LXXXII.Bubbles and drops and Stokes' law

Ascending air bubbles in solutions of surface-active molecules: Influence of desorption kinetics

“…As first noticed by Bond [2] and later formalized by Levich [3], the hydrodynamic behavior of drops or bubbles can be modified by adsorbed surface-active molecules through the so-called Marangoni effect. The fluid surrounding a moving bubble is responsible for the advection of adsorbed molecules along the interface and their accumulation at the rear of the bubble.…”

The transition in settling velocity of surfactant-covered droplets from the Stokes to the Hadamard–Rybczynski solution

“…In 1953, Savic (1953 introduced the stagnant cap model (SCM) as an explanation of the experimental results obtained by Bond (1927); Bond and Newton (1928). The SCM incorporates the effect of surfactants through a rigid cap where a no-slip boundary condition is used.…”

“…But experimentally observed terminal velocities of small drops do not match the Hadamard-Rybczynski result, but rather the Stokes result for the vast majority of combinations of "clean" fluids, see e.g. the work by Nordlund (1913); Lebedev (1916); Silvey (1916); Bond (1927); Bond and Newton (1928). In the latter work, a distinguished jump was found in the terminal velocity, going from the Stokes result to the Hadamard-Rybczynski result as the drop radius was increased.…”

Effects of confinement on bubble dynamics in a square duct

“…Early works of Allen (1900), Hadamard (1911), Rybczynski (1911), Bond (1927) and Bond and Newton (1928) examined the validity of Stokes' drag law (of a rigid sphere) for a rising bubble and a falling liquid drop. Since bubbles and drops allow internal circulation and tangential velocity at their surfaces, Stokes' theory needed correction to account for the different boundary condition (Bond (1927), Bond and Newton (1928) and Levich (1962)).…”