Julien R. Landel

Spherical cap bubbles with a toroidal bubbly wake

The prediction of the rise speed of large buoyant bubbles is a fundamental fluid mechanics problem relevant to a number of applications ranging from carbon sequestration technology to chemical engineering or astrophysics. Single large bubbles typically have a spherical cap shape with bubbles of larger volume rising faster than the ones of smaller volume. However, except in well-controlled experiments, the released gas splits into a leading cap bubble, followed by a crown of satellite bubbles that can contain up to 50% of the total volume of gas. We find that in this case the satellite bubbles rearrange in a characteristic toroidal crown and the leading bubble takes a lenticular shape. The rise speeds of these multipart bubble systems and the ratios of the torus radii to the leading cap curvature radii are quite constant and predictable in the mean and are furthermore independent of the gas partitioning between the leading lenticular bubble and the crown of satellite bubbles. We also find that this multipart bubble system rises slightly faster than a single cap bubble with the same total injected volume of gas.

Traces of surfactants can severely limit the drag reduction of superhydrophobic surfaces

Significance Whereas superhydrophobic surfaces (SHSs) have long promised large drag reductions, experiments have provided inconsistent results, with many textures yielding little or no benefit. Given the vast potential impact of SHSs on energy utilization, finding an explanation and mitigating strategies is crucially important. A recent hypothesis suggests surfactant-induced Marangoni stresses may be to blame. However, paradoxically, adding surfactants has a barely measurable effect, casting doubt on this hypothesis. By performing surfactant-laden simulations and unsteady experiments we demonstrate the impact of surfactants and how extremely low concentrations, unavoidable in practice, can increase drag up to complete immobilization of the air–liquid interface. Our approach can be used to test other SHS textures for sensitivity to surfactant-induced stresses. Superhydrophobic surfaces (SHSs) have the potential to achieve large drag reduction for internal and external flow applications. However, experiments have shown inconsistent results, with many studies reporting significantly reduced performance. Recently, it has been proposed that surfactants, ubiquitous in flow applications, could be responsible by creating adverse Marangoni stresses. However, testing this hypothesis is challenging. Careful experiments with purified water already show large interfacial stresses and, paradoxically, adding surfactants yields barely measurable drag increases. To test the surfactant hypothesis while controlling surfactant concentrations with precision higher than can be achieved experimentally, we perform simulations inclusive of surfactant kinetics. These reveal that surfactant-induced stresses are significant at extremely low concentrations, potentially yielding a no-slip boundary condition on the air–water interface (the “plastron”) for surfactant concentrations below typical environmental values. These stresses decrease as the stream-wise distance between plastron stagnation points increases. We perform microchannel experiments with SHSs consisting of stream-wise parallel gratings, which confirm this numerical prediction, while showing near-plastron velocities significantly slower than standard surfactant-free predictions. In addition, we introduce an unsteady test of surfactant effects. When we rapidly remove the driving pressure following a loading phase, a backflow develops at the plastron, which can only be explained by surfactant gradients formed in the loading phase. This demonstrates the significance of surfactants in deteriorating drag reduction and thus the importance of including surfactant stresses in SHS models. Our time-dependent protocol can assess the impact of surfactants in SHS testing and guide future mitigating designs.

Convective mass transfer from a submerged drop in a thin falling film

We study the fluid mechanics of removing a passive tracer contained in small, viscous drops attached to a flat inclined substrate using thin gravity-driven film flows. A convective mass transfer establishes across the drop-film interface and the tracer in the drop diffuses into the film flow. The Peclet number for the tracer in the film is large. The Peclet number Pe_d in the drop varies from 0.01 to 1. The characteristic transport time in the drop is much larger than in the film. We model the mass transfer of the tracer from the drop bulk into the film using an empirical model based on Newtons law of cooling. This model is supported by a theoretical model solving the quasi-steady 2D advection-diffusion equation in the film coupled with a time-dependent 1D diffusion equation in the drop. We find excellent agreement between our experimental data and the 2 models, which predict an exponential decrease in time of the tracer concentration in the drop. The results are valid for all drop and film Peclet numbers studied. The transport characteristic time is related to the drop diffusion time scale, as diffusion within the drop is the limiting process. Our theoretical model predicts the well-known relationship between the Sherwood and Reynolds numbers in the case of a well-mixed drop Sh~Re_L^{1/3}=\gamma L^2/\nu_f, based on the drop length L, film shear rate \gamma and film kinematic viscosity \nu_f. We show that this relationship is mathematically equivalent to a more physically intuitive relationship Sh~Re_\delta, based on the diffusive boundary layer thickness \delta. The model also predicts a correction in the case of a non-uniform drop concentration, which depends on Re_\delta, the Schmidt number, the drop aspect ratio and the diffusivity ratio. This prediction is in agreement with experiments at low Pe_d. It also agrees as Pe_d approaches 1, although the influence of Re_\delta increases.

Anticyclonic precession of a plume in a rotating environment

Motivated by potential effects of the Earths rotation on the Deepwater Horizon oil plume, we conducted laboratory experiments on salt-water point plumes in a homogeneous rotating environment across a wide range of Rossby numbers 0.02 < Ro < 1.3. We report a striking physical instability in the plume dynamics near the source: after approximately one rotation period, the plume tilts laterally and starts to precess anticyclonically. The mean precession frequency ω scales linearly with the rotation rate Ω as ω≈0.4Ω. We find no evidence of a critical Rossby number above which precession ceases. We infer that a conventionally defined Rossby number is not an appropriate parameter when the plume is maintained over a long time: provided Ω ≠ 0, rotation is always important to the dynamics. This indicates that precession may occur in persistent oceanic or atmospheric plumes even at low latitudes.

Video: Soap opera in the maze: Geometry matters in Marangoni flows

Fernando Temprano-Coleto,1,* François J. Peaudecerf,2 Julien R. Landel,3 Frédéric Gibou,1,4 and Paolo Luzzatto-Fegiz1 1Department of Mechanical Engineering, University of California Santa Barbara, Santa Barbara, California 93106, United States 2Department of Civil, Environmental, and Geomatic Engineering, ETH Zürich, 8093 Zürich, Switzerland 3School of Mathematics, Alan Turing Building, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom 4Department of Computer Science, University of California Santa Barbara, Santa Barbara, California 93106, United States