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

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. Yet, testing this hypothesis is challenging. Careful experiments with purified water show large interfacial stresses and, paradoxically, adding surfactants yields barely measurable drag increases. This suggests that other physical processes, such as thermal Marangoni stresses or interface deflection, could explain the lower performance. To test the surfactant hypothesis, we perform the first numerical simulations of flows over a SHS inclusive of surfactant kinetics. These simulations 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 amounts below typical environmental values. These stresses decrease as the streamwise distance between plastron stagnation points increases. We perform microchannel experiments with thermally-controlled SHSs consisting of streamwise parallel gratings, which confirm this numerical prediction. We introduce a new, 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.Comment: 25 pages including supplemental information, 7 figures; videos available on reques

A theory for the slip and drag of superhydrophobic surfaces with surfactant.

Superhydrophobic surfaces (SHSs) have the potential to reduce drag at solid boundaries. However, multiple independent studies have recently shown that small amounts of surfactant, naturally present in the environment, can induce Marangoni forces that increase drag, at least in the laminar regime. To obtain accurate drag predictions, one must solve the mass, momentum, bulk surfactant and interfacial surfactant conservation equations. This requires expensive simulations, thus preventing surfactant from being widely considered in SHS studies. To address this issue, we propose a theory for steady, pressure-driven, laminar, two-dimensional flow in a periodic SHS channel with soluble surfactant. We linearise the coupling between flow and surfactant, under the assumption of small concentration, finding a scaling prediction for the local slip length. To obtain the drag reduction and interfacial shear, we find a series solution for the velocity field by assuming Stokes flow in the bulk and uniform interfacial shear. We find how the slip and drag depend on the nine dimensionless groups that together characterize the surfactant transport near SHSs, the gas fraction and the normalized interface length. Our model agrees with numerical simulations spanning orders of magnitude in each dimensionless group. The simulations also provide the constants in the scaling theory. Our model significantly improves predictions relative to a surfactant-free one, which can otherwise overestimate slip and underestimate drag by several orders of magnitude. Our slip length model can provide the boundary condition in other simulations, thereby accounting for surfactant effects without having to solve the full problem.Raymond and Beverly Sackler Foundation, the European Research Council Grant 247333, Mines ParisTech, the Schlumberger Chair Fund, the California NanoSystems Institute through a Challenge Grant, ARO MURI W911NF-17- 1-0306 and ONR MURI N00014-17-1-267

Slip on three-dimensional surfactant-contaminated superhydrophobic gratings

Trace amounts of surfactants have been shown to critically prevent the drag reduction of superhydrophobic surfaces (SHSs), yet predictive models including their effects in realistic geometries are still lacking. We derive theoretical predictions for the velocity and resulting slip of a laminar fluid flow over three-dimensional SHS gratings contaminated with surfactant, which allow for the first direct comparison with experiments. The results are in good agreement with our numerical simulations and with measurements of the slip in microfluidic channels lined with SHSs, which we obtain via confocal microscopy and micro-particle image velocimetry. Our model enables the estimation of a priori unknown parameters of surfactants naturally present in applications, highlighting its relevance for microfluidic technologies.Comment: 6 pages, 3 figures, 11 supplemental pages, 2 supplemental figure

A model for slip and drag in turbulent flows over superhydrophobic surfaces with surfactant

International audienceSuperhydrophobic surfaces (SHSs) can reduce the friction drag in turbulent flows. In the laminar regime, it has been shown that trace amounts of surfactant can negate this drag reduction, at times rendering these surfaces no better than solid walls (Peaudecerf et al., Proc. Natl. Acad. Sci. USA 114(28), 7254-9, 2017). However, surfactant effects on the drag-reducing properties of SHSs have not yet been studied under turbulent flow conditions, where predicting the effects of surfactant in direct numerical simulations remains expensive by today’s standards. We present a model for turbulent flow inclusive of surfactant, in either a channel or boundary-layer configuration, over long but finite-length streamwise ridges that are periodic in the spanwise direction, with period and gas fraction . We adopt a technique based on a shifted log law to acquire an expression for the drag reduction. The average streamwise and spanwise slip lengths are derived by introducing a local laminar model within the viscous sublayer, whereby the effect of surfactant is modelled by modifying the average streamwise and spanwise slip lengths. Our model agrees with available laboratory experimental data from the literature when conditions are clean (surfactant-free), or when there are low surfactant levels. However, we find an appreciable drag increase for larger background surfactant concentrations that are characteristic of turbulent flows over SHSs for marine applications

Exogenous-endogenous surfactant interaction yields heterogeneous spreading in complex branching networks

Experiments have shown that surfactant introduced to a liquid-filled maze can find the solution path. We reveal how the maze-solving dynamics arise from interactions between the added surfactant and endogenous surfactant present at the liquid surface. We simulate the dynamics using a nonlinear model solved with a discrete mimetic scheme on a graph. Endogenous surfactant transforms local spreading into a non-local problem with an omniscient view of the maze geometry, key to the maze-solving dynamics. Our results offer insight into surfactant-driven transport in complex networks such as lung airways.Comment: 5 pages, 4 figure

Migration and accumulation of bacteria with chemotaxis and chemokinesis

Abstract: Bacteria can chemotactically migrate up attractant gradients by controlling run-and-tumble motility patterns. In addition to this well-known chemotactic behaviour, several soil and marine bacterial species perform chemokinesis; they adjust their swimming speed according to the local concentration of chemoeffector, with higher speed at higher concentration. A field of attractant then induces a spatially varying swimming speed, which results in a drift towards lower attractant concentrations—contrary to the drift created by chemotaxis. Here, to explore the biological benefits of chemokinesis and investigate its impact on the chemotactic response, we extend a Keller–Segel-type model to include chemokinesis. We apply the model to predict the dynamics of bacterial populations capable of chemokinesis and chemotaxis in chemoeffector fields inspired by microfluidic and agar plate migration assays. We find that chemokinesis combined with chemotaxis not only may enhance the population response with respect to pure chemotaxis, but also modifies it qualitatively. We conclude presenting predictions for bacteria around dynamic finite-size nutrient sources, simulating, e.g. a marine particle or a root. We show that chemokinesis can reduce the measuring bias that is created by a decaying attractant gradient. Graphic abstract

Combining SIMS and mechanistic modelling to reveal nutrient kinetics in an algal-bacterial mutualism

Funder: Raymond and Beverly Sackler ScholarshipFunder: Mines ParisTechFunder: Swedish Museum of Natural HistoryFunder: University of IcelandFunder: Consortium of Danish geoscience institutionsMicrobial communities are of considerable significance for biogeochemical processes, for the health of both animals and plants, and for biotechnological purposes. A key feature of microbial interactions is the exchange of nutrients between cells. Isotope labelling followed by analysis with secondary ion mass spectrometry (SIMS) can identify nutrient fluxes and heterogeneity of substrate utilisation on a single cell level. Here we present a novel approach that combines SIMS experiments with mechanistic modelling to reveal otherwise inaccessible nutrient kinetics. The method is applied to study the onset of a synthetic mutualistic partnership between a vitamin B12-dependent mutant of the alga Chlamydomonas reinhardtii and the B12-producing, heterotrophic bacterium Mesorhizobium japonicum, which is supported by algal photosynthesis. Results suggest that an initial pool of fixed carbon delays the onset of mutualistic cross-feeding; significantly, our approach allows the first quantification of this expected delay. Our method is widely applicable to other microbial systems, and will contribute to furthering a mechanistic understanding of microbial interactions

Migration and accumulation of bacteria with chemotaxis and chemokinesis.

Bacteria can chemotactically migrate up attractant gradients by controlling run-and-tumble motility patterns. In addition to this well-known chemotactic behaviour, several soil and marine bacterial species perform chemokinesis; they adjust their swimming speed according to the local concentration of chemoeffector, with higher speed at higher concentration. A field of attractant then induces a spatially varying swimming speed, which results in a drift towards lower attractant concentrations-contrary to the drift created by chemotaxis. Here, to explore the biological benefits of chemokinesis and investigate its impact on the chemotactic response, we extend a Keller-Segel-type model to include chemokinesis. We apply the model to predict the dynamics of bacterial populations capable of chemokinesis and chemotaxis in chemoeffector fields inspired by microfluidic and agar plate migration assays. We find that chemokinesis combined with chemotaxis not only may enhance the population response with respect to pure chemotaxis, but also modifies it qualitatively. We conclude presenting predictions for bacteria around dynamic finite-size nutrient sources, simulating, e.g. a marine particle or a root. We show that chemokinesis can reduce the measuring bias that is created by a decaying attractant gradient.EPSRC Studentship EP/L504920/1 and EP/N509620/1 (T.J.), and the Winton Programme for the Physics of Sustainability (T.J.,O.A.C.), funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 798411 (F.J.P.