ASSESSMENT OF SOME PHYSICAL FACTORS AND DESIGN FEATURES OF ROTORS IN THERMAL EFFECTS CAUSED BY CENTRIFUGATION

In separating the components of highly dispersed heterogeneous systems, use is made of centrifuges with very high rotation velocities, this leading to samples heating. The said above is due to the friction of the rotor against the air from the centrifuge chamber to the movement of heating from centrifuge engine towards the samples and to compression of samples liquid. However, heating of samples sensible to temperature can generate in these samples the intensification of some uncontrolled chemical processes. This paper is devoted to the investigation of the increase of centrifuged samples temperature depending on the time and relative centrifugal acceleration for model-samples (water and glycerine) using two constructively different types of rotors. The obtained results can be taken into account when elaborating some more rigorous methods for studying finely-dispersed heterogeneous systems.


INTRODUCTION
Centrifugation is one of the procedures used for separating the components of heterogeneous systems in a centrifugal field [1,2].The latter is distinguished from the gravitational one by non-homogeneity (depends on the number of rotations velocities and the centrifugation radius), and by the fact that its lines of force are radially divergent.Centrifugal acceleration is expressed by formula (1): where: ω is angular velocity (rad/s), R is centrifugation radius (m), n is rotational frequency (s -1 ), π =3.14.
Centrifugation is used at solid / liquid separation [3], liquids decantation [4,5], mineral concentration [6] etc.The efficiency of the centrifugation process is expressed through the efficacy (or the separation) factor: where g is the acceleration of gravity (9.81 m/s 2 ).
In industrial and laboratory centrifuges this factor (z) reaches values of up to 20,000 and 350,000, respectively [2].
The current tendency of rapid development of new technologies (centrifugal casting [7], membrane separation [8] and chemical processing in centrifugal field [9,10]), need for new effective methods for use in scientific research [11][12][13][14] shall entail a much wider utilization of centrifugation processes in the future.
From the point of view of construction, and for security and other reasons, the rotor of the centrifuge is placed in a closed chamber.Having a very high rotation velocity, the rotor includes in turbulent movement the air from the centrifuge chamber which, due to friction, leads to the increase of air temperature, of the rotor and of centrifuged samples.Another source of heating can be the rotor axis that delivers the heating from the centrifuge engine.One should not rule out the heating of samples due to their compression under the impact of high centrifugal acceleration.There are centrifuges with cooling and vacuuming, but they are relatively expensive, have a big mass and size, this making their utilization difficult in laboratory conditions.
In the case of a prolonged centrifugation, chemical phenomena (reactions) that get intensified along with temperature increase, may occur in the samples under investigation.The number that characterizes the increase of chemical reaction's velocity at 10 0 C heating is called the thermal coefficient of reaction's speed.For most of the chemical reactions, the value of this ratio is within the 2-4 limits (the average being 3) [15].Heating by To work out some more rigorous methods for studying the highly dispersed systems, it is necessary to know the impact of various factors, including that of centrifugation, upon these systems so as to rule out possible errors.The purpose of this work has been to study the increase of temperature of samples subjected to centrifugation depending on the time and relative centrifugal acceleration for chemical substances with close specific thermal capacities and densities, but with different viscosities, when applying various types of rotors.

Materials and instruments
Distilled water and glycerine have been used for investigation.The water had pH 5.45 and specific conductance 3 .4   μS/cm.Glycerine had the characteristics of a pure chemical reactive.Centrifugations have been done in T 52.1 centrifuge (Leipzig, Germany) using 100 mL glasses hermetically closed with rubber cork.
Samples temperature measuring has been done by infrared thermometer (AR 872A, China) with 0.1 0 C gradation value.Technical specifications of the centrifuge as well the constructive peculiarities of used rotors are given in Figure 1 and Table 1.Maximal value of separation factor, a/g 22 0.45 6300 5100

Methods
The principal work method consisted in performing a series of consecutive operations of optimum timing, the latter being established before the experiment.When experimenting with water, two sets of glasses (introduced in metal ones) well balanced and with the some quantity of water (75 g) were used.First, the initial temperature of samples was measured, then the balance of glasses closed with cork was controlled and, finally, they were subjected to centrifugation.The rotational speed (min -1 , or number of revolutions: 2, 3, 4, 5 thousands rotations/min, see Table 2) was set using the centrifuge tachometer, while the duration of centrifugation (15, 30, 45, 60 min) was checked by means of a time relay of 1s error.After centrifugation, immediately after the rotor stopped its operation, the temperature of the liquid contained in the glasses was measured.Measurement lasted no more than 3 minutes.In both types of rotors, centrifugation was done applying the same method.Investigations on glycerine were done in the same way, the parallel samples (water and glycerine) being placed in separate glasses and the mass of each sample being 59 g.

RESULTS AND DISCUSSIONS
The dependence, in water samples, at temperature increase ( t  ) upon the rotation speed (n) and the centrifugation time (τ) is given in Figure 2. As it can be seen from the latter, the rise of samples temperature increases depending both on the rotation velocity, and on the length of centrifugation, reaching values from 1 to about 9 0 C.
However, the form of this dependence does not allow us to make any conclusions concerning the raison of samples heating.To determine the impact of the centrifuge engine in the samples temperature increase, additional measurements were carried out when the engine operated without the rotor, the glasses being in direct contact with the cone of engine's axis.
The obtained data are given in Table 3. Comparing the data from the Table for the same centrifugation conditions, we can draw the conclusion that the impact of the engine in the samples temperature increase is (depending on the centrifugation conditions) about 23-57 %.  2 and 3  Fig. 3.The same dependencies as presented in Figure 2, but for the glycerine samples.
However, in view of the fact that during centrifugation the glasses are at a bigger distance (14 cm) from rotor's axis, the impact of the engine in samples heating will be much less than the indicated one.
The results of glycerine samples heating investigation during centrifugation (parallel with those for water) are given in Figure 3 and Table 4.As it can be seen from these data, heating of glycerine samples is according to the same natural laws as is the case of water samples, thus demonstrating that liquid's viscosity doesn't play an important role in this process.The difference of t  values both of glycerine and water samples is explained by the different specific thermal capacity of liquids (for water 4.19•10 3 J/kg•grad, for glycerine 2.40•10 3 J/kg•grad), [16].
Table 5 shows how the construction of the centrifuge rotor influences upon the process of samples heating in similar condition.From this table, one can see that samples heating in the angular rotor (more aerodynamic) is lower, this being explained by smaller air turbulence in the centrifuge chamber when using this type of rotor.It is difficult to determine experimentally the share of liquid compression in the total thermal effect caused by centrifugation.That is why we have done theoretical calculations.The change of liquid volume of pressure increase can be expressed by following equation, see [16]: where: V are liquid volume (m 3 ), β its compressibility coefficient (m 2 /N), P are pressure exercised upon liquid (N/m 2 ).
During centrifugation, pressure P depends on the liquid density (ρ), centrifugal acceleration (a), as well as on the height (h) of the liquid column from the glass: Inserting in equation ( 4) the values: where: m is sample mass, S is the area of glass bottom, we shall obtain: Differentiating the introduce fractions, we came to the following relationship: The mechanical work (L) done at liquid compression (as in the case of gas compression) is the function of pressure (P) and volume (V): By introducing in (9): the values of dP from equation ( 8) and of dV from equation (3), we obtain: In the formula expressing the first law of thermodynamics [17]: where Q is the amount of the heat and U is the internal energy of the system, considering dU=0 (the system after centrifugation returns to the initial state), by introducing values: with: c is thermal capacity and L  = δQ from equation (12), we obtain following: Integrating the expression ( 14) with respect to t in the interval t 1... t 2 (duration of the process) and to a in the interval a 1... a 2 (initial and final values of centrifugal acceleration), we obtain: were of: or, if we introduce the value of z from equation (2), we obtain: where: t  are sample temperature increase, 0 C, m, V, c are sample mass, volume and specific thermal capacity, respectively, kg, m 3 , J/kg·grad, S represent area of glass bottom, m 2 , g is acceleration of gravity, m/s 2 , z is separation factor (or relative centrifugal acceleration), a/g; β is compressibility coefficient, m 2 /N.
Calculations done by means of formula (17) using data from [16] have shown that the share of liquid compression in the thermal effect caused by centrifugation is insignificant of 0.1 -0.5 0 C order (for centrifugation conditions presented in Table 2).

CONCLUSIONS
1. Samples get heated when centrifuged.The heating degree depends on the rotation velocity and duration of centrifugation, and can reach values that may accelerate chemical processes in samples.
2. The extent of samples heating (for water and glycerine) does not depend on the viscosity but only on the specific thermal capacity of centrifuged substances.
3. Heating of centrifuged samples is mainly due to friction between the rotor and the air from the centrifuge chamber.Much less this heating is caused by movement of heating from the centrifuge engine towards samples.The heating caused by compression of centrifuged liquids is of the order of 0.1 -0.5 0 C.
4. The degree of samples heating depends on the construction of centrifuge rotor and is smaller with the rotor that has a more aerodynamic shape.
accelerate the speed of reaction by 3 n times,

Fig. 2 .
Fig. 2. Dependence of temperature increase Δt on rotational speed n (the left) and on centrifugation time τ (the right) for water samples in the swing-out rotor (with move aside glasses).

Table 2 .
Centrifugation conditions used in experiment.

Table 3 .
The temperature increase of non-centrifuged (1) water samples (75 g) put in direct contact with the cone of the rotor axis, depending on the rotor's axis centrifugation time (τ) and rotation speed (n), in comparison with that of centrifuged (2) samples.

Table 5 .
The increase of temperature (Δt) of water samples (75 g) for 4000 min -1 rotational speed, depending on the time (τ) and the type (Figure1) of centrifuge rotor.