Propagation of compression waves in bubbly liquid with hydrate formation

Processing ores and anthropogenic Cu-Ni feedstock with the application of technology of jet air-steam flotation

“…(4) that the condition (8) corresponds to the complete steam condensation in a bubble, which is finished for time t k = 2.1 × 10 -2 s for bubbles with size R = 0.6 × 10 -3 m floating with veloc ity ω = 16.7 × 10 -2 m/s at thermal and mode parame ters of the steam-air flotation. We can determine a temperature at the interphase surface [11,12]: (9) where Nu is the Nusselt number; j is the mass flux den sity, kg/(s cm 2 ); and l is the specific heat of condensa tion, J/kg, from the condition of heat balance at the interphase surface (10) Here, the first summand (11) is the heat flux from a bubble to the interphase surface per its unit area, J/(s m 2 ), under the condition that while the second summand (12) is the heat flux from the bubble surface into liquid with the velocity of the steam-air mixture in a bubble (v νl , m/s) and condition A boundary layer of a bubble is heated due to the heat of condensation; however, due to the high ther mal conductivity of liquid, the heat flux is intensely removed from the interphase surface overheated by ΔT = (T s -T l ) = 2.5-3.5°C, which is characteristic of the flow of gas-liquid media [13][14][15][16].…”