**5. Materials and methods**

604 Mass Transfer - Advanced Aspects

At any time of the process duration τ the number of transformed microorganisms is Nd. The transformed cells can be in any place in space V. The number of living microorganisms

According to Eq. (28), after time τ of the process, microbial cells at mean concentration S<sup>α</sup>

n

=

Naturally, the overall concentration of microorganisms in space V will be determined by Eq. (29). The concentration will be recorded, for instance, in the suspension samples taken from

*<sup>N</sup> <sup>S</sup>*

*dN S dV <sup>d</sup>* = α

Volume dV displaced from Vαji to Vγji in time increment dτ depends on the size of limiting surface F through which dV is displaced and on the displacement rate u. This is described

*dV uFd* =

Upon substitution of Eq. (28) and (31) to Eq. (30) we obtain Eq. (32) which describes the

*<sup>d</sup> dN kNd* =

The process rate constant k of the transformation of microbial cells is described by Eq. (33).

*n*

= ∪

Based on Eq. (33) the loss of non-transformed objects can be represented by Eq. (34).

*<sup>F</sup> k u V*α

1

Surface F is the sum of these parts of surface F<sup>γ</sup>αji through which microbial cells pass to

*dN k N N d* =− − ( <sup>0</sup> *<sup>d</sup>* )

*i*

=

*i*

τ

τ

τ

The rate of conversion of microorganisms after time τ of the process is given by Eq. (26). The increase of the number of transformed objects dNd in all volumes Vγji after arbitrarily

*<sup>N</sup> <sup>S</sup>*α

= ∪

i i 1 V

α

*NN N* = <sup>0</sup> − *<sup>d</sup>* (27)

α

*V*= (29)

(30)

(31)

(32)

(33)

(34)

(28)

*<sup>i</sup>* are introduced to all

*<sup>i</sup>* is determined by Eq. (27).

present only in volume ∪*V*

volumes Vγji.

by Eq. (31).

volume Vγji.

α

the mill and in the inlet or outlet reservoir.

short time interval dτ is specified by Eq. (30).

increase of objects transformed in volumes Vγji.

determined by number N of unconverted cells in volume ∪*V*

Microorganisms were disintegrated in a horizontal bead mill with a multi-disk impeller. The working chamber about 1 dm3 in volume had the diameter of 80 mm. The impeller was equipped with six round disks 66 mm in diameter. They were mounted centrally on the shaft at a distance of 30 mm from each other. The mill was filled in 80% with ballotini of the diameter ranging from 0.8 to 1.0 mm. They were made of lead-free glass of specific density around 2500 kg/m3. 50% water solution of ethylene glycol at the temperature 275 K was supplied to the cooling jacket of the mill. Experiments were carried out in the mill at periodic operating conditions (constant feed). Rotational speed of the impeller was 261.8 rad/s.

The experiments were performed for commercial baker's yeast *S. cerevisiae* produced by Lesaffre Bio-corporation (Wołczyn, Poland). The concentration of yeast suspension ranged from about 0.002 to over 0.17 g d.m./cm3. Microorganisms were dispersed in the water solution containing 0.15 M NaCl and 4 mM K2HPO4.

The kinetics of cell disruption was determined on the basis of the count of living microorganisms present in the suspension samples. A computer-aided analysis of microscopic images (method I) was used. Cells were counted under the Olympus BX51 microscope (Olympus Optical Co.). Photographs were taken using a CCD digital camera of resolution 2576×1932×24 bit (Color View III, Soft Imaging System). Preparations were stained with methylene blue. Thom neu chamber (Paul Marienfeld & Co.) was used to count cells. Photographs were analyzed by means of a specialist software (analySIS 5, Soft Imaging System).

The amount of protein *R* dissolved in the continuous phase was determined by Bradford's method (1976) (method II). The supernatant was obtained after 20 min centrifugation at centrifugal force 34000 g. Measurements were made in a spectrophotometer at the wavelength 595 nm (Lambda 11, Perkin Elmer). A standard protein concentration curve prepared for bovine albumin (Albumin A 9647, Sigma) was applied.

The degree of release of intracellular compounds was analyzed also on the basis of light absorbance A in the supernatant (method III). The measurements were made using a Lambda 11 spectrophotometer (Perkin Elmer) at the wavelength λ = 260 nm (Middelberg et al., 1991; Heim & Solecki, 1998, 1999). Near the applied wavelength, spectral characteristics of RNA and DNA nucleic acids reach maximum values. The supernatant was obtained after centrifugation of the suspension in a 3K30 B centrifuge (Braun Biotech International) for 20 min at centrifugal acceleration of 34 000 g. The inside of the centrifuge was cooled down to 4°C.

In rheological investigations a RC 20 rotational rheometer (RheoTec) operating in a two-slot cylindrical tank – bell-shaped stirrer system was used. Measurements for the suspension of yeast cells and supernatant were made at the temperature 4°C. The degree of disintegration of microbial cells was changed from 0 to nearly 100%. Supernatant was obtained after 20 minute centrifugation of the suspension at centrifugal force 40 000 *g*.
