We consider two systems of active swimmers moving close to a solid surface, one being a living population of wild-type E. coli and the other being an assembly of self-propelled Au-Pt rods. In both situations, we have identified two different types of motion at the surface and evaluated the fraction of the population that displayed ballistic trajectories (active swimmers) with respect to those showing randomlike behavior. We studied the effect of this complex swimming activity on the diffusivity of passive tracers also present at the surface. We found that the tracer diffusivity is enhanced with respect to standard Brownian motion and increases linearly with the activity of the fluid, defined as the product of the fraction of active swimmers and their mean velocity. This result can be understood in terms of series of elementary encounters between the active swimmers and the tracers.

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The induced diffusion of tracers in a bacterial suspension is studied theoretically and experimentally at low bacterial concentrations. Considering the swimmer-tracer hydrodynamic interactions at low-Reynolds number and using a kinetic theory approach, it is shown that the induced diffusion coefficient is proportional to the swimmer concentration, their mean velocity and a coefficient β, as observed experimentally. The coefficient β scales as the tracer-swimmer cross section times the mean square displacement produced by single scatterings. The displacements depend on the swimmer propulsion forces. Considering simple swimmer models (acting on the fluid as two monopoles or as a force dipole) it is shown that β increases for decreasing swimming efficiencies. Close to solid surfaces the swimming efficiency degrades and, consequently, the induced diffusion increase. Experiments on W wild-type Escherichia coli in a Hele-Shaw cell under buoyant conditions are performed to measure the induced diffusion on tracers near surfaces. The modification of the suspension pH vary the swimmers' velocity in a wide range allowing to extract the β coefficient with precision. It is found that the solid surfaces modify the induced diffusion: decreasing the confinement height of the cell, β increases by a factor 4. The theoretical model reproduces this increase although there are quantitative differences, probably attributed to the simplicity of the swimmer models.

BackgroundIn October 2014, Chile implemented a tax modification on sugar-sweetened beverages (SSBs) called the Impuesto Adicional a las Bebidas Analcohólicas (IABA). The design of the tax was unique, increasing the tax on soft drinks above 6.25 grams of added sugar per 100 mL and decreasing the tax for those below this threshold.Methods and findingsThis study evaluates Chile’s SSB tax, which was announced in March 2014 and implemented in October 2014. We used household-level grocery-purchasing data from 2011 to 2015 for 2,836 households living in cities representative of the urban population of Chile. We employed a fixed-effects econometric approach and estimated the before–after change in purchasing of SSBs controlling for seasonality, general time trend, temperature, and economic fluctuations as well as time-invariant household characteristics. Results showed significant changes in purchasing for the statistically preferred model: while there was a barely significant decrease in the volume of all soft drinks, there was a highly significant decrease in the monthly purchased volume of the higher-taxed, sugary soft drinks by 21.6%. The direction of this reduction was robust to different empirical modelling approaches, but the statistical significance and the magnitude of the changes varied considerably. The reduction in soft drink purchasing was most evident amongst higher socioeconomic groups and higher pretax purchasers of sugary soft drinks. There was no systematic, robust pattern in the estimates by household obesity status. After tax implementation, the purchase prices of soft drinks decreased for the items for which the tax rate was reduced, but they remained unchanged for sugary items, for which the tax was increased. However, the purchase prices increased for sugary soft drinks at the time of the policy announcement. The main limitations include a lack of a randomised design, limiting the extent of causal inference possible, and the focus on purchasing data rather than consumption or health outcomes.ConclusionsThe results of subgroup analyses suggest that the policy may have been partially effective, though not necessarily in ways that are likely to reduce socioeconomic inequalities in diet-related health. It remains unclear whether the policy has had a major, overall population-level impact. Additionally, because the present study examined purchasing of soft drinks for only 1 year, a longer-term evaluation—ideally including an assessment of consumption and health impacts—should be conducted in future research.Trial registrationClinicalTrials.gov Identifier: NCT02926001