Absorption of particles from a melt by the surface of a bubble of variable size—Part III

The process of absorption of particles by the surface of a bubble in a melt is considered. The particles are also in the melt. Besides the particles, the melt also contains a surfactant which is adsorbed on the particles and on the surface of the bubble. There occurs an interaction which causes the particles to move towards the surface of the bubble. It is shown that during the movement of the bubble boundary the absorption of particles is determined by the parameter Δ = 16m2 co/(Dwoζ2κ2)R which depends on the velocity of motion of the bubble boundary R and on a parameter which does not depend on the velocity of motion of the boundary co/D. The parameters are as follows: m is the mass of a particle ζ is the area of a particle κ is a coefficient which determines the adsorption properties of the particle surfaceD is the diffusion coefficient of the surfactant in the meltwo = 2D/3πaa is a characteristic size of a particle = ζκτTRg/mT is the temperatureRg is the gas constant τ is the characteristic time of Stokesʹ attenuation of a particle in the melt. At small values of Δ the solution is close to that of the previous investigation [1], if a small correction to the flux of particles onto the bubble surface is introduced. At large values of Δ and positive velocities of the bubble-melt interface, a characteristic flux Jo can be distinguished which characterizes the running of the boundary on particles. It turns out that at co/D > 1, the flux . If the condition co/D < 1 is fulfilled, the flux of particles onto the bubble surface . In both cases the maximal value of the flux is on the bubble boundary. When the velocities of the boundary are negative, an interesting result is obtained at Δ > 1. Here we consider two cases. At co/D < 1 the flux is maximal near the surface of the bubble and increases exponentially in time. Strong absorption of particles in the area near the bubble boundary takes place. At co/D > 1 an N-wave is formed: the flux is maximum near the bubble boundary, and behind this area there is a trough. All this construction moves towards the bubble surface. We can say that an extremely strong dependence of the absorption regimes on parameters of the system and the velocity of the interface is a characteristic feature of the particle absorption at the moving interface.