Selection of structural parameters of a cylindrical-conical hydrocyclone for separation of suspensions by dual-stage flotation

Abstract

A mathematical model for separation of suspensions with a non-Newtonian disperse medium by dual-stage pressurized flotation in a cylindrical-conical hydrocyclone is developed. A system of differential equations of the convective diffusion and movement of a complex of particles-bubbles is solved by a numerical method. The concentration field is modeled, and integral separation indicators are determined. Values of structural parameters of the hydrocyclone for which the separation indicators depend heavily on the taper angle of the conical section of the housing and the rheological properties of the disperse medium are established.It is demonstrated that dual-stage pressurized flotation makes it possible to reduce considerably the residual concentration of solid-phase particles as compared with single-stage flotation.Cylindrical-conical hydrocyclones, which provide for high efficiency of the separation of dissimilar chemical systems in various branches of industry, are distinguished by high reliability, and simplicity of installation, and do not require extensive energy outlays for the separation process. Dual-stage pressurized flotation, which is realized in a cylindrical-conical hydrocyclone, can be used in a number of productions to achieve a high degree of extraction of solid-phase (SP) particles from a suspension.Dual-stage flotation takes place in the following manner: a preliminarily aerated suspension is delivered tangentially under elevated pressure (up to 0.8 MPa) to the cylindrical chamber of a hydrocyclone via an inlet pipe mounted in its upper section. By forming a rotating film (the velocity components are: circumferential v ϕ , axial v z , and radial v r ), the suspension that has entered the hydrocyclone moves downward along its walls. When the pressure is reduced to atmospheric, supersaturation of dissolved gas is created, and the suspension "effervesces." The centrifugal force moves the SP particles toward the wall of the housing of the hydrocyclone, while Archimedes buoyant centripetal force moves the air bubbles toward the SP particles to the surface of the film.In the first stage of pressurized flotation, formation of flotation complexes, which carry SP particles onto the surface of the film in a foam layer, the latter being removed by the upper branch pipe of the hydrocyclone, occurs when the SP particles collide with the gas bubbles. Bubbles of secondary gas that enters via the porous wall of the housing have a diam-

Regression equation for selection of design parameters and operating regimes of hydrocyclones used to separate suspensions by dual-stage flotation

“…Yablonskii [7,8] solves the separation problem of heterogeneous liquid systems with non-Newtonian properties by dual-stage pressure floatation in a film-flow regime in cylindrical and cylindrical-conical hydrocyclones.…”

“…Schematic of cylindrical-conical hydrocyclones for separation of suspension by dual-stage flotation: 1) inlet pipe; 2) upper discharge pipe; 3) gas-feed pipe; 4) porous permeable wall; 5) collector; 6) lower drain connection. [7,8], a feed of secondary gas to the hydrocyclone via the porous permeable wall will result in appreciable intensification of flotation. The purified suspension is removed from the apparatus through lower discharge connection 6.…”

“…In performing the calculations based on formula (1) by the numerical method, the axial velocity component of the free solid-phase particles and those bound in complexes H p (R, Z) was assumed equal to the axial velocity component of the dispersion medium H l (R, Z), since the inertia of the free solid-phase particles and the particle-bubble complexes in the axial direction were disregarded [7,8]. Approximation relationships for the axial velocity component of the dispersion medium H l (R, Z) are presented in [10].…”

“…Separation of heterogeneous liquid systems possessing non-Newtonian properties, which can be described by the Ostwald de Vila exponential law, by dual-stage pressure flotation in a hydrocyclone is characterized by the following determining similitude numbers [7,8]:…”

“…(2), we analyzed the separation of suspensions by dual-stage flotation in cylindrical-conical and cylindrical hydrocyclones [7,8] for the case most prevalent in flotation-separation practice, when the volume fraction of gas bubbles within the volume of the vessel appreciably exceeds the volume fraction of solid-phase particles.…”