Abstract
The area of the contact surface of phases is one of the main hydrodynamic indicators determining the separation and heat and mass transfer equipment calculations. Methods of evaluating this indicator in the separation of multicomponent two-phase systems were considered. It was established that the existing methods for determining the interfacial surface are empirical ones, therefore limited in their applications. Consequently, the use of the corresponding approaches is appropriate for certain technological equipment only. Due to the abovementioned reasons, the universal analytical formula for determining the interfacial surface was developed. The approach is based on both the deterministic and probabilistic mathematical models. The methodology was approved on the example of separation of two-phase systems considering the different fractional distribution of dispersed particles. It was proved that the area of the contact surface with an accuracy to a dimensionless ratio depends on the volume concentration of the dispersed phase and the volume of flow. The separate cases of evaluating the contact area ratio were considered for different laws of the fractional distribution of dispersed particles. As a result, the dependence on the identification of the abovementioned dimensionless ratio was proposed, as well as its limiting values were determined. Finally, a need for the introduction of the correction factor was substantiated and practically proved on the example of mass-transfer equipment.
Highlights
Adsorption, rectification, and separation processes are accompanied by heat and mass transfer.As known, the transfer of heat and mass derives through the surface of the phase contact, which is obtained from the surfaces of dispersed gas or liquid particles in a continuous phase
Considering the abovementioned studies, the aim of the research is to create a mathematical model to determine the interfacial surface for the separation of multicomponent systems
In the case of the normal distribution law of the continuous random variable distribution of dispersed particles, the probability density is determined by the following formula [38]:
Summary
The transfer of heat and mass derives through the surface of the phase contact, which is obtained from the surfaces of dispersed gas or liquid particles in a continuous phase. Processes 2020, 8, 306 design of heat–mass transfer and separation equipment. This parameter is basic for calculations of technological modes of heat–mass transfer and separation processes, the dimensions and number of single contact and separation sections, and the main unit dimensions. The specific interfacial surface a per unit volume is commonly determined depending on the average diameter of the dispersed particles dp and gas volume fraction φ as a = 6φ/dp , where coefficient 6 corresponds with the case of particles of the equal diameters. Despite the wide use of this expression, there is no theoretical foundation to evaluate this coefficient for different distribution laws of particle size
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