Numerical Investigation of Marangoni Convection Around a Vapor Bubble in Aqueous Surfactant Solutions

Abstract

The effect of surfactant concentration on the Marangoni convection around vapor bubbles has been numerically investigated. The model consists of an adiabatic, hemispherical bubble on a downward facing constant temperature heated wall, in a fluid pool with an initial uniform temperature gradient. The time-dependent liquid mass, momentum, energy, surfactant bulk and surface transport, and adsorption kinetic rate equations are solved simultaneously. Conditions for bubble sizes varying from boiling nuclei to growing bubbles, and different surfactant bulk concentrations and wall heat flux levels are represented by a range of Marangoni and Rayleigh numbers: 100 ≤ MaT ≤ 6000, 0 ≤ MaS ≤ 2.2×106, 0 ≤ Ra ≤ 2.2. In the early transients, liquid motion is found to be induced by the temperature non-uniformity over the bubble surface, which along with self-diffusion, transports surfactant molecules from the bulk liquid towards the bubble surface. Consequently, the surface excess concentration is higher at the bubble base and decreases along the interface towards the bubble crown. The resulting concentration gradients promote diffusocapillary flows, which act in the same direction as the temperature-gradient induced thermocapillary flows, thereby enhancing the convection significantly. Also, for conditions representing boiling nuclei (in both partially and fully developed boiling regimes), the initial time transients appear to be heat flux independent.