The stability of the horizontal interface of two immiscible viscous fluids in a Hele-Shaw cell subject to gravity and horizontal vibrations is studied. The problem is reduced to the generalized Hill equation, which is solved analytically by the multiple scale method and numerically. The long-wave instability, the resonance (parametric resonance) excitation of waves at finite frequencies of vibrations (for the first three resonances), and the limit of high-frequency vibrations are studied analytically under the assumption of small amplitudes of vibrations and small viscosity. For finite amplitudes of vibrations, finite wave numbers, and finite viscosity, the study is performed numerically. The influence of the specific natural control parameters and physical parameters of the system on its instability threshold is discussed. The results provide extension to other results [J. Bouchgl, S. Aniss, and M. Souhar, Phys. Rev. E 88, 023027 (2013)10.1103/PhysRevE.88.023027], where the authors considered a similar problem but took into account viscosity in the basic state and did not consider it in the equations for perturbations.
Instant food products are extremely popular, and food industry knows numerous ways and methods of their production. To remain competitive, an instant drink production process should be efficient and flawless. The research objective was to improve the physical profile of granular instant products.
The study featured a vibrating drum unit controlled segregated flows. The granulometric composition, porosity, and strength of the obtained granules were tested in a vertical vibration cl assifier.
The new design of the drum with an installed classifier was able to grind larger granules. The research revealed the effect of frequency and amplitude on the porosity and strength of the granules. The rotation rate of the belt mixer had a greater effect on the agglomeration process than the amplitude and frequency of the vibrations in the generator. The porosity and strength of the granules depended on the parameters of the classifier. Therefore, the new drum design made it possible to control the operating parameters depending on the required properties of the finished product. The rational parameters were obtained as follows: frequency and amplitude of the vibration generator – 1 mm and 40 Hz, respectively; rotation speed – 7 rpm; drum tilt angle – 3°; amplitude and frequency of the classifier – 2 mm and 100 Hz, respectively.
The study revealed the optimal technological parameters for a new instant drink. The new vibration classifier increased the distribution density of the granular composition.
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