Bubble hydrodynamics and mass transfer at high reynolds number and surfactant concentration

Microscopic Visualization of Insect Cell‐Bubble Interactions. I: Rising Bubbles, Air‐Medium Interface, and the Foam Layer

“…The high surfactant condition existing in the medium further complicates the flow around the bubble. As reported by Andrews et al (1988), at high surfactant concentrations a third hydrodynamic regime for these bubbles was observed, which was referred to as "large-wake" hydrodynamics. In this regime the high concentrations of surfactant alter the boundary condition around the rising bubbles such that the flow separation is moved to the front stagnation point, thus creating a large wake around the rising bubble.…”

The Effect of Surfactant on the Motion of a Buoyancy-Driven Drop at Intermediate Reynolds Numbers: A Numerical Approach

“…For a contaminated drop translating at moderate Reynolds numbers, ∇ S γ < 0 and τ ξη > 0 at the front of the drop, and ∇ S γ > 0 and τ ξη < 0 in the wake region. A similar conclusion has also been given using the boundary layer theory (41). On the other hand, it has also been found from Fig.…”

“…9c and 9d, it is found at the point with ∇ S γ = 0 that the surface concentration reaches its maximum value. At creeping flow, Andrews et al predicted that surface concentration increases and surface tension decreases monotonically along the interface (41). This simple case leads to many "intuitive" ideas of how surfactant accumulates at the back of a drop.…”

“…[40] Beside the boundary conditions at the interface, the following initial and boundary conditions are specified for the governing equation [33]: [41] c ξ 1 , η 1 , t = 1 (at the far remote boundary, ξ 1 = 0), [42] ∂c ∂η 1 = 0 (on the axis of symmetry, η 1 = 0).…”

Modeling particle transport by bubbles for performance guidelines in airlift fermentors

“…The liquid velocity is assigned a normal distribution (standard deviation 10%) and the bubble velocity a Poisson distribution, both on the basis of data presented by Serizawa et al? 3 The data of P.S. Hatton and N.H. Thomas (1990, University of Birmingham) indicates that the time between bubble encounters is apparently normally distributed with a standard deviation about 10% of the mean value.…”