pressure in the lyophilization enclosure (9), the second (2b), the partial pressure of water vapor between the product (7) during lyophilization and said means (6) for condensing the water vapors and the third (2c), the partial pressure of vapor d on the surface of said means (6), as well as an interpretative member (3) connected to these three sensors (6) and determining the difference between the values of the quantity of water vapor escaping from the product (7) towards said means (6) according to, on the one hand, a mixed convection-diffusion mode, valid during sublimation and, on the other hand, a purely diffusive mode, valid at the end of sublimation, the moment when this difference substantially reaches the value 0 corresponding to the end of the sublimation.

8. Device according to one of claims 6 or 7, characterized in that it is connected to a control member (5) of the dehydration apparatus (1) which, when the water content has reached a predetermined value , automatically proceeds to a new phase of operation, in particular the procedure for stopping the installation, a modification of the operating conditions or another treatment, of a physical, chemical or mechanical nature.