Hydrodynamics of an ensemble of drops (or bubbles) in the presence or absence of surfactants

摘要: Hydrodynamic effects of surfactants and neighbor particles on the terminal velocity an ensemble falling drops or bubbles have been analyzed formulated. A free surface cell model which takes into account hindering among has used to solve equations viscous fluid motion continuity simultaneously with a conservation equation for diffusing surfactants. The in presence absence expressed as where γ is retardation coefficient due Φ dispersed-phase holdup fraction. This generalization Levich's solution single drop (Φ → 0), Happel's solid ((μd + γ) ∞), Hadamard—Rybczynski 0, Stokes (μd ∞). Hence, this can predict velocities ensembles particles, drops, bubbles. Using same model, components present be employed heat, mass, charge transfer rates various particulate systems. general stream function formulated describe flow patterns continuous dispersed phases. An analysis hydrodynamics presented some specific domains.