INTRODUCTION
Dispersed gas–liquid systems (foams) in both the liquid and solid form find wide application in different industries (oil-and-gas, food, and metallurgical industries, firefighting, etc.). The mechanism of the foam formation process is complicated due to the combined effect of numerous physicochemical, physicotechnical, and other factors. The regularities governing the formation of dispersed systems strongly depend on the conditions of a chemical engineering or engineering process, and both the formation and destruction of an obtained gas–liquid layer occur simultaneously in the process of foam generation [1–14]. As a consequence, these features complicate to a great extent the mathematical description of the foaming process [3–5, 15–18].
Among the principal characteristics of a foam are the expansion factor (foam-to-solution volumetric ratio), the dispersion (air bubble size), and the stability (time period from the formation of a foam to its partial or complete destruction) [3–8]. The foam stability applicable to any foam independently of its purpose may be considered as a basic characteristic.
It is known that foams based on protein solutions, an increase in the concentration of which improves the foaming properties of a system as a whole, are highly stable [9, 10, 19–24]. The formation of bubbles generally depends on the composition of a foamed solution (foaming agent) and the intensity of a mechanical action, whereas their destruction proceeds under the action of both internal and external forces. For this reason, the entire foam generation process representing a process flow may be considered as a dynamic system of flows or a queueing system. This queueing system will be studied by the methods of stochastic processes and queueing theory [25–27].
The objective of this study is to create a stochastic model, which would systematically describe the processes of foaming in protein solutions and determine the time of the formation of a foam of specified quality.
OBJECTS AND METHODS OF STUDY
Foam formation regularities were studied via the gas saturation of a protein solution (skim milk protein concentrate; protein mass fraction, 4.4%) in a rotor-stator device (GID-100/1 hydrodynamic disperser, which was developed, manufactured, and mounted in the All-Russian Research Institute of Dairy Industry) at a rotor revolution speed from 1750 to 3000 rpm, a working chamber filling coefficient of 0.3, a rotor-stator gap of 0.1 mm, and a processed solution temperature of 13 ± 2°C. Control measurements were performed each three minutes after the freezing of samples in a nitrogen atmosphere and their transmitted-light microscopy on an AxioVert.A1 microscope with an AxioCamERc5 camera and a photo recording block. The number of bubbles was calculated from digital images with the use of corresponding software (the comparison of automatic and manual calculation results for the number of bubbles in the frozen samples shows that the former were underestimated by 18% on average).
